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1. esses 24 Il 2 2 Mach Zehnder Modulator eese enne enne entente 26 11 3 Why optical single Sideband ccccconococoonnnncnonononannnnnononnnonononnnnnnnnnnnnnonnnnnnncnnnnnnnnnnnnnnnnos 29 II 4 Optical OFDM detection eter tte et ode toes E a Tav e ERR A 30 11 5 Optical OFDM transmission systems esses eene enne nnn nnns 32 11 5 1 Modulation techniques ccccccccccccssssssssececcceceesesseaeseeeesseeseseaeceeeeuseeseseaeeeeeeeseeseaaeas 32 1 5 2 Detection techniques e deter e e e e ee esi en avena hee 35 MS Equalization neni enter 41 CHAPTER II MPI DEMOS Lee ttn eae RE ee erae eR PR aiii aiii Rie 43 111 1 VPI Transmission Maker as a simulation tool seen 43 111 1 1 Graphical User Interface essere nennen ennemi nnns 43 111 1 2 Simulation hierarchies essceeccecescceeeseceesaeceeaceseeneeesaececaaeceeaaeesaeeeeaaeceeaaenseeeeenes 45 III 1 3 Simulation parameters ccccccccccccsssessssececeescesseseeaeeececsseeseseeaeseesesssesesesseeeeecesseseaaees 46 IIl 31 4 Custom modules rettet A e ere E rab epo qe hun 48 111 2 OFDM Generation and Detection Demo esee nennen nenne nennen nnn nnun 52 111 2 1 General sChematiC ccooononnccncnncnnnnonannnnnnnnnonononanannccnn nono nnnncn cnn n nono nnnnan nc cnnn nono nnnncanicinnns 52 111 2 2 Coder and decoder parameters ccccococcccnccncnnnonononnnnnnnnnn
2. When a new file is created by clicking File 2New in the toolbar menu or using the corresponding shortcut an empty schematic as the one in 3 appears In order to add already existing modules the Quick Find or Search tabs in 4 can be selected to look for them If the name of the desired module is not known the Tree tab in 4 should be selected and by pressing the 7C Modules button in 5 all the available modules can be accessed by categories Another interesting option is offered by the Optical Systems Demos button 6 which displays the category panel 7 containing all the demonstration simulations offered by VPI By selecting a category another panel containing CHAPTER III VPI DEMOS 45 the corresponding demos appears In Figure Ill 1 this is indicated by 8 where the OFDM Generation and Detection demo is selected highlighted in blue Finally the schematic s Package Explorer is highlighted in 9 consisting of a folder browse panel 9a and a contents panel 9b The folder panel is used to attach and store any data to be used by the schematic The contents panel shows the files and documents contained in the currently selected folder in the folder panel 111 1 2 Simulation hierarchies VPI is hierarchically organised This allows an easier management of the modules taking part in a simulation as they can be treated independently or as a group when necessary Figure 111 2 shows the three levels in which modul
3. CHAPTER IV CUSTOMIZED SIMULATIONS 105 Numerical Fig IV 37 Received constellation without optical channel VPI The next step is to run a simulation with the same parameters as in the OFDM for Long Haul Transmission demo Thus the optical channel has been added again as in Figure IV 22 for a 1000 km fibre link without using equalization The received constellation depicted in Figure IV 38 is very similar to the one obtained with VPI demos as it was shown in Figure 111 27 in Chapter Ill Although the EVM value is not relevant for a case in which no equalization is applied its value was 0 715 Numerical P Fig IV 38 Received constellation diagram without equalization VPI When equalization is applied though cyclic prefix and zero padding are still not used the left constellation in Figure IV 39 is received where a constant phase error makes it different from the equalized constellation in VPI demos shown in Figure 111 25 106 FIBER BASED OFDM TRANSMISSION SYSTEMS Numerical Numerical Fig IV 39 Equalized constellation with and without constant phase error left and right respectively VPI This phase shift appears because the reference frequency has been set to the middle of the OFDM band fo frr so the expected difference of 55 over the squared constellation see section IV 3 4 can be appreciated in the figure By correcting the equalizer code in Matlab by 45 55 10 the
4. Fig IV 33 Single sideband optical OFDM signal VPI CHAPTER IV CUSTOMIZED SIMULATIONS 103 The following step is to transmit the optical OFDM signal through the fibre link Figure IV 34 shows the spectrum of the received signal after a 1000 km transmission 10 loop circuit where a slight out of band power growth can be appreciated with respect to the last figure Optical Spectrum before photodetection 64 OFDM subcarriers Power dBm J o 5 Frequency relative to 193 1 THz GHz Optical Spectrum before photodetection 64 OFDM subcarriers Power dBm 5 o o E Frequency relative to 193 1 THz GHz Fig IV 34 Optical OFDM signal after the fibre link VPI The electrical spectrum of the received OFDM signal can be represented once the signal is photodetected In Figure IV 35 the noise component composed by the mixing products appearing due to direct detection can be easily distinguished falling off in the created gap ranging from 0 to near 5 GHz Electrical Spectrum Power Bm ed Frequency Hz Electrical Spectrum Fig IV 35 Electrical OFDM signal after photodetection VPI 104 FIBER BASED OFDM TRANSMISSION SYSTEMS The obtained photocurrent representing the received OFDM signal will then go through an RF downconversion stage where ideally the transmitted OFDM signal is recovered Figure IV 36 shows the recovered quadrature component spectrum which should be
5. N 2 f Ynn DC y 2f Ya Yost Fig 1 10 IFFT block and the frequency domain OFDM symbol at its output P4 The first output channel y is located at DC so it is not used for modulation because carrier leakage of the modulator disturbs the quality of this channel and it would put stringent requirements on the low pass characteristics of all electronic and also optic components Furthermore in a complex valued IFFT the first half of the rows corresponds to the positive frequencies while the last half corresponds to negative frequencies Thus the so called Nyquist channel is located at yne 2 1 which corresponds to the highest frequency that the subsequent digital to analogue converter can modulate the Nyquist frequency fw or half the sampling frequency f according to the sampling theorem In a practical system if the superposition of subcarriers results in complex valued time domain signals two D A converters may be applied in parallel for conversion of the real and imaginary IFFT output though other techniques like the imposition of Hermitian symmetry among samples can be applied in order to have a perfect real IFFT output as explained in Annex A 1 2 2 D A and A D conversion As it can be seen from figures 1 8 and 1 9 a digital to analogue converter DAC is needed to convert the discrete value of s nj sample to the continuous analogue value of s t and an analogue to digital converter ADC
6. Optical Intensity Quadrature Point Drive voltage Null Point Optical Field Fig 11 6 Transfer functions of the optical intensity and optical field Either if the MZM is biased in the quadrature or null point the signal produced by a standard MZM is a so called double sideband as the OFDM signal is present symmetrically at both sides of the optical carrier This is shown in Figure II 7 where A is the complex conjugate of the main OFDM signal A Electrical spectrum Optical A frequency i i i Optical input Bias frequency frequency Fig 11 7 Optical OFDM modulation using a standard MZM P4 The duplicated sideband generated by the MZM entails some considerable disadvantages for optical OFDM systems so it needs to be removed by an optical filter Section 11 3 describes this process 11 2 2 3 IQ Mach Zehnder Modulator The previous solution does not make an efficient use of the spectrum and depends on the performance of the optical filters being used so another option of modulating an electrical signal onto an optical carrier can be considered This is the optical IQ modulation CHAPTER II OPTICAL OFDM 29 The IQ MZM basically consists of two null biased standard MZ modulators arranged as in Figure 11 8 with a 90 phase difference among them consisting of one RF input for each component of the OFDM signal I and Q Electrical a input A IQ mi
7. is needed to convert the continuous received signal r t to discrete sample nn 12 FIBER BASED OFDM TRANSMISSION SYSTEMS In order to build a real system the fact of being able to use commercial off the shelf converters at both ends of the transmission scheme becomes one of the main issues This is why many techniques are available to take advantage from the digital signal processing stages and simplify the analogue processing lowering the requirements for both the DAC and the ADC 1 2 2 1 Pulse shaping Inside the DAC symbols are applied to a transmit filter which produces a continuous time signal for transmission over the continuous time channel A simple transmit filter has a rectangular impulse response shown in figure 1 11 where a symbol sequence using 2 bits per symbol and its corresponding continuous time signal are also represented 3 1 1 2 t t 0 T 3T o X AT TRANSMIT FILTER SYMBOLS g t 3 1 3 3 i Y A g r mT p cw m Fig 1 11 Rectangular impulse response B6 The impulse response g t of the transmit filter is called the pulse shape The output of this filter is the convolution of the pulse shape with the symbol sequence so the resulting signal can be interpreted as a sequence of possibly overlapped pulses with the amplitude of each determined by a symbol An ideal low pass filter as the one represented in Figure 7 has a sinc function impulse response with equidistant zero crossings at the sa
8. so the CoSimOutputMxCx module has been chosen for this purpose indicating the output vector y in the Name parameter 78 FIBER BASED OFDM TRANSMISSION SYSTEMS The obtained vector size is then declared as an MxN matrix by means of the UnPkCx_M module The size of this vector will depend on the number of bits used to represent each QAM symbol so the matrix size to be indicated in this module will be 1 row x BitRate TimeWindow BpS columns IV 1 4 OFDM Decoder The description of the OFDM decoder Matlab code in section IV 1 2 indicated that 5 variables where extracted from it after the execution Here just two of them will be explained for simplicity The 5 output configuration for the OFDM decoder will be seen in the simulations performed in section IV 3 Thus the OFDM decoder module will consist of two inputs and two outputs as shown in Figure IV 6 This is because the real and imaginary parts are treated independently during the OFDM signal transmission so the inphase and quadrature components can be created as described in Chapter for a proper signal representation Fig IV 6 OFDM decoder The parameters to be created in this module are the same as those of the coder shown in Figure IV 4 All of these parameters will be used by the Matlab code executing the decoder functions Internally the decoder configuration is not so different from that of the coder though four variables are processed Figure IV 7 shows the decode
9. 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 i 0000i 1 0000 1 0000i 1 0000 1 0000i Fig IV 1 Nc x NTS OFDM matrix containing the information symbols Matlab After that the indicated amount of zero padding is inserted as rows in the middle of the matrix obtaining a N_FFT x NTS_OFDM matrix This is shown in Figure IV 2 xxi OFDM ZP 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 00001 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 00001 1 0000 1 00001 D D D D D D D D 0 D D D D D D 0 D D D D D o D 1 0000 i 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000 1 0000 1 0000i 1 0000 1 0000 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 i1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i Fig IV 2 N FFTx NTS OFDM matrix with zero padding Matlab The 16 rows of this matrix form the input sequence of the IFFT Thus one inverse fast Fourier transform will be applied to each column obtaining anoth
10. 2 Coder and decoder parameters Figure 111 13 shows the OFDM coder parameters that can be changed from its PEW The same parameters are shared by the decoder module which performs the same functions as the coder in the reverse order CoderOFDM_vtms1 Parameter Editor Name Coder OFDM vtms ID CoderOFDM vtmsi amp PW x Name Value Physical f SampleRate SampleRate Default f BitRate BitRate Default 3 OFDMType OFDM i Bits Per Symbol QAM Bits Per Symbol QAM li Number Of Carriers 16 F CyclicPrefix 0 2 QuantizeOutputValues No OOOOOOOO 5 Coding mPSK Fig 111 13 Coder decoder parameters VPI Three of the parameters are shared with those of the universe schematic SampleRate BitRate and BitsPerSymbolQAM Thus any change in their values will not have any effect on the simulation unless it is done in the upper level The rest of the parameters all of them belonging to the Physical category are 56 FIBER BASED OFDM TRANSMISSION SYSTEMS e OFDMType This parameter allows to choose between three different modulation types OFDM where no zero padding is used DMT Discrete Multi Tone where half of the inputs of the IFFT are the complex conjugate of the other half so a real OFDM signal is created at the transmitter output as explained in Annex 1 and Zero Padding The latter technique is used to create a gap between the OFDM signal and the DC component as described in Chapter e Codin
11. EVM 68 FIBER BASED OFDM TRANSMISSION SYSTEMS The received optical spectrum is plotted just after the fibre link before the signal is detected by the photodiode The result is shown in Figure 111 26 Optical Spectrum E 5 E o a B l 10 Frequency relative to 193 1 THz GHz Fig 111 26 Optical signal before photodetection VPI The frequency values in GHz in the x axis are relative to 193 1 THz so this is the real frequency for the O Hz value in the graph This will also be the frequency for the optical carrier signal which is separated by a 5 GHz gap from both the suppressed lower sideband left in the graph and the optical OFDM signal centred at 7 5 GHz from the optical carrier This gap is the one in which the mixing products appearing due to direct detection will fall off This is the only graph showing the OFDM signal in the schematic so other analyzer modules will be used in the next chapter s simulations in order to evaluate the signal spectrum at each stage At the receiver if the Equalization parameter is set to No there is no phase correction and the received constellation continuously rotates as explained in section 11 2 This is shown in Figure 111 27 which results in an EVM of 1 007 Fig 111 27 Received constellation without equalization VPI CHAPTER III VPI DEMOS 69 Figure 111 28 shows the received constellation when the Equalization parameter is set to Yes and the before
12. In contrast in a typical optical transmission system the information is carried on the intensity of the optical signal and therefore it can only be positive unipolar Generally no laser is used at the receiver acting as a local oscillator and direct detection rather than coherent detection is used An initiative towards the application of OFDM modulation in optical networks is the Accordance A Novel OFDMA PON Paradigm for Ultra High Capacity Converged Wireline Wireless Access Networks a European research project in which UPC takes part along with other universities and companies from around the continent Within this collaboration a new communications system is being developed based on OFDM access technology and protocols 2 INTRODUCTION UPC is in charge of performing simulations and feasibility studies for this low cost high capacity hybrid communications system where optical fibre is used as the transmission channel The results described in this Master Thesis will add to the UPC collaboration within the Accordance project The goal in this Master Thesis is to study the basis of OFDM systems applied to fibre optic networks both from an analytical point of view and from a simulation software environment using the Virtual Photonics Inc VPI software The starting point will be the main theoretical concepts that distinguish OFDM from other modulations making special emphasis in the peculiarities of its implementation in opti
13. In this case the input vector to the IFFT is given by lo Iy 4 Xo Xn 0 0 The IFFT output is then a single sided analytic 2 signal and its real and imaginary components are used for the and Q inputs of the complex optical modulator for OSSB transmission without an optical filter 12 FIBER BASED OFDM TRANSMISSION SYSTEMS Here the frequency guard band is created by setting the corresponding inputs to zero This design requires two DACs each with the same sample rate as the Band shifted from DC design in section C 3 ANNEX D MATLAB CODE 13 ANNEX D MATLAB CODE D 1 OFDM coder OFDM coder function y ofdm_coder prbs TimeWindow BitRate BpS Nc N_FFT CP SSSINPUT VARIABLES x Number of prbs bits x1 Data input vector length x Time window Bitrate It must be an integer multiple of BpS N FFT number of total carriers for FFTs It must be a power of two Nc number of info carriers N FFT ZP It must be an integer multiple of 2 because half of the zeros are located in the middle of the input sequence of the IFFT Oversampling BpS Bits per symbol QAM CP Cyclix prefix SGlobal variables are defined NTS OFDM NTS INFO NTB INFO Ignore Bits 535 xl prbs x xl prbs 1 TimeWindow BitRate identify the info bits to send and how many to discard NTS OFDM floor length x1 BpS ceil N FFT 1 CP STotal number of OFDM symbols NTS INFO NTS OFDM Nc Total number of QAM inf
14. OFDM transmitter where subcarriers are modulated in the digital domain by means of an IFFT The transformed symbols at the output of the IFFT block are then serialized and converted into an analogue signal before transmitting them to the channel For simplicity some other blocks have been omitted though they are going to be described during this chapter R Parallel To DAC s t 11010001 Serial Fig 1 8 Use of an IFFT block to modulate an OFDM signal In a similar way the subcarriers forming the received signal r t are demodulated by an FFT operation after being analogue to digital A D converted and parallelized to form the FFT block inputs as shown below Fig 1 9 Use of an FFT block to demodulate an OFDM signal CHAPTER OFDM BASICS 11 In order to understand the concepts that are going to be explained in the next sections it is useful to know which frequencies of an OFDM signal are represented in each branch of an IFFT operation Figure 1 10 shows a schematic of the IFFT block where x xy are the input sequence symbols from subcarrier 1 to the total number of subcarriers N and y yy is the corresponding output sequence Moreover the frequency domain OFDM symbol generated at the IFFT output is depicted The inverse procedure can be applied to the FFT block at the receiver end amplitude Frequency domain Time domain X gt Y x2 gt Ya _ E ia Input lt i F i N E N is 40 t yg
15. Sopt t eJ fot geJ2nUo Dt s t 11 16 Where f is the main optical carrier frequency Af is the guard band between the main optical carrier and the OFDM band as in Figure 11 16 and is a scaling coefficient that describes the OFDM band strength related to the main carrier ideally 1 The term s t represents the baseband OFDM signal given in expression 1 1 in Chapter I Thus the real valued electrical OFDM signal is available after upconversion and drives directly the e o modulator Figure II 17 shows the schematic designed by Lowery and Armstrong in P12 for one of the first direct detection optical OFDM published simulations using VPI software where the offset single sideband technique OSSB was used It dates from year 2007 and it has been the basis of the system designed in this work 36 FIBER BASED OFDM TRANSMISSION SYSTEMS au Modualor Orive Power dE OSA Power dam RX Modulate _ inverse FFT Parallel to Serial Data Channels Data Channels 5 c m 2 3 is o oO Fiber Link Photodiode Fig 11 17 DDO OFDM Long haul optical communication system P12 After the signal passes through fibre link with chromatic dispersion the OFDM signal can be approximated as 1 2Nc r t eJ 21 fot Pp Af o ac Qn Uo Af t o t 2 cy e nf kt epo k 5Nct1 pisqoXI E 11 17 where p fk is the phase delay due to chromatic dispersion for the kin subcarrier D is the accumulated
16. VPI software are introduced and the required steps to create a new simulation are described Moreover two optical OFDM demonstration scenarios provided by VPI are analyzed in detail so it can be seen how the concepts explained in the previous chapters are applied to a simulation environment INTRODUCTION 3 The VPI built in demos studied in Chapter III will serve as the base for the customized simulations in Chapter IV where an insight is given into the main modules created in VPI for the customized demos The resulting scenarios will perform the same functions as the built in demos in VPI though this time the user will be able to change any parameter of the simulation in order to see its effect on the transmission results Also some improvements have been added to the original functions in the demos allowing a better understanding of each of the simulation stages and results Conclusions and future lines are developed in Chapter V This work will set the basis for upcoming optical OFDM simulations studies hoping to serve as a source of inspiration to other contributions to the subject For this purpose propositions to improve the current work as well as the study of other available optical OFDM techniques to explore are given as a future possibility Furthermore 4 Annexes are attached which are referred along the work They contain complementary theoretical information as well as secondary configurations for possible simulated scenari
17. a pulse shaping filter and the resulting electrical signal is fed to the OFDM decoder module which provides the decoded versions of the inphase and quadrature components The constellation diagram representation is done in a similar way as in the OFDM Generation and Detection demo though this time another function is used between the decoder and the signal analyzer two switches are connected to a rectangular pulse generator lower module in the figure This modification is used to extract the redundant information inside the sequence which was mentioned before The rectangular pulse indicates the period of time in which the switches allow the signal to flow as an input to the signal analyzer module The rest of time any sequence coming from the decoder is going to be discarded This way only the received information symbols are going to be represented in the constellation diagram omitting the padded zeros used to compensate for any differences between the effective and transmitted data rates 64 FIBER BASED OFDM TRANSMISSION SYSTEMS The decoded OFDM sequence is also connected to another module on the right edge of the image This module is called BER El mQAM and its function is to estimate the Symbol Error Rate SER and or the EVM of an electrical mQAM signal taking and Q electrical signals as inputs The module automatically performs clock recovery amplitude and phase correction of the received constellation Thus it will be abl
18. and the effects resulting from changing their value However after several tests some limitations have been observed This has been the reason why new simulation scenarios have been developed in order to overcome these limitations Previously an introduction to the simulation environment offered by VPI has been done emphasizing the required techniques to create a customized simulation For that purpose a Matlab code implementing the OFDM coder and decoder functions has been programmed and implemented in VPI to execute the modulating and demodulating functions for the OFDM signal in the optical OFDM system 110 FIBER BASED OFDM TRANSMISSION SYSTEMS Two different simulation scenarios have been created to implement the same functions as the VPI demos This time though the transparency of the customized modules allows the user to fully explore and understand the working principle of the system in order to relate them with the theoretical concepts described in the first chapters Different tests on the customized simulation scenarios have allowed to select the optimum parameters in order to obtain the desired results The theoretical model for the optical channel considering chromatic dispersion as the most relevant effect has proven to be a useful approximation to design an equalizer for the custom simulations and to understand the role played by the reference frequency parameter in the fibre simulator s model in order to make a good choic
19. baseband OFDM signal as in 1 1 For wireless systems this signal could be modulated by a complex IQ modulator and then transmitted Otherwise it would be necessary to transmit real quantities which can be accomplished by first appending the complex conjugate to the original input block See Annex A for a detailed description of the process 22 FIBER BASED OFDM TRANSMISSION SYSTEMS CHAPTER II OPTICAL OFDM The growing interest for optical OFDM due to an increase of the demanded data rates has fostered the appearance of a large variety of solutions for different applications so this chapter will deal with its classification into different categories The preference for simple and low cost solutions based on the use of direct detection photodiodes which operate according to the square law detection technique and the requirement of a linear system between the transmitter IFFT input and the receiver FFT output are common in almost all of these solutions Moreover basic concepts of optical communications will be described in order to make it easier to understand the simulations performed in the following chapters such as the available types of optical modulation and demodulation and the main characteristics of an optical channel Some of these concepts are not usually referred in the current bibliography of optical OFDM though they are the basis for creative contributions to the subject 11 1 The optical channel Chromatic Dispersion Ch
20. by means of zero padding the input sequence of the IFFT Also the same optical transmission channel as in the demo has been applied This means that a 100 km optical fibre with the same physical parameters as before is going to be used as a component of an N loop transmission circuit along with the corresponding amplification and filtering stages In this customized scenario equalization is based on the fibre model described in Chapter Il meaning that it will just compensate for chromatic dispersion Also 4 signal analyzers are used so that apart from the constellation diagram the spectrum of the signal can be seen at specific points of the system At the receiver end the decoder galaxy has been modified over the previous version in the Electrical OFDM Generation and Detection schematic This is because the EVM of the received constellation and the BER of the received bit sequence are going to be measured so the corresponding variables of the CHAPTER IV CUSTOMIZED SIMULATIONS 91 Matlab code have to be extracted from the cosimulation process as explained in section IV 1 2 The new modules inserted to measure the EVM and BER values are also explained in this chapter The schematic parameters for this simulation can be seen in Figure IV 23 where no new categories are used Note that as in the VPI simulations 64 4 QAM information subcarriers are going to represent the OFDM signal though 128 IFFT FFT inputs will be necessary in
21. case of optical OFDM applications it will be necessary to remove the duplicated sideband by using an optical filter This is because the phase shifts of the upper and lower sidebands always result in symbols allocated in the real axis as shown in Figure 11 10 Optical carrier 0 10 Imaginary k k OFDM eese Subcarriers gt eS Real Optical Frequency Fig 11 10 Detection of double sideband optical OFDM P6 This way any phase shift of n 1 7 2 will null the subcarrier power On the other hand if the lower sideband is filtered out there is only one photodetection component at each electrical frequency so there is no nulling at certain frequencies This situation is represented in the next figure Optical carrier Imaginary Symbol 0 OFDM A e Subcarriers Ei gt Optical Frequency Fig 11 11 Detection of one optical OFDM band P6 The phase shift 6 due to dispersion can be easily equalized in the electrical domain at the receiver 11 4 Optical OFDM detection Basically there are two techniques in which an optical OFDM signal can be detected at the receiver direct detection DD and coherent detection CO D All of the existing applications or designs concerning an optical OFDM receiver are variations of these two options CHAPTER II OPTICAL OFDM 31 Although the direct detection configuration is going to be explained in detail throughout this chapter it is import
22. frequency choice In order to simulate the chromatic dispersion effect in a fibre the simulator takes the following Taylor expansion which is analyzed in Chapter II up to the fourth term centred in a user specified reference frequency fref 0B lo o p le o L Blo Blo W o 2 30e E E 00 6 00 1V 13 e e B o 7 P 6 ute That sets a limit on the total bandwidth around fef that can be correctly approximated and that is why it is important to choose it carefully The first term in the expansion is then a constant phase for all signals travelling through the fibre and as such it is neglected since it represents a change in the phase reference which is set to zero at the reference frequency The second term is the group delay and it is set to zero in the fref In the simulator this is equivalent to setting the clock to zero at the time when the fref is expected at the fiber s receiver end that is it sets the time where the temporal simulation window starts The delays of the rest of the frequencies are then set accordingly The Taylor expansion is therefore only left with two terms which are respectively quantified by the user defined parameters D chromatic dispersion and S dispersion slope The slope will be considered negligible even when in the simulations is set to the typical value in third window 0 08 10 s m Here the attention will be focused on focused on the 2 order term According to
23. frequency wo provided its bandwidth is not too large as the Taylor expansion would no longer be valid It can also be thought that this delay is a kind of average delay of all the frequencies in a small bandwidth around the carrier 24 FIBER BASED OFDM TRANSMISSION SYSTEMS e is the Group Delay Dispersion GDD given by py PRELATI 11 6 8o Qc And thus it gives the frequency dependency of the group delay The GDD T 0 can also be related to the chromatic dispersion parameter D 9 aa of an optical fibre by 2 _ Ao _ C 2nc 2mf2 f2 D 11 7 Being c the speed of light and A the corresponding wavelength If the references for phase and time are set at a certain reference frequency W er approximately located at the centre of the signal s bandwidth the transfer function of the fibre can be expressed as H w exeo y Fey 11 8 Where L is the fibre length and wef is the reference frequency for the fibre under study For the works carried out in this Master Thesis it is important to understand how the simulator applies this fibre transfer function and this is why section IV 3 4 is devoted to describe its relation with the chosen reference frequency 11 2 Optical modulation techniques In Chapter I it has been described how to generate an electrical OFDM signal In order to transmit this signal through an optical channel optical modulation is required For that purpose many different m
24. in section IV 3 4 that an additional equalization should be performed in order to compensate for a temporal delay which is different for each arriving subcarrier due to chromatic dispersion and the FFT window starting point which is going to be changed with the CP extraction strategy explained in the same section Once equalized the signal is serialized again and the inphase and quadrature components are ready to be extracted The final step is to demap the sequence ideally obtaining the transmitted sequence of information bits which is also going to be compensated zero padded for BER measuring 76 FIBER BASED OFDM TRANSMISSION SYSTEMS IV 1 3 OFDM Coder This module is responsible for coding a pseudo random bit sequence PRBS into an OFDM signal It has been seen that inside the coder the bit sequence will be transformed into a complex valued matrix with each column representing an OFDM symbol ready to be transmitted according to the indicated coding parameters The module s output y will be a serial sequence of this matrix Externally this module consists of an input connected to a PRBS generator and an output carrying the coded OFDM signal as shown in Figure IV 3 Fig IV 3 PRBS generator connected to the OFDM coder VPI The six parameters which will be accessed by the Matlab code must be created for this galaxy all of them indicating the universal parameter name in the value field so they can be changed from the univ
25. main function of the decoder is expressed as function I Q I EVM Q EVM zz ofdm decoder simu y real y imag BitRate TimeWindow BpS Nc N FFT CP IV 6 Here the same operations as in the coder are applied in the opposite order First the zeros used to compensate for the bitrate difference are extracted and then the sequence is parallelized converted into a matrix before extracting the rows corresponding to the cyclic prefix and performing the fast Fourier transform on a column by column basis Next the zero padded rows used for oversampling are removed from the FFT output matrix so the matrix containing the original QAM information symbols should be recovered It will be seen that this is true for the simulations performed in the next section where an ideal channel is used to transmit the electrical OFDM signal However when being transmitted on optical fibre the received signal will suffer from phase errors due to chromatic dispersion so the corresponding equalization should be applied at this point For this reason expression IV 8 has been added to the Matlab code after performing the FFT operation based on the ideal phase compensation expression 11 19 in Chapter II ephase exp lambda 2 c D pi BW 0 1 Nc 2 1 Nc 2 1 1 N FFT 2 L i IV 7 Previously the variables needed to perform this calculation should be defined according to the desired parameters see Annex D However it will be seen
26. presented before leads to an extremely complex CHAPTER OFDM BASICS 9 architecture involving many oscillators and filters at both the transmit and receive ends In present day OFDM transmissions though this complexity is reduced by transferring it from the analogue to the digital domain To see this take Equation 1 4 where just one OFDM symbol of the signal s t in 1 1 is sampled at an interval of T N Then the ne sample of s t becomes N 1 j2nfynTs N 1 jamkn dd s nTs N Yx 0xXe8 XkzoCk N F cx 1 4 Where F is the Fourier transform and n 1 N Thus it can be said that the discrete value of the transmitted OFDM signal s t is merely a simple N point inverse discrete Fourier transform IDFT of the information symbol c The same case can be applied at the receiver where the received information symbol will be a simple N point discrete Fourier transform DFT of the received sampled signal This superposition of independent modulated subcarriers is typically performed by the inverse fast Fourier transform IFFT where the input channels are spaced equivalently according to Expression 1 2 In fact IFFT FFT blocks in an OFDM system are mathematically equivalent versions of an IDFT and a DFT of the transmitted and received OFDM signal with the advantage of providing lower computational implementation Because of the orthogonality property as long as the channel is linear the OFDM receiver will ca
27. symbol problem appearing in VPI s OFDM Generation and Detection demo has been solved IV 2 2 Raw transmission The first simulated transmission doesn t include zero padding nor cyclic prefix and the PRBS generator has been established to transmit only ones at a rate of 10 Gbps so that every single subcarrier can be identified after plotting the generated OFDM signal This is why it can be called a raw transmission Figure IV 16 shows the comparison between this first simulation and the same one with the PRBS generators Type parameter set to PRBS mode where 32 modulated subcarriers are carrying information in a 4 QAM modulation Fig IV 16 Raw OFDM transmission Ones vs PRBS VPI As in VPI s demos both the real and imaginary parts are superimposed in the graphs only representing half of the OFDM band Thus the 16 subcarriers corresponding to each side of the spectrum can be identified the last one of them being centred at 2 5 GHz 86 FIBER BASED OFDM TRANSMISSION SYSTEMS Note that there is no bandwidth excess meaning that the spectrum falls off very abruptly This will not happen in a practical filter so a roll off factor needs to be applied in order to simulate a more realistic scenario Thus the resulting effect of a change in this parameter will be the next test to conduct IV 2 3 Roll off factor The pulse shaping modules in charge of retaining the and Q components of the OFDM signal are ideally rectangular H
28. the model for chromatic dispersion described in section Il 1 the fibre transfer function has the form H w eiX Oref a y EL IV 14 96 FIBER BASED OFDM TRANSMISSION SYSTEMS Where wres is the angular reference frequency for which the Taylor expression is considered L is the fibre length w depends on the evaluated frequency Within the performed simulations there are basically two natural choices for this reference frequency fref one is the optical carrier frequency f and the other one is the frequency where the optical OFDM spectrum is centred f fer While VPI s Long Haul demo uses the latter several tests have been performed in order to understand the reason why this is done and the implications behind the choice of one or the other The tests have revealed a rather symmetric behaviour of either one of the natural choices e For fref f the constellation is not phase shifted but the received temporal sequence is delayed with respect to the emitted temporal sequence This delay is longer the higher is the optical carrier frequency or the longer the optical fibre e For fref fo frr the constellation suffers a phase shift which also grows proportionally to the fiber length and fp though no delay in the temporal received sequence is observed For a better understanding of these concepts a mathematical model has been developed If the spectrum of the input signal to the fibre is expressed as Xiyl
29. to monitor the OFDM signal spectra through the most significant stages of the transmission so it can be noticed how the main modules participating in the simulation affect the signal First the electrical OFDM signal spectra is plotted for different stages inside the RF upconversion module as it can be seen by the positions of the signal analyzers in Figure IV 24 After that the optically modulated OFDM signal is represented before and after the transmission link and finally the received electrical spectrum will be compared to the one originated in the transmitter The first representation corresponds to the spectra of the coded OFDM signal before the pulse shaping module just after being sampled to convert the floating numbers representing the analogue values of the signal into electrical samples In a real OFDM system this point would correspond to the digital to analogue conversion stage once the sampling is completed but the filtering has still to be done 100 FIBER BASED OFDM TRANSMISSION SYSTEMS The resulting spectrum is the same as in the Electrical OFDM Generation and Detection simulation where no negative frequencies are represented so the main OFDM signal spans from 0 to 2 5 GHz though the alias have not been filtered out yet so they appear together in a periodic sequence This time only one component of the signal will be represented in this case the quadrature Figure IV 29 shows the mentioned spectrum where the upper
30. used 38 FIBER BASED OFDM TRANSMISSION SYSTEMS image noise real noise Noise detection gt C b A NL By SC x noise below it B Noise SC gt sdb Sesion gt a e B gap By B B sc Carrier x ASE ASE x Subcarriers ASE x ASE By gap 0 I Ei By Fig 11 21 Unwanted inband terms P13 The single tap equalizer function in the OFDM receiver corrects for the amplitude distortions caused by frequency roll off of the components and the phase distortions caused by CD and OFDM symbol timing offsets It should be taken into account that there may be other mixing products because of nonlinearities in the system or I Q imbalance in the transmitter Figure 11 22 represents a typical DD receiver used in optical OFDM where the optical and electrical spectrums before and after the photodetector are also represented fint 1 Simplified OFDM receiver t Guard bandB Data puta Bandwidth B_ 4 RX in ctual data Unwanted gt a DC bandwidth subcarrier E mixing mr OFDM bandwidth IB ADC bandwidth Fig 11 22 Direct detection at the receiver P4 It can be seen that the second order intermodulation is located in the guard band from DC to the OFDM signal bandwidth B whereas the OFDM spectrum spans from B to 2B Then the RF spectrum of the intermodulation does not overlap with the OFDM signal meaning that the intermodulation does not cause detrimental effects after proper electr
31. 1 015 02 Normalized Frequency Fig B 2 Subcarrier PSD for different symbol periods P20 If T is increased by increasing the cyclic prefix length with a fixed IFFT size N the subcarrier spacing remains constant Taking this into account since the individual subcarrier spectrum decreases in width an increase in the cyclic prefix length induces ripples with larger amplitudes in the in band region of the OFDM PSD This is shown in the next figure for the cases where the cyclic prefix length C takes values of 0 4 and 16 samples T 16 C 0 T 20 C 4 T 32 C 16 Normalized Amplitude Normalized Frequency Fig B 3 OFDM PSD for different symbol periods T and CP length C P20 6 FIBER BASED OFDM TRANSMISSION SYSTEMS This ripple may require a reduction of the transmitted power in order to obey regulatory spectrum masks that is the transmitted power cannot be made as large as it potentially could because of the overshoot in the power density This power reduction may lead to a loss in the signal to noise ratio at the receiver since the transmitted power usually has to stay inside regulatory spectrum masks On the other hand in P20 a spectral method of carrier tracking is presented where the mentioned ripple is used in order to provide an estimate of the carrier offset ANNEX C DIRECT DETECTION OPTICAL OFDM TRANSMITTER CONFIGURATIONS 7 ANNEX C DIRECT DETECTION OPTICAL OFDM TRANSMITTER CONFIGURATIONS Many diffe
32. 1 3 Gap generation As it can be seen in Chapter Il when the conventional opto electrical direct detection technique is used in the receiver due to the square law characteristic unwanted mixing products among the subcarriers may interfere with other subcarriers in the electrical domain Also when using the conventional intensity modulation technique replicas of the signal appear on the optical spectrum In order for these replicas not to overlap with the OFDM signal guard bands with respect to the optical carrier are also required This is described in more detail in Chapter II To prevent these interferences a frequency gap may be allocated between the optical carrier and the OFDM spectrum which width at least equals that of the signal s bandwidth In this section two strategies to create a spectral gap between the carrier and the OFDM spectrum are described namely the RF upconversion and the low frequency zero padding CHAPTER OFDM BASICS 19 1 3 1 RF upconversion In the RF upconversion technique the complex baseband OFDM signal s t generated with QAM subcarrier modulation as depicted in Figure 1 17 is upconverted into a passband signal centred at an intermediate frequency IF as shown in Figure 1 21 Note that the cyclic prefix stage has been omitted in this schematic though it will be used in the simulation Also note that two DACs are used to process the real and imaginary parts of the signal after the IFFT operat
33. 3 AttenuationDescription AttenuationParameter fl attenuation 0 2e 3 t ReferenceFrequency 193 1e12 7 5e9 5 DispersionDescription DispersionParameters f Dispersion 1786 Ef DispersionSlope 0 08e3 F PMDCoefficient 0 1e 12 31 62 OOSOOOOO Fig 111 25 Optical fibre physical parameters VPI The used attenuation and chromatic dispersion coefficient 17 107 s m2 are typical values for a transmission in 3 window The rest of values are set to default CHAPTER III VPI DEMOS 67 Another important parameter to take into account is the ReferenceFrequency This frequency is where the dispersion characteristic of the fibre is centred It means that the optical group delay is considered zero at the specific frequency and therefore the waveforms in that subcarrier frequency are the ones at the beginning of the time sequence at the receiver end Since the dispersion coefficient D derivative of the group delay against wavelength in 3 window is positive the lower frequencies will arrive later after the reception window time has started and higher frequencies will arrive sooner before the reception window time has started This will be an important concept to bear in mind for the correct choice of this reference frequency in the simulations It is interesting to see that this reference frequency is set in the demos equal to the sum of the optical carrier and the RF carrier just at the optical frequency where the OFDM spec
34. 5 2277312e 001 4 3974641e 001 0816652e 001 3 5987323e 001 3 3098928e 001 3 0215140e 001 6586525e 001 2 5848681e 001 2 2973098e 001 2 0955423e 001 1413641e 001 Sephase exp pi 4 i exp Lowery coefs i sephase exp Lowery coefs i N D OY OF RP jm NN FE 0 y Sephase exp lambda 2 D pi 5e9 0 Nc 2 1 Nc 2 1 1 1 7Ne 2 L 1 4 e Sephase exp pi 4 i exp lambda 2 D pa 5e9 Os Nco 2 1 No 2 1 1 NG 2 1 1 4 6 Sephase exp lambda 2 c D pi 7 5e9 5e9 0 1 Nc 2 1 No4 2 1 1 7N EFT 492 6 3 7 Ultima para fref 193 ephase exp pi 4 i exp lambda 2 c D pi BW 0 1 NcC 2 1 Nc 2 1 1 N FFT 2 L i For fref 193 1 THz 7 5 GHz ephase ephase exp 0 1 Nc 2 1 Nc 2 1 1 i 2 pi ceil CP 2 N FFT N FFT Sephase exp lambda 2 c D pi 2 5e9 5e9 0 1 Nc 2 1 No 2 1 1 N FFT 2 L i Eq con fref 193 1 THz 10 GHz Sephase exp lambda 2 D pi 5e9 Nc 2 1 1 0 Nc 1 1 NGC 2 s N FEDDIiT 2 5 1 e Sephase exp pi 4 1 exp l mbda 2 D pa 5e9 0 No 2 1 Nc 2 1 1 7N EFI 2 L 3 60 3 Mod Edu yyl QAM diag ephase yyl OAM yyl QAM exp 1 6023e4 1000e3 i yyl QAM fin eq parallel to serial yyl OAM serial yyl QAM S I real yyl preQAM Q imag yyl preQAM I real yyl QAM serial zeros 1 BitRate TimeWindow BpS length yyl QAM serial Q imag yyl QAM seria
35. ASED OFDM TRANSMISSION SYSTEMS Time Window Transmitted Symbols Fig IV 27 Transmission and detection temporal simulation window for 3 optical OFDM symbols It can be seen that the subcarriers experience different delays due to chromatic dispersion and therefore have different arrival times In the figure a positive dispersion coefficient D has been represented so that the higher frequency subcarriers are the first to arrive Since the reference frequency is set to the central frequency this is where the temporal simulation window begins zero group delay considered and therefore the higher frequency subcarriers should be out of the temporal window Owing to the Periodic Boundary Conditions PBC characteristic of VPI it will appear at the end of the temporal window Likewise the last part of the slower frequency stream falls outside the temporal window and is moved to the beginning of the temporal simulation window as it can be seen from Figure IV 27 From the received symbols stream the part where information coming from different OFDM symbols overlap should be removed in order to avoid ISI problems This part as shown graphically in Figure IV 28 is found CP 2 to the left with respect to the CP part in the emitter and therefore for a correct CP extraction a CP 2 shift to the right of the FFT window should be taken into account Time Window Transmitted Symbols Received Symbols CP 2 CP 2 Fig IV 28 Periodic Bound
36. DM BASICS 7 Fig 1 4 Spectrum of an OFDM symbol with overlapping subcarriers P2 Note that each subcarrier is centred at f and separated by 1 Ts from its neighbours When this happens the orthogonality condition is being fulfilled so a great spectral efficiency for the transmission is achieved This way the subcarriers can be recovered at the receiver without intercarrier interference ICI despite strong signal spectral overlapping by means of the orthogonality condition 1 3 using a bank of oscillators and low pass filtering for each subcarrier as shown in Figure 1 5 Fig 1 5 Frequency division multiplex Analogue receiver Note that many analogue components are needed in case of using a large number of subcarriers This factor gives rise to a tradeoff between the desire to 8 FIBER BASED OFDM TRANSMISSION SYSTEMS use as many subcarriers as possible to make the OFDM signal stronger against transmission impairments and the system complexity associated to the use of analogue components especially when many of them are needed In single carrier systems the symbol period is given by the reciprocal baud rate 1 R Since in multicarrier systems such as OFDM the symbol period is N times longer the effect of channel dispersion is typically lower and the inter symbol interference ISI decreases Moreover as it will be seen in the next section ISI can be almost eliminated by introducing a guard time in every OFDM symbol such that mo
37. DM signal bandwidth is calculated as the transmission bitrate divided by the number of bits per symbol so the expected electrical bandwidth for this case should be 2 5 GHz as just half of the spectrum is depicted The exceeding bandwidth of nearly 300 MHz that can be identified in Figure 111 15 is due to the roll off factor of the filter applied in the pulse shaping module Two more simulation results are shown in Figures 111 16 and Ill 17 representing the transmitted electrical spectrum and received constellation diagram for the other two possible modulation types Zero Padding and DMT The parameters used for these simulations are the same as before received constellation teal SB maginary SB A JA Power dBm A uu 2 Frequency GHz Fig 111 16 Zero Padding modulation VPI CHAPTER III VPI DEMOS 59 For the Zero Padding simulation zeros have been added at both edges of the IFFT input sequence as said before The resulting gap represents nearly half of the ideal signal bandwidth that is 2 5 GHz as it can be seen in Figure III 16 Again the received constellation is ideal though just half of the received information symbols are being represented due to the use of zero padding for half of the IFFT input sequence This could be appreciated in a non ideal channel transmission where dispersion would separate the received symbols in the constellation diagram The zero padding observed could be us
38. ER dif NTB INFO IV 10 This value will be extracted from the Matlab code by means of the CoSimOutputFit module connected to the CoSim output and then displayed by the VPI Photonics Analyzer through a numerical analyzer module More numerical analyzer modules can be placed at the sequence comparer inputs to display the whole transmitted and received sequences though this should just be done when working with short sequences IV 2 Electrical OFDM Generation and Detection IV 2 1 Universe schematic The customized coder and decoder modules have been used to create this simulation which functions are similar to those presented in the OFDM Generation and Detection demo in Chapter Ill Figure IV 14 shows the Electrical 84 FIBER BASED OFDM TRANSMISSION SYSTEMS OFM Generation and Detection schematic where some modifications have been done with respect to the demo in order to adapt the customized modules HU pr Sample steDetsul j BUR ateDetsat eps L Fig IV 14 Generation and detection of an OFDM signal VPI These modifications are the same as in the first part of the RF upconverter galaxy that is the complex sequence coming from the coder is split into its real and imaginary components and then upsampled to compensate for the number of samples to process in the following modules before the signal representation As in VPI s demo the coder and decoder are connected through VPI wires so there are no disto
39. ESTA 2 En EA Global 4 TimeWfindow BitsPerSymbolQAM 4 s InBandNoiseBins OFF ES Boundary Conditic Periodic ES Logicalinformatio ON f SampleMode Bar 1280e9 f SampleMode Cer 193 1612 f SampleRateDefa 4 BitsPer Symbol QAM 1 f BitRateDefaut 10e9 3 DesignRules Scheduler Player gomg Fig 111 12 Configurable parameters from the universe schematic VPI 54 FIBER BASED OFDM TRANSMISSION SYSTEMS Once the bits have been converted to QAM symbols the coder will perform an IFFT operation for each N symbols forming an OFDM symbol resulting in a sequence of floating numbers of size TimeWindow BitRate BitsPerSymbolQAM meaning a reduction of a factor log M for the sequence length By checking the Reference Manual for the coder module it can be seen that its two outputs represent electrical samples of the real and imaginary components of the complex OFDM symbols After several tests and careful readings of the available documentation on the subject it has been deduced that an upsampling operation is carried on the sequence at the output of the IFFT stage in order to be converted into electrical samples Another key to the above conclusion lies on the UnPackBlockEl 6 and Downsample 7 modules used to convert the electrical samples at the output of the decoder into numerical samples as it will be seen later Thus the original sequence length TimeWindow BitRate is recovered to match the sa
40. ICAL OFDM 23 At reception the same signal will be obtained without any distortion but with a constant delay On the other hand in a dispersive channel the phase constant has a nonlinear dependency with frequency and as a consequence of the different arrival times of the frequency components the recovered signal at the reception end will differ from the transmitted one Assuming a slow variation of the phase constant inside the signal s frequency bandwidth it is possible to consider a Taylor expansion of the propagation constant about a central pulse frequency w as follows 0B o o p le o L plo Blo lo o 7 Pes B N gt 00 6 00 11 2 O O p t o P 6 fs Where the third and higher order terms can be neglected if it is considered that Aw w wo Wo Which enables the possibility to rewrite 11 2 as 2 Bw Bo Ao 11 3 The coefficients in 11 3 are related to the following parameters e f relates to the Phase Velocity vpn which verifies fy 11 4 Vph And it can be defined as the velocity at which the phase of a pure tone at frequency would propagate e is related to the Group Velocity v of the pulse by B 1 11 5 Qc Vg The group velocity can be defined as the rate with which changes in the envelope of the wave amplitude propagate The Group Delay Tg given in 1 5 in seconds fibre length gives the delay experienced by an envelope centred at
41. IV 3 4 The lack of transparency in the coder and decoder operations can also be pointed again as an aspect to improve for this demo Moreover the use of zero padding for the OFDM coder and decoder is configured to create a gap between the OFDM signal and the optical carrier though in this demo this gap is created by means of frequency upconversion Thus the use of zero padding is useless in this scenario as long as the up downconversion stages are not removed Another possibility that will be taken into account in the next chapter s simulations is the use of zero padding as an oversampling technique 70 FIBER BASED OFDM TRANSMISSION SYSTEMS CHAPTER IV CUSTOMIZED SIMULATIONS This chapter deals with the customized simulations performed in VPI These simulations were built to perform the same functions as the last chapter s demos though they present a transparent operational system which can be modified even from the lowest level that is from the code sentences Before describing the simulations the customized modules built in VPI and its related parameters are described so the different system operations can be understood when having a look at the simulation scenarios In order to understand each step for the creation of these modules it is necessary to comprehend the Matlab code that will be executed when running the simulations Hence brief extracts of the code are introduced while describing the modules All the coding fu
42. M in Optical Systems Demos Long Haul rd a SSMF Length 100 0e3 m NoiseDescription None Dispersion 17e 6 sim k Loops 10 Tx El OFDM NumberOfCarriers 64 Error Vector Magnitude EVM CyclicPretix 0 2 QuantizationLevels 2 10 erker 5 CarrierFrequency 7 5e9 Hz _ In inp Phase 90 degs Sm M ra R OFDM Rx El OFDM BER OHM E Equalization No WUL SCHEMATIC PARAMETERS TimeVVindow 8 1024 BitRateDefault s SampleRateDefault 4 BitRateDefault Hz BitRateDefault 1069 bit s BitsPerSymbolQAM 2 a u Fig 111 18 Universe of the OFDM for Long Haul Transmission demo VPI The OFDM coder module is now placed inside an OFDM transmitter galaxy left bottom in the figure where a frequency upconversion is applied to the signal after being generated as it will be seen later by looking inside the galaxy This technique was described in section 1 3 1 and is used to create a gap between the OFDM signal spectrum and the electrical DC component so the unwanted mixing products appearing due to the IM modulation and direct detection DD method used fall outside the OFDM bandwidth For a 10 Gbps bitrate with 4 QAM modulation an OFDM bandwidth of 5 GHz is required and thus an RF carrier of 7 5 GHz is used to generate a 5 GHz gap This will be seen at the simulation results section at the end of the chapter Once the signal is upconverted to an RF frequency it is opti
43. OFDM dispersed spectrum It has been checked that the simulation results match the theoretical values of the calculated delay and phase shift for the simulated parameters In this case a delay of nearly 0 5 ns has been observed when setting fref fo though no phase shift has affected the signal On the other hand no delay was observed when fref fo frr but a phase shift of 55 appeared This will be seen in the simulation results section In any case while a phase shift can be compensated at the receiver it is not that easy to try to compensate for a time delay in the simulator Thus it has been concluded that in this matter it is best to follow the example set by the VPI demo and set f fo frr in the performed simulations 1V 3 4 2 Cyclic prefix extraction Once that it has been seen that the best choice for the reference frequency is the centre of the optical OFDM spectrum this section analyzes which is the best cyclic prefix extraction strategy In Figure IV 27 the transmission and reception simulation window in VPI for three optical OFDM symbols with their corresponding cyclic prefix are represented They consist of a temporal sequence of length Time Window For simplicity each OFDM symbol is composed by just three subcarriers where number 1 will be the lower frequency subcarrier number 2 will be the subcarrier centred in the middle of the OFDM band and number 3 represents the highest frequency subcarrier 98 FIBER B
44. OFi nic oe treten teet ARES EENE NE RES EES E es 85 IV 2 3 Roll off factors o aena ad 86 1M2 4 Zero Paddington eese dere eaa ve ERE iS 87 1V 2 5 Cyclic Pr A eese es ere reete ces esee d 88 IV 2 6 Received Constellation a a iA E nnne nn nennen 89 IV 3 Optical OEDM Gies entere oett orti es hess Ee EE cando 90 IV 3 1 Uniiverse schemiatic steer eee A da as 90 IV 3 2 Custom modules modifications eese nennen nennen 92 IV 3 3 Error Vector Magnitude and Bit Error Rate measuring ooocccccccononononononononnnanononnos 93 IV 3 4 Reference frequency choice and cyclic prefix extraction sesssssseese 95 IV 3 5 Simulation results I OFDM signal spectra esee nnns 99 IV 3 6 Simulation results Il Decoded signal cccoconooconnnncncnnonooonancnnnnnnnnnnonnnnnnnonannno nacos 104 CHAPTER V CONCLUSIONS AND FUTURE LINES esses eere 109 VAL CONGIUSIONS os E hate ee 109 APIS FUTURE INES sek teeth I Ste ted ee od e el tla e ne bed ao 111 fe E M 112 Papers and tutorials ette e tte ett 112 ccm 113 ACRONYMS EE 114 INTRODUCTION 1 INTRODUCTION Orthogonal frequency division multiplexing OFDM is a widely used modulation and multiplexing technology which is now the basis of many telecommunications standards including wireless local area networks LANs digital terres
45. QP the bias is set to 0 The laser operating at CW provides the optical carrier to be modulated and its most relevant parameters are e Emission frequency 193 12 THz e Average power 5 mW e Linewidth 1 MHz Meaning that the laser operates at 3 window and thus the dispersion coefficient of the optical fibre has to be set accordingly A random noise is generated in the laser where the maximum allowed spectral density variation within the noise bandwidth is set to 3 dB An optical filter is then used to suppress the lower sideband resulting from the optical modulation The used filter is of Gaussian type centred at f f far where f is the optical carrier frequency 193 12 THz and fpris the electrical carrier frequency at which the electrical OFDM band was upconverted 7 5 GHz The filter bandwidth is set to 18 GHz As it can be seen from Figure 1II 18 the fibre link is composed of a loop where a universal fibre module simulates the wideband nonlinear signal transmission over optical fibre After the fibre span the signal goes through amplifying and filtering stages to compensate for attenuation The number of loops of the link is set to 10 so for a fibre length of 100 km default the transmission distance will be 1000 km The most important parameters of the fibre for this simulation are the ones belonging to the Physical category as represented in Figure 111 25 Physical NumberOfFiberSpans 1 f Length 100 0e
46. RECTOR Concepci n Santos Blanco DATE October 27th 2010 INDEX ANNEX A INSIGHT INTO THE OPERATION OF AN OFDM SYSTEM eene 1 ANNEX B CYCLIC PREFIX EFFECT ON THE OFDM SIGNAL SPECTRUM seen 4 ANNEX C DIRECT DETECTION OPTICAL OFDM TRANSMITTER CONFIGURATIONS 7 CT Real drive sigrial m t e eto cett ede ve reed e mee et eve reset 7 C 2 Trigonometric interpolation oversampling esses 8 C3 Band shifted from DC eret tete erede EX eng eaa ee Te Rede 9 CARE pconvetslonD cio c ee eerte A A eee e reve te es eee e eere E 10 C 5 Colourless transmitter o re EP a Pr a abba ete eta E eee 11 ANNEX D MATEAB CODE eret amari ipe etr n tet RE Rem areae oi eee eate peo deia ende 13 D 1 OFDM Od6rt ite ette estelar eese etre iore tein eee reete pa 13 D 2 OEDM decoder Ert etn ite ete re ete 15 ANNEX A INSIGHT INTO THE OPERATION OF AN OFDM SYSTEM 1 ANNEX A INSIGHT INTO THE OPERATION OF AN OFDM SYSTEM In Chapter it has been said that the output of an IFFT operation results in an approximately bandlimited signal s t consisting of sinusoids of the baseband subcarrier frequencies Because of the nature of this procedure this signal will consist of both real and imaginary components P3 which in wireless OFDM systems results in a complex signal feeding an IQ modulator for upconversion to the carrier frequency On the other hand in baseband sy
47. a lower level in the optical modulation scheme for instance by using an IQ MZM or coherent detection at the receiver Another option to consider is to continue improving the customized simulations presented in this Master Thesis As ideal equalization has been used to compensate for the phase errors at the receiver one of the proposed improvements is to use a training sequence with pilot subcarriers in the OFDM symbols in order to compensate for these errors Moreover other configurations can be implemented for the optical system scenarios presented in Chapter IV for instance the use of zero padding to generate the frequency gap already implemented in the Matlab code to avoid using the upconversion and downconversion stages Currently a practical implementation of an optical OFDM system is under way in the TSC Optical Communications Group Labs The obtained results from the simulations performed in this work have also contributed to its development 112 REFERENCES REFERENCES Books B1 William Shieh and Ivan Djordjevic Orthogonal Frequency Division Multiplexing for Optical Communications 1st edition 2010 B2 Godvind P Agrawal Nonlinear fiber optics 1st edition 1989 B3 Eduard Bertran Alberti Procesado digital de se ales Fundamentos para comunicaciones y control II 1st edition 2006 B4 Richard Van Nee and Ramjee Prasad OFDM for wireless multimedia communications 1st edition 2000 B5 Ye Li and Gor
48. according to certain parameters The value for these parameters can be changed from the corresponding Parameter editor window PEW Figure 111 3 is an example of a PEW corresponding to a laser module LaserCW_ytms1 Parameter Editor Name LaserCW vtms ID LaserCW vtmsi BA Wee Name Value ft Sh 3 Physical i EmissionFrequency 193 1612 Hz Fi SampleRate SampleRate Default Hz F AveragePower 5 0e 3 Wr F Linewidth 166 Hz Azimuth deg F Ellipticity deg F InitialPhase deg OOOOOOO Enhanced Fig 111 3 Parameter editor window PEW of a VPI laser module VPI The Parameter editor of a module can be accessed by right clicking on it and selecting the Edit Parameters option or just by double clicking on the module In the case of a universe or when being inside a galaxy the same operations can be done by clicking on the background Because of the hierarchical organization any parameter which is shared by more than one module even if it is used in different levels will take the value of the highest level in which it is used For instance consider a transmission system where the scenario itself is a universe containing various galaxies Say one coder and one decoder and these galaxies contain at the same time other modules stars to implement its respective functions If for example the roll off parameter of a pulse shaping filter acting as a star inside both the coder and decoder modules i
49. adaptive constellations at the receiver side Thus the generation of subcarriers in the analogue domain is not of interest for the performed simulations in Chapter IV and it will not be considered in this work At the same time optical OFDM systems with subcarriers generated in the digital domain can be classified according to many other parameters In order to understand the system simulated in VPI the most important ones are the modulation technique used in the electrical to optical e o conversion and the type of detection at the receiver Many system configurations will appear from the combinations of the modulation techniques and the type of detection at the receiver though just one will be considered for the simulations in VPI This will be seen in Chapter III 11 5 1 Modulation techniques The way in which data is allocated at the input sequence of the IFFT gives rise to many different transmitter configurations Thus different optical modulations should be applied depending on the type of electrical OFDM signal obtained at the transmitter output Here two different configurations are emphasised one using a standard MZM and the other based on an optical IQ modulation Both of them avoid the CHAPTER II OPTICAL OFDM 33 transmission impairments caused by dispersion by applying the optical single sideband technique though they do it in different ways Other interesting transmitter configurations such as the Real drive sign
50. al where a real OFDM signal is obtained by means of Hermitian symmetry can be found in Annex A at the end of this work 11 5 1 1 RF upconversion based on Intensity Modulation It has been said that when performing optical modulation over a baseband OFDM signal with a standard MZM one of the two resulting sidebands must be suppressed in presence of dispersion Thus an optical band pass filter can be used for the separation of both complex bands requiring the allocation of a guard band with respect to the carrier If the size of this guard band is equal to the OFDM signal s bandwidth direct detection can be used at the receiver To that effect the baseband OFDM electrical signal can be first upconverted to a proper RF frequency as depicted in Figure 11 14 Baseband Optical OFDM OFDM RF to optical Main optical carrier up conversion Af gt f 0 fo fo Fig 11 14 Electrical upconversion of the complex OFDM baseband signal B1 As shown above the optical spectrum of the optical OFDM signal at the optical transmitter output is a linear copy of the RF OFDM spectrum plus an optical carrier that is usually 5096 of the overall power This is the technique used in the RF upconversion based on Intensity Modulation kind of optical OFDM and Figure 11 15 shows its schematic In this configuration the whole input sequence of the IFFT is carrying data though the zero padding oversampling method described in Chapter can be appl
51. ameter value of the module s Parameter editor This process is shown in Figure 111 9 for the case of a Matlab code CoSiminterface_vtms1 Parameter Editor Name CoSiminterface mms ID CoSiminterface_vtms1 C Show ID r Description This is the main module of the cosimulation interface driving simulation in external tools It supports cosimulation with Matlab Python and dynamic link libraries EBAY Dra Name Value General ES Interface Type Matlab ES Logicallnformation No E Attachments AT RunCommand x ofdm_decoder_simu a Inputs A WrapupCommand Inputs E s Outputs amp Sharelnterface On Reports er simu m i Resources Fig 111 9 Main code function indicated in the HunCommand parameter VPI In this case the variable x will take the output value of the function ofdm decoder simu Note that this name is the same for the Matlab file attached to the nput folder of the schematic 52 FIBER BASED OFDM TRANSMISSION SYSTEMS VPI provides other cosimulation modules which act as inputs and outputs of the Cosiminterface module Those are used to indicate the type of data that is going to be inserted and extracted from the cosimulation allowing the use of electrical or optical signals floating numbers complex numbers etc As an example Figure Ill 10 shows an interconnection of a Cosiminterface module with one optical input CosiminputOpt and one optical output Cosi
52. and the complete DAC bandwidths usage when no oversampling is applied Moreover few electronic devices are needed for the implementation of this scheme though two DACs are required and three bias voltages have to be adjusted for the IQ MZM CHAPTER II OPTICAL OFDM 35 11 5 2 Detection techniques As said before there are two basic kinds of techniques allowing the demodulation of an optical signal into the originally transmitted electrical signal those are the direct and coherent detection Both techniques have its pros and cons and this section describes them As the simulated transmission scenarios within this work use direct detection this technique will be described in more detail than coherent detection 11 3 2 1 Direct Detection Optical OFDM There are many publications in which different forms of direct detection methods are presented P7 P9 P10 P11 each with some advantages over the others However all of them share a very important characteristic which is the use of a simple receiver For instance five different transmitter configurations using DD method at the receiver are presented in Annex C where the use of different components such as IQ and e o modulators varies depending on the input sequence of the IFFT The performed simulations in Chapter IV will use the RF upconversion based on IM technique with DD at the receiver For this configuration the optical OFDM signal Sopt t can be described as
53. ange on the galaxy will not be applied to the original one On the other hand selecting the Link option will cause that the galaxy is executed from the original location so any modification will be saved affecting it even when it is added to other scenarios 111 1 4 2 Creating and linking parameters Although any value of a star module parameter can be changed when running a simulation the parameter properties cannot be edited Thus new parameters can only be created for either galaxies or universes This can be done by accessing the PEW and clicking the Create parameter button as shown in Figure III 5 RF_Upconversion vimg Parameter Editor Name RF Upconversion vtmg ID RF Lpconversion vtmg eG 008 mat Namd create parameter Value Unit Player Show im HF galaxies SS SSS amp Coding Parameters E Galaxy Global Scheduler Ce ee Fig 11 5 Create parameter button VPI After clicking the button a menu in which the parameter settings can be configured will appear as shown in Figure III 6 New parameter Name Minimum Value Type Float Player Maximum Value Units Mm Default Value Description Context j Parameter name Condition Value CarrierFrequency NE zz Y CarrierFrequency And Cor Not Expression Cancel Context skied eT Fig 111 6 New parameter settings VPI 50 FIBER BASED OFDM TRANSMISSION SYSTEMS In this case a new parameter i
54. ant to introduce its principle of operation prior to describing each optical OFDM system Despite coherent detection based systems represent the best performance in receiver sensitivity spectral efficiency and robustness against polarization dispersion this work will be mainly focused on direct detection This is because coherent detection based systems require the highest complexity in the transmitter design so just its main operation principle will be briefly introduced at the end of this chapter The square law detection technique has been mentioned in this work as a typical solution for optical OFDM systems As no other components than a single photodiode are required to detect the transmitted optical signal this technique is usually known as direct detection The mathematical expression for the square law technique and the study of the spectral components derived from it can be found in section II 5 2 but before that an overview of its main repercussions within an optical transmission can be realized Because the optical signal is obtained in reception as the squared modulus of its electric field square law detectors the signal mixes with itself producing at the detectors output harmonics at frequencies multiples of the modulated frequency Since usually in a transmission the conventional IM modulation is used in an ideal case the spectral components of the signal would have the precise amplitudes and phases to cause each of the co
55. ary Conditions and ISI affecting the third subcarrier CHAPTER IV CUSTOMIZED SIMULATIONS 99 The figure shows that if the CP is extracted at the same point where it was inserted we will have some unavoidable ISI no matter how big this CP could be This is something that was seen in the simulations and solved it by the CP 2 shift to the right explained above In practice a correct FFT window synchronization is critical P4 Since every subcarrier experiences a different phase shift due to the CP 2 temporal shift a phase correction needs to be included in the equalizer The following expression shows the programming sentence which has been inserted in the OFDM decoder Matlab code in order to move half cyclic prefix to the beginning of every OFDM symbol yyl yyl NTS QAM CP ceil N FFT CP 2 1 NTS QAM CP yyl 1 NTS QAM CP ceil N FFT CP 2 IV 21 After that the symbols corresponding to the CP are extracted yyl SP reshape yyl ceil N FFT 1 CP NTS OFDM yyl CP yyl SP ceil N FFT CP 41 size yyl SP 1 IV 22 Moreover an additional equalization has to be performed on the ephase coefficients resulting from the ideal equalization in expression IV 8 to compensate for the CP 2 extraction as each subcarrier will change its phase in a different way phase ephase exp 0 1 Nc 2 1 Nc 2 1 1 i 2 pi ceil CP 2 N FFT N FFT IV 23 IV 3 5 Simulation results OFDM signal spectrum The main interest of this section is
56. as shown in figure C 3 13 ts E u o o Lis o 2 2 S8 i Conjugate Inputs Real Output Zero Inputs Frequency Shifting Gives guard band close to DC Bit Rate Sample Rate 0 5 4 QAM Optical Spectrum Fig C 3 Band shifted from DC configuration P6 The remaining half of the input sequence is formed by the QAM symbols and their conjugates to achieve a real OFDM signal at the DAC output As in the real drive configuration the alias is close to OFDM spectra because there are no zeros in the middle of the IFFT sequence However it is common to set the IFFT input corresponding to the Nyquist frequency to zero In a vector of N inputs ranging from X to Xy the Nyquist frequency would correspond to the Xy 2 1th input representing the highest frequency component If the guard band width is equal to the bandwidth used for the OFDM signal then only N 4 independent complex values can be transmitted per OFDM symbol This means that only 128 data subcarriers can enter a typical IFFT stage consisting of 512 points 10 FIBER BASED OFDM TRANSMISSION SYSTEMS Again a single input optical modulator and an optical filter are used before transmitting the signal into the fibre link C 4 RF upconversion This time the gap between the DC component and the OFDM subcarriers is created through a frequency upconversion stage previous to the e o conversion This allows the complex baseband OFDM signal to be mixed with an RF carrie
57. at all while in the second one some of the concepts explained in the previous chapter are applied so the signal can be optically modulated transmitted through optical fibre and detected at the receiver end where the transmission quality is assessed in presence of various transmission impairments The simulation results presented in this chapter as well as the ones in Chapter IV have been displayed by means of the VP Photonics Analyzer tool which is automatically executed after the simulation is run when using in the setup any of the analyzer modules provided by VPI In order to understand VPI s simulation environment Section III 1 describes its basic structure and the most important settings to take into account when creating a simulation For more information about it see the VPI Transmission Maker user s manual in W6 111 1 VPI Transmission Maker as a simulation tool lll 1 1 Graphical User Interface When starting VPI the basic screen layout is similar to other simulation programs based on interconnection of modules to create design and simulate the operational characteristics of determined systems Figure Ill 1 shows VPI s graphical user interface GUI where some numbers have been added in order to identify each of the parts which are going to be mentioned during this section Ass FIBER BASED OFDM TRANSMISSION SYSTEMS VPItransmissionMaker amp VPIcomponentMaker OS OA AP DAR File Edit View Insert Format Tools S
58. ax maximum level of input signal Qmin minimum level of input signal A amplification Qbits 32 QbitsQ Qbits QbitsI Qbits y I real yyl y Q imag yyl oo REAL PARTS QmaxI max y I QminI min y I DRI QmaxI QminI if DRI 0 if input signal is a constant the adc doesn t act dI y I else dqI DRI 2 QbitsI FI y I floor y I dq1 0 5 bI FI floor y I dqI 1 FI ceil y 1 dq1 AI 2 max bI min bI end 16 FIBER BASED OFDM TRANSMISSION SYSTEMS SIMAGINARY PARTS QmaxQ max y Q QminQ min y Q DRQ QmaxQ OminQOQ if DRO 0 if input signal is a constant the adc doesn t act dO y O else dqQ DRO 2 QbitsQ FQ y _0 floor y_0 dq0 lt 0 5 bo FO floor y_0 dq0 1 FQ ceil y_0 dq0 AQ 2 max bQ min bQ end A median AQ AI 2 dI bI AI dO bQ AOQ oe Plots igure Subplot Ll 2 1 plot 1 50 dI 1 ceil N_FFT 1 CP Soptional draw the figure of a quantificated OFDM symbol real data subplot 1 22 plot 1 50 d0 1 ceil N_FFT 1 CP Soptional draw the figure of a quantificated OFDM symbol imaginary data i f oe oe oe oe yyl_adc dI dQ i O Q O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O yyl7 yyl adc NTS QAM CP ceil N FFT CP 2 1 NTS QAM CP yyl adc 1 NTS QAM CP ceil N FFT CP 2 The last half CP is moved to the start of the string yyl SP reshape yyl ce
59. cal fibre systems Then the main optical OFDM characteristics are studied and simulated through built in demonstrations available at VPI software These demos provide a convenient way to study some basic features of OFDM optical transmission systems but their use is limited to specific scenarios In order to obtain a flexible platform for tests and exploration of optical OFDM systems a new setup will be built by exploiting the VPI Cosimulation functionality which allows the use of other simulation software to operate as specific modules within VPI Thus in this Master Thesis two VPI modules have been created based on Matlab programs to perform the OFDM modulator and demodulator inside the VPI optical OFDM transmission system simulation setup While VPI s built in demonstrations are quite rigid in terms of configuring different simulation setups the use of the Matlab code in the customized simulations allows the user to perform different configurations for the transmission scenario which are impossible to obtain from the demos The document is organized as follows In Chapter the basic concepts of OFDM are described so it can be understood how an OFDM system works and which is the role of each of its parts After that the most typical optical configurations in which OFDM can be implemented are listed in Chapter Il giving emphasis to those related with the simulations performed in the last part In Chapter Ill the basic parameters of
60. cally modulated by a Mach Zehnder modulator MZM giving rise to the RF upconversion based on Intensity Modulation configuration described in section II 5 1 1 Figure 11 15 Then the optical signal is filtered to suppress the lower sideband see section 11 3 to see why optical single sideband is needed and transmitted through a fibre link consisting of a loop circuit where the signal covers 100 km with amplification and filtering stages for each loop At the receiver side a single photodiode is used in DD configuration and the resulting photocurrent is fed to the OFDM receiver galaxy which holds the CHAPTER III VPI DEMOS 61 OFDM decoder module inside The frequency downconversion is also applied within this module to recover the original baseband OFDM signal just before the decoding functions Three kinds of output results are provided by this demo by using the corresponding visualizer modules e Received constellation the required numerical analyzer is located inside the receiver galaxy e Spectrum at the receiver input right bottom visualizer in Figure 111 18 e The error vector magnitude EVM at the receiver output This value can be considered as an indicator of how far the received constellation points are from their ideal location The 1D numerical analyzer in charge of calculating the EVM will obtain information about the emitted sequence by means of the virtual optical channel feature of VPI This means that the
61. cepts of OFDM and the requirements implied by its adaptation to the optical field are explained along with a brief description of the main VPI modules that have been used in the simulations INDEX INTRODUCTION 30 ieee teh oet er tn e HERR aie ie e pet e ree dete ins 1 CHAPTER l OFDM BASICS zi eco tte sae ta Long id 4 ccce vances ads 4 1 2 Digital generation of SUDCAarrierS ccocononoooonnnnonnnonononnnnnnncnnnnannnnnnnnnnnnnnnnnnnononnnnnnnnnnnnnanannnnnos 8 2 1 Fast Foutier Transform a eee dde 8 1 2 2 D A and A D CONVESSION ccccccccccecesssssnececceeceesensaececesecsesesncaeceeeeeesesenteaeeeeceecsenenaees 11 I 2 3 CycliGPrefixi aii E e aa Ra 15 1 2 4 Mapping and demapping sesenta nnne ensis 17 1 3 Gap generatlon a o ee teta eere a e e Re ea Eye ean 18 LIT RF UpCOnVerslOn uiii id ias 19 1 3 2 Zero padding at the edges of the IFFT input SequenCe coconococnncnoccnononononnnnnnnonananonanoss 20 1 4 General system schematic mineiro aieia eaaa eaa E aea kaa ai ARE AEE aiea iKa 20 CHAPTER OPTICAL OFDM air restet Ce ete venter A ANE Re 22 11 1 The optical channel Chromatic Dispersion ccccccccccccsssessssscecececessessaeseeeeseessessaeeeeess 22 11 2 Optical modulation techniques cccconocoononcnncnonononannnnnonnnananononnnnnnnnnnnnnnnnnnnnncnnnnannnonannnnnos 24 11 2 1 Conventional Intensity Modulated Direct Detection systems
62. chematic Window Help 1 Deis t mearv OS Resources x Tree Quick Find Search 44 i irc TC Modules 2 5 os Optical Systems Demos Optical Systems Demos H 0 Access amp Aggregation 3 Analog Systems 3i Characterization E Dynamics amp Transients 64 High Capacity WOM 2 High Speed TDM Long Haul E E Short Reach 3 3 Simulation Techniques amp j C3 Subsystems E Test amp Measurement B Gbps C Amplitud cP RH CD Zr Zr BER vs O Coherent fons ar DO DO DBPSK Di DmPSK Di Qp OOF SK Rx DPSK 3A Br ar Lor Do Duobinar Measure D D ImPSK No fom DO ES He Resources fom DO Untitled 1 vtmu OS OA AP TE Untitled 1 vtmu Y Schematic Untitled 1 vtmu et No job information available Fig 111 1 VPI Graphical User Interface VPI The highlighted toolbar menu in 1 has the same function as in the most part of software programs menu as any available action offered by VPI can be executed from here creating and editing a simulation scenario preferences configuration visualization of parameters etc In 2 the most typically used options from the toolbar menu are available as shortcuts with functions such as creating a new scenario saving Zooming executing or stopping the simulation etc
63. chromatic dispersion in unit of picoseconds per picometer ps pm fo is the centre frequency of O OFDM spectrum and cis the speed of light At the receiver only one photodetector is used which can be modelled as the square law detector so the resultant photocurrent is 1 I t r t 1 2a Re emn p T certes Fo es am d Nc 1 2Ne 1 H la y XM 21 S f t9 ois 9 oU x2 11 18 Cy Cy k1 Nc 1 k2 Nc 1 k2 Ka The first term is a DC component that can be easily filtered out The second term is the fundamental term consisting of linear OFDM subcarriers that are to be retrieved The third term is the second order nonlinearity term that needs to be removed Those terms will be easily identified in the next set of figures which shows the contributions and results of the mixing products that appear at the receiver when the optical carrier mixes with the optical subcarriers to regenerate the electrical OFDM signal First the received optical spectrum for an OSSB O OFDM transmission is depicted in Figure 11 18 and then each of its components are analyzed in Figures 11 19 11 20 and 11 21 CHAPTER II OPTICAL OFDM 37 Subcarriers Carrier SC STEAM A Fig 11 18 Received optical spectrum P13 The OFDM subcarriers have a bandwidth B and there is a gap Byap between the carrier and the subcarriers which can be produced by RF upconversion of the electrical OFDM signal or by zero paddi
64. conjugate of the input symbol sequence of the IFFT to form a real valued OFDM signal In this case though zero padding is used in the middle of the sequence to shift the alias away from the useful signal as depicted in figure C 2 Alias Electrical Spectrum d Fiber Link Parallel to Serial Zero Inputs Trigonometric Interpolation Shifts alias away from the signal Bit Rate Sample Rate 0 5 4 QAM Fig C 2 Trigonometric interpolation configuration P6 ANNEX C DIRECT DETECTION OPTICAL OFDM TRANSMITTER CONFIGURATIONS 9 As explained in Chapter I this technique can be translated into a trigonometric interpolation in the discrete time domain achieving a narrower spectra for the signal and its aliases and thus allowing the use of cheaper filters for a real system Note that the bit per sample rate has been halved with regard to the previous configuration as usually half of the input IFFT sequence is used for zero padding C 3 Band shifted from DC The purpose of this configuration is to create a gap between the DC component and the OFDM subcarriers so that the unwanted mixing products generated due to the square law detection of the photodiode at the receiver fall on it as described in Chapter Il This is achieved by using the same quantity of zero padding as in the trigonometric interpolation configuration though this time the zeros are not inserted in the middle of the IFFT input sequence but at its edges
65. correct ChannelLabel value should be assigned to the module providing this information which is placed inside the receiver galaxy see section III 3 3 The schematic parameters of this demo are the same as those of the OFDM Generation and Detection demo s universe parameters in Figure 111 12 allowing the change of global parameters and the number of bits used to represent one QAM symbol However the galaxies that represent the OFDM modulator and demodulator have a much more complicated structure as described in the following sections 111 3 2 Inside the OFDM transmitter module As it can be seen from Figure Ill 19 the structure of the OFDM coding and pulse shaping functions is identical to the one used in the OFDM Generation and Detection demo see Figure Ill 11 OFDM coding Pulse shaping RF up conversion e 9 annel F li Fig 111 19 Schematic of the OFDM transmitter module VPI 62 FIBER BASED OFDM TRANSMISSION SYSTEMS However this time an RF upconversion stage is added to convert the baseband OFDM signal into a passband centred at an RF frequency in this case 7 5 GHz This is simply done by multiplying both the real and imaginary components of the OFDM signal that is inphase and quadrature by an electrical sine waveform provided by the FuncSineEl module A 90 constant phase shift will be applied to the quadrature component and both parts are added to form the upconverted el
66. d by the QAM symbols and the other half are the conjugates of each of the symbols As explained in Annex A this technique is called the Hermitian symmetry and provides a real valued OFDM signal that will be formed after a serialization of the IFFT outputs and the subsequent digital to analogue conversion Figure C 1 shows the transmitter scheme Note that only one DAC is needed after the data serialization as the imaginary component of the signal has been removed due to the Hermitian symmetry technique The resulting electrical spectrum is shown as in inset in figure C 1 Because no zero padding has been used there is no gap between the DC component 0 Hz frequency and the OFDM subcarriers and the alias is very close to it The following configurations may suffer one of these problems but not both at the same time 8 FIBER BASED OFDM TRANSMISSION SYSTEMS li Electrical Spectrum T d Parallel to Serial Fiber Link x l Conjugate Inputs Real Output Bit Rate Sample Rate 1 4 QAM Optical Spectrum Fig C 1 Real drive signal configuration P6 A single input optical modulator is used to generate a double sideband optical signal and then an optical filter is used to suppress one of the two optical sidebands The resulting optical signal lower inset in figure C 1 is transmitted to the fibre link C 2 Trigonometric interpolation oversampling This configuration is similar to the previous one as it uses the
67. d with zeros before transmitting the sequence and then extracted at the receiver side as soon as the input sequence is detected As in the VPI demos cases the reason to do that is the need to compensate for the difference between the original and the effective bitrates or symbol rates in this case so the signal can be properly processed in VPI Following with the last example once the required values to allocate the bit sequence are calculated the amount of bits corresponding to the signal representation 80 is modulated in 4 QAM according to the BpS parameter obtaining a set of 40 complex symbols These symbols are reorganized into a matrix of Nc rows and NTS OFDM files resulting in an 8x5 matrix containing the OFDM symbols used to represent the OFDM signal This matrix is shown in Figure IV 1 where the coder functions for the parameter values of the example have been executed in Matlab 74 FIBER BASED OFDM TRANSMISSION SYSTEMS xxi OFDM INFO 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 i 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 i 0000i 1 0000 i 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000 1 0000 1 0000i 1 0000 1 0000 1 0000 1 0000i 1 0000 1 0000i 1 0000 1 0000i 1 0000
68. don L St ber Orthogonal Frequency Division Multiplex for Wireless Communications 1 edition 2006 B6 Edward A Lee and David G Messerschmitt Digital Communication 2nd edition 1999 B7 A Art s Rodr guez et al Comunicaciones Digitales ed Pearson Prentice Hall 2007 B8 John G Proakis and Dimitris G Manolakis Digital Signal Processing Principles Algorithms and Applications 3rd edition 1996 Papers and tutorials P1 Jean Armstrong OFDM for Optical Communications Journal of Lightwave Technology vol 27 2009 P2 Fred Buchali Roman Dischler and Xiang Liu Optical OFDM A Promising High Speed Optical Transport Technology Bell Labs Technical Journal 2009 P3 Louis Litwin and Michael Pugel The principles of OFDM RF Signal Processing Magazine 2001 P4 Sander L Jansen SC341 OFDM for Optical Communications Short Course OFC 2010 P5 Wang Hongwei FFT Basics and Case Study using Multi Instrument Virtins Technology 2009 P6 Arthur Lowery and Jean Armstrong Adaptation of OFDM to Compensate Impairments in Optical Transmission Systems Monash University 2007 P7 Arthur Lowwery Du L and Jean Armstrong Orthogonal frequency division multiplexing for adaptive dispersion compensating in long haul WDM systems Opt Fiber Commun Conf 2006 P8 I B Djordjevic and B Vasic Orthogonal frequency division multiplexing for high speed optical transmission Optics Express 2006 P9 D F He
69. e Escola Polit cnica Superior P de Castelldefels UNIVERSITAT POLITECNICA DE CATALUNYA MASTER THESIS TITLE Fiber based Orthogonal Frequency Division Multiplexing Transmission Systems MASTER DEGREE Master in Science in Telecommunication Engineering amp Management AUTHOR Eduardo Heras Miguel DIRECTOR Concepci n Santos Blanco DATE October 27 2010 Title Fiber based Orthogonal Frequency Division Multiplexing Transmission Systems Author Eduardo Heras Miguel Director Concepci n Santos Blanco Date October 26th 2010 Overview Orthogonal frequency division multiplexing OFDM is a modulation technique which is now used in most new and emerging broadband wired and wireless communication systems because it is an effective solution to intersymbol interference caused by a dispersive channel Very recently a number of researches have shown that OFDM is also a promising technology for optical communications though its application in real optical systems is still under study In this work an optical OFDM transmission is simulated in a scenario created by means of Virtual Photonics Integrated VPI software which allows the design of many configurations regarding optical communications The programming of the OFDM coder and decoder has been done with Matlab software and custom modules have been created in VPI to perform the functions implemented in the codes Before that the basic theoretical con
70. e RF galaxies category that is CarrierFrequency Phase and RollOff Any change in the main schematic of the next section s simulations will affect both modules IV 1 6 Sequence comparer Another galaxy has been created to compare the original sequence coming from the PRBS generator and the decoded bit sequence extracted from the OFDM decoder module This will lead through a simple operation to obtain the BER for the simulated transmission Figure IV 12 shows a possible interconnection scenario for the sequence comparer where a new version of the OFDM decoder module has been designed to output the decoded sequence Fig IV 12 Sequence comparer interconnection scenario VPI CHAPTER IV CUSTOMIZED SIMULATIONS 83 Internally this module declares both sequences to a CoSim module which will access the corresponding Matlab code in which the sequences are compared Figure IV 13 shows the schematic for this galaxy A gt InterfaceType Matlab IntToFloat Cosiminpu Fig IV 13 Sequence comparer schematic VPI The Matlab sentence used to perform the comparison for sequences a and bis dif sum ne a b IV 9 As a result the dif variable will take the value of the total number of bits or vector positions which are not equal between both sequences Thus a simple operation relating the number of errors in the transmission dif and the total number of information bits will provide the value for the BER as B
71. e for its value Moreover some modifications with respect to the coding and decoding functions of the VPI demos have been applied to correct the observed limitations One of the main improvements that have been achieved with the realization of our own simulation scenarios is to see the effect of adding a cyclic prefix relative to an OFDM symbol into the transmitted sequence This effect could not be seen in the simulation results offered by the VPI demos but after a methodical study it has been observed that the chromatic dispersion inherent to the fibre requires a different procedure for the cyclic prefix extraction at the decoder This modification has been applied on the customized simulations and it has been checked that the addition of cyclic prefix provides the expected results The Accordance project has been interested in this strategy implementing it on their studies and simulations Moreover the oversampling technique has been implemented in the coder functions by means of zero padding the central positions of the IFFT input sequence This technique was not applied in the demos and allows the use of conventional filters in a practical OFDM system CHAPTER V CONCLUSION AND FUTURE LINES 111 V 2 Future lines As future lines the work carried out in this project can be continued by applying the optical OFDM concepts in other kinds of systems such as multiuser environments Also some modifications can be included at
72. e to perform these calculations as long as its ChannelLabel parameter indicates the right logical channel name The following figure shows those parameters of the OFDM receiver module which have not appeared until now EN Equalization Equalization Yes if EqualizAmp 11 A Equaliz Phase 2 1203982e 001 2 18054 EVM BER A Outputs EVM UseSymmetry No MuttipleBlockMode IndependentBlocks Analyzer 14 Title Received Constellation Update Mode Custom El UpdatePeriod TimewWindow Bit Rate Defau Analyzer Active On OOOO OOO DIDI Fig 111 22 OFDM receiver parameters VPI The EVM BER and Analyzer categories deal with the representation settings for the EVM SER and the received constellation respectively Thus the parameters indicated in these categories are going to be applied on the BER_El mQAM and signal analyzer modules The Equalization category if the Equalization parameter is set to Yes allows the compensation of the chromatic dispersion suffered by the OFDM signal during the optical channel transmission The amplitude and phase coefficients to be used have to be written as values in the corresponding parameters in order to obtain the desired results This should improve the EVM measure as well as achieving a proper constellation representation with less dispersion between points as shown in section III 3 5 The equalizer coefficients for this demo are shown in Figure 111 23 where Matlab
73. eate a gap between the OFDM signal and the DC component as in the DD receiver setups The principle of coherent OFDM is depicted in Figure 11 23 Optical Electrical RX in Local Oscillator Tunable Laser OFDM signal gt oz Laser local V A oscillator Fig 11 23 Principle of coherent OFDM receivers P4 In coherent OFDM systems the optical carrier is not transmitted with the optical OFDM signal but generated locally by a laser This makes this kind of system to require less transmitted optical power than DD OOFDM though it is more sensitive to phase noise As shown above a local oscillator LO is mixed with the OFDM signal by means of a 90 hybrid that performs the optical IQ detection If both signals are 40 FIBER BASED OFDM TRANSMISSION SYSTEMS aligned in polarization the mixing of the optical OFDM signal with the LO signal results in the desired electrical OFDM signal In case of orthogonal polarizations there are no mixing products available There are two frequently used configurations regarding to coherent receivers for optical OFDM Those are depicted in Figures 11 24 and 11 25 and are called homodyne and heterodyne respectively Simplified OFDM receiver 2 DAC bandwidth 0 1 Quent 1 I Ld 1 gt FFT size Actual data _ _A _ _ _ _ A freq T local EME e oscillator K freq Fig 11 24 Homodyne CO OFDM receiver P4 In this ca
74. ectrical OFDM signal described in expression l 6 This operation is performed by the PhaseShiftEl module which connects the sine function generator to the lower branch of the schematic Once the final electrical OFDM signal is obtained it is added to the LogicAddChannel module along with the original PRBS sequence As it was said for the definition of the Logicallnformation global parameter this module is used to send information between modules within the same simulation For instance the EVM will be calculated at the receiver without the need of any wires between it and the OFDM transmitter galaxy The available parameters of the transmitter module are shown in Figure 111 20 where some new categories have been defined in order to achieve a better organization Two of them are important to understand the simulation so they are described below Bit Rate Default i Sample Rate Sample Rate Default 4 ChannelLabel QAM OFDM Ch1 2 QAM OFDM Signal 3 PRBS Generator i BitsPerSymbolQ4M BitsPerSymbolQ4M l Number Of Carriers 64 Cyclic Prefix 0 2 DAC ES quantize Output Valu Yes QuantizationLevels 210 If HighestQuantization 1 RF Fal Carrier Frequency 7 5e9 F Phase 90 Filter NyquistResponse squareRootRaisedCosine f Rollo 02 Enhanced ES PRBS OutputFilename ES PRBS ControlFlagReset Continue ES PRBS ControlFlagWirite Overwrite HHO OOO ONO NE opa oo Fig 111 20 OFDM t
75. ed obtaining expression 11 14 where it can be seen that the modulated signal is composed by the information signal and its corresponding harmonics Equt t 1 s t s t Es 0 11 14 For a pure RF tone that is s t cos wt if Intensity Modulation is used each of the Taylor series terms will give rise to harmonics at multiples of frequency w with amplitudes which decrease with the harmonic order as the modulation order is smaller than 1 This will cause several sidebands separated at a distance n w where n is the harmonic order Figure 11 3 represents the resulting spectrum for an intensity modulated optical signal Fig 11 3 Spectrum of an intensity modulated optical signal 11 2 2 Mach Zehnder Modulator 1 2 2 1 Standard Mach Zhender Modulator The direct modulation of a laser is cheap and also easy to adapt to low cost applications for moderated distances or transmission rates However for advanced applications involving high data rates or long distance links resorting to external modulation is a good solution CHAPTER II OPTICAL OFDM 27 The most typical external modulator is the Mach Zehnder modulator MZM which modulates the light generated in a laser operating in continuous wave mode The MZM has typically an RF input and another input for a DC bias as it can be seen from Figure II 4 optical waveguides si 1 a Pout Tl D2 microwave electrodes Fig 11 4 Mac
76. ed in accordance with the following section as a technique to avoid the RF upconversion stage and yet provide the required guard band for the use of conventional IM DD optical transmission systems The spectrum of the transmitted signal for a DMT modulation can be seen in Figure Ill 17 where only the real part of the signal is represented while the imaginary component is zero It can be seen how the use of the complex conjugate in half of the input IFFT sequence allows the elimination of the negative band at a cost of reduced bitrate efficiency see Annex A Real SB imaginary SB A hw Peer yal N PSP Power dBm o i Frequency GHz Fig 111 17 DMT modulation VPI Other parameters such as cyclic prefix or bits per symbol will be changed in the simulations performed with custom modules in Chapter IV so it can be seen the effect on both the signal spectrum and the received constellation 60 FIBER BASED OFDM TRANSMISSION SYSTEMS 111 3 OFDM for Long Haul Transmission Demo 11 3 1 General schematic In this simulation scenario the OFDM signal is generated and detected as in the last demo though two major changes are applied those are RF frequency up downconversion and optical signal modulation and demodulation Also the transmission is done over a 1000 km optical fibre link Figure 111 18 shows the universe schematic for the simulation which can be found in the left panel labels of VPI T
77. ed number of bits may be left aside since they are not enough to form another complete OFDM symbol For instance for a 200 bit input sequence if the OFDM coder uses 8 subcarriers to modulate the information symbols with a 4 QAM and 2xoversampling configuration N_FFT 16 the total number of bits when a cyclic prefix of 10 is being used would be allocated into 00 2 NTS_OFDM floor amor 5 OFDM symbols IV 5 From these 5 OFDM symbols 40 information symbols would contain the 80 bits of the sequence used to represent the OFDM signal An OFDM symbol would have a total length of 36 bits from which only 16 would contain information and 20 would be overheads 16 for zero padding and 4 for cyclic prefix Therefore in the 200 bits sequence 5 OFDM symbols can be allocated yielding a total of 80 40 information bits QAM symbols 80 40 zero padding bits QAM symbols 20 10 CP bits QAM symbols 180 90 bits QAM symbols The residual 20 10 bits QAM symbols are the left aside since they are too few to form another complete OFDM symbol For this 36 bits 18 QAM symbols would be required These left aside bits would have also to be taken into account for an errorless simulation to be carried out Note that these means a bitrate efficiency of 80 200 40 of the original bitrate Instead of transmitting just 90 of the 100 possible symbols the simulator would not allow it anyway the remaining 10 symbols will be padde
78. eferred during this work as oversampling or frequency zero padding Modulation with oversampling Modulation of all subcarriers without oversampling frequency i frequency a a a J 2 8 oT sos a E il gt a so a E 3 0 gj 8 o x Zea S X E 2 n Ni 9 a o a I gt a 8 5 P e o e Impossible to separate Electrical a ey aliasing components fromthe Over low pass filter 5 OFDM signal cnp 3 g gt a E H p ses ail i s a Aliasing 9 Vi d Aliasing p LJ a LI LI a a Fig 1 13 Oversampling used to shift aliases away P4 14 FIBER BASED OFDM TRANSMISSION SYSTEMS Note that the zero padded frequencies are those around the Nyquist channel This ensures the zero data values are mapped onto the highest positive frequencies and lowest negative frequencies those around fy while the nonzero data values are mapped onto the subcarriers around O Hz preserving the main OFDM signal The reason why the aliases are shifted away from the OFDM signal can be understood by looking at Figure 1 14 In the upper case no oversampling is applied while the lower case represents a typical 2xoversampling transmission where half of the IFFT inputs those in the centre around the Nyquist frequency have been used for zero padding in the same way as in Figure 1 13 In this case the number of IFFT inputs has to be doubled in order to allocate the same number of OFDM subcarr
79. eived intensity for an ideal channel is a function of the PIN diode s responsivity R and the different gains of the amplifier devices in reception G Ip t RGP 1 m s t 11 11 Figure 11 2 shows an example of an electrical information signal s t being modulated over an optical carrier At the emission stage the signal is converted from the electrical into the optical domain E O and vice versa at the reception stage O E This kind of optical transmission is known as Intensity Modulation Direct Detection IM DD Bias Electrical Jua Electrical information Tr information signal s t gt NA signal s t E O O E Fig 11 2 Schematic of an Intensity Modulation and Direct Detection 26 FIBER BASED OFDM TRANSMISSION SYSTEMS The direct detection process is mathematically equivalent to applying the squared modulus I t s t 11 12 As this is a modulation of the optical power or intensity not directly from the amplitude of the transmitted electrical field its spectrum is composed by various sidebands replicas from the one being modulated Mathematically starting from expression 11 9 about the optical power at the laser output and applying the square root the low pass equivalent of the electrical field being transmitted on the fibre is obtained Eout t JP J1 m s t 11 13 In order to give an insight into the spectral content of the signal the Taylor expansion of the previous expression is consider
80. er 16 x 5 matrix of complex numbers representing the symbol values for the temporal sequence of the OFDM signal After that the corresponding CP quantity is added In this case it has been said that the CP requires the space for 10 QAM symbols so the last 2 rows of the matrix 2 rows x 5 columns means 10 symbols are copied to the beginning of a new matrix where the rest of it is left as before resulting in an 18x5 matrix The last matrix will be serialized into a vector y which will be the sequence at the output of the coder including the 10 zero valued symbols at the end of it to compensate for the expected symbol rate The Matlab code corresponding to the decoder module will also need the same input parameters as in the coder except for the input sequence which will not be the original one but the real and imaginary components of the OFDM signal y real and y imag as explained in Chapter III for the VPI demos CHAPTER IV CUSTOMIZED SIMULATIONS 75 Moreover no less than 5 variables are going to be extracted from the code once it is processed Those are the decoded bit sequence zz and two versions of the decoded real and imaginary components of the signal one without symbol rate compensation and Q and a compensated one EVM and Q EVM As it can be deduced by their name the latter components will be used for EVM calculation while the first ones will be represented as constellation points by the signal analyzer Thus the
81. ernal operations carried on inside them The problems indicated in the last paragraphs have been the cause of a need for new coding and decoding tools where every operation can be checked and even modified Hence custom coder and decoder modules have been developed to implement the same operations as those of VPI as it will be seen in Chapter IV 11 2 3 Simulation results When running the simulation two graphs are going to be shown in the Analyzer tool the electrical signal spectrum and the received constellation diagram As the signal transmission is done over an ideal channel no dispersion will appear on the constellation diagram so for case of 4 QAM modulation mQAM coding with BitsPerSymbolQAM parameter set to 2 it will be displayed as 4 points forming a square each of them representing one information symbol CHAPTER III VPI DEMOS 57 This case is represented in Figure Ill 14 for the OFDM type of coding The parameters for this simulation are BitRateDefault 10 Gbps BitsPerSymbolQAM 2 SampleRateDefault 4 BitsPerSymbolQAM 10 e9 2 BitRateDefault TimeWindow BitsPerSymbolQAM 4 1024 10e9 8192 BitRateDefault NumberOfCarriers 16 CyclicPrefix 0 2 Moreover the pulse shaping filter has been set with the following parameters e RollOff 0 18 e Symbolhate BitRateDefault BitsPerSymbolQAM received constellation Fig 111 14 4 QAM received constellation diagram VPI Apart from the 4 possible info
82. erse schematic where they should also be defined Figure IV 4 shows the resulting Parameter editor for the OFDM coder galaxy which will be the same for the OFDM decoder galaxy OFDM_Coder vimg Parameter Editor x Name OFDM Coder Raul vtmg Se p OFDM Coder Raul vtmg EJE S v x 8h 48 Name Value i Show E Coding Parameters i Bps f cP i N FFT E Galaxy Global F BitRate BitRate Default F TimeWfindow TimeWfindow s i Nc a E Scheduler Fig IV 4 OFDM coder and decoder Parameter editor VPI By looking inside the module it can be seen that the incoming bit sequence needs to be adapted in order to be used inside a Matlab code Figure IV 5 CHAPTER IV CUSTOMIZED SIMULATIONS 77 shows the OFDM coder galaxy schematic where the blue arrows represent the input left and output right ports The main block in this schematic is the CoSim module which will act as an interface between VPI and Matlab The rest of blocks are used to first declare the input bit sequence to the CoSim module and then indicate the desired variable to extract from the code once it has been executed Ya i9 LL IntToFloat ack CosimlnpuMxFlt nterfaceType Matlab AO c C prbs y Fig IV 5 Internal view of the OFDM coder VPI For this the PRBS coming from the input port is first converted from integer to floating values by means of the ntToFloat star This is because
83. es can be classified those are the universe galaxy and star As it can be deduced by their names the star represents the lowest level of the simulation interface the galaxy belongs to the second level and the universe is the third and highest level Universe No Port Holes or Variables to Star Galaxy Galaxy higher layers Galaxy Port Holes to Galaxy Star Star higher layers Star No Schematic Terminal Terminal underneath a b Fig 111 2 VPI hierarchy VPI manual A star represents a unique module with a specific function which can t be subdivided into other modules Thus a galaxy can be described as a second level module formed by a set of interconnected stars or even other galaxies In order to be implemented on a universe a galaxy must contain at least one input or output port see Figure 111 2 46 FIBER BASED OFDM TRANSMISSION SYSTEMS The universe is the only module that can be executed by the user It represents the whole simulation scenario and it can consist of a combination of interconnected stars and galaxies From a universe point of view a galaxy acts as another unique module and the stars inside this galaxy can t be seen from the main schematic However the galaxy schematic can be displayed by right clicking on it from the universe schematic and selecting the Look inside option 111 1 3 Simulation parameters When executing a simulation any star galaxy or universe belonging to it will operate
84. ethods could be applied though just three of them have been chosen as the most representative for this work s purposes those are the directly modulated laser and two versions of a Mach Zehnder modulator MZM the standard mode and the IQ MZM 11 2 1 Conventional Intensity Modulated Direct Detection systems In this case a laser diode is directly modulated by an electrical signal through its bias current Figure Il 1 shows the characteristic curve of a laser diode where a linear behaviour zone can be identified The slope of this zone is known as slope efficiency Moreover the schematic of a diode laser is also shown where IL and Po refer to the bias current and optical power respectively CHAPTER II OPTICAL OFDM 25 k L E a Diode Laser L mA Fig 11 1 Schematic and characteristic curve of a laser diode This is the most straight forward method to send information through optical fibre based on causing variations of the bias current of a diode laser above a given threshold These current variations Im lead to proportional variations of the output optical power Pout which are detected by a PIN diode at the receiver end carrying out the reverse process to recover the sent information signal s t as Pout B m s t 11 9 Where P is the power associated to the laser bias and m is the used modulation index which is also related to the laser bias current 1 as m 11 10 Finally the total rec
85. etween using N emitter receiver sets and using a single one Figure 1 2 shows the OFDM modulation idea schematically A bit sequence with rate R is parallelized into N different channels each with a different frequency The total bitrate is distributed in equal parts over each channel at a rate R N The data in each channel will be mapped to represent an information symbol and then multiplied by its corresponding frequency The summation of these parallel information symbols will form one OFDM symbol Parallel To Freq see s t High Bitrate R To Parallel Mapping Low sad R N 1 Freq N Fig 1 2 Frequency division multiplex Analogue transmitter Each OFDM symbol has thus a duration T N R Hence the OFDM signal in the time domain s t can be expressed as a summation of each information symbol c being carried in the Ath subcarrier within the ith OFDM symbol Depending on the modulation used for the subcarriers this superposition of subcarriers forming s t can result in complex values though this case will not be taken into account yet Then with the OFDM symbol having a period T s t RL eo Vero Cin ekt P t iT 1 1 Where P t is an ideal square pulse of length T the number of subcarriers is represented by N and f is the subcarrier frequency This frequency has to fulfil the orthogonality condition D i 1 2 6 FIBER BASED OFDM TRANSMISSION SYSTEMS This means that each
86. f an OFDM system could be the one depicted in Figure 1 23 In order to correct the channel s response a single tap equalizer should be used at the receiver end to calculate any possible phase shift The optical modulation and demodulation stages as well as the channel impairments affecting an OFDM transmission over optical fibre are explained in detail in the next chapter CHAPTER OFDM BASICS 21 Add 0 x cos 27f t Cyclic Prefix et Real To sup t Serial s t Optical Modulation N 4 Symbols Add Complex Output Imag a sin 27f t 11010001 Padding N 4 Symbols Channel Extract 0 x Optical cos 2rf t Cyclic Prefix Demodulation Real N 4 Symbols Extract N 2 Zero Serial Padding Demap 11010001 Complex FFT Input N 4 Symbols Q Imag sin 27f t Fig 1 23 OFDM system schematic Before the RF upconversion s t is approximately bandlimited consisting of sinusoids of the baseband subcarrier frequencies For the simulations carried out in this work the signal s t after the RF mixer will form the electrical input to an optical modulator after being upconverted to the carrier frequency Thus the upconverted electrical OFDM signal at the output of the front end block is Syp t R s t cos Znf t Sts t sin 2r fet amp s t e t 1 7 Where s t is the complex
87. g Select either mQAM or mPSK coding to modulate subcarriers e NumberOfCarriers Number of subcarriers taking part on the modulation If the Zero Padding technique is used only half of the subcarriers will be used to encode the signal meaning a loss of 5096 of the effective data rate The same will happen with the DMT modulation type e CyclicPrefix The length of the cyclic prefix relative to the symbol length ranging from 0 0 to 1 e QuantizeOutputValues If this parameter is set to Yes the output values of the coder are quantized The number of quantization levels and the higher quantization level should be indicated afterwards This technique is useful to simulate the effect of a DAC and also to clip the signal when it exceeds a determined level If any of these parameter values needs to be changed it should be done in both coder and decoder Thus one way to achieve an easier configuration of the schematic would be to create schematic parameters as explained in the last section so just a single parameter change is required to affect both modules However the main disadvantage of the coder and decoder modules is that all the performed operations are internal meaning that they don t allow looking inside them for a detailed analysis of the working procedures Despite some basic concepts are explained in the Reference Manual it can be said that those modules are quite rigid in terms of showing the structure and organization of the int
88. g information symbols for the subcarriers within one OFDM symbol The incoming bits to send have to be packed and mapped to a symbol generally using a complex modulation format such as for example M QAM or QPSK For the 4 QAM modulation used in this work s simulations the incoming serial data uses two bits to create each of the 4 possible complex valued QAM symbols or information symbols as it can be seen from Figure 1 19 10101100 Real Complex Fig 1 19 4 QAM mapping P4 18 FIBER BASED OFDM TRANSMISSION SYSTEMS The inverse procedure will take place at the receiver side each complex valued received symbol will be demapped and the obtained symbol sequence will be serialized to ideally obtain the original bit stream from the transmitter However because data is not going to be transmitted over an ideal channel a decision of which constellation point is received has to taken before demapping This process is called slicing and it is depicted in Figure 1 20 we 00 I k te amp amp 1 0540 9j gt 14 11 gt I 1 0140 95j tj 10 4 F 1 02 1 04j gt t j 01 gt t 4 InPpase Complex Real Quadlsture Fig 1 20 4 QAM slicing and demapping P4 The most commonly used method for slicing is a hard decision threshold though many other methods have been introduced to perform it with soft decision thresholds at a cost of an increased system complexity
89. graph shows the resulting signal when no oversampling is used Note that the aliases are right next to the main OFDM signal and also very close between them which would require the use of an ideal filter to eliminate them If 2xoversampling is applied the spectrum s bandwidth is halved Thus the OFDM signal aliases can easily be filtered out as shown in the lower graph in Figure IV 29 As the used sampling rate is 4 times the bitrate 4 signal spectrums are represented in each figure where only the first half or the first 2 5 GHz of the spectrum has to be recovered Electrical Spectrum Power dBm 1e10 Frequency Hz Electrical Spectrum Power dBm Fig IV 29 OFDM spectrum before the DAC s filter VPI All of the following figures in this section will represent the case where no oversampling is applied in the upper part and the 2xoversampling case in the lower one Next the PulseHaisedCosQAM module filters the aliases out preserving the main OFDM signal As in previous simulations a roll off factor of 0 2 has been used to simulate a close to real OFDM system Figure IV 30 shows the resulting spectrum with and without the use of zero padding CHAPTER IV CUSTOMIZED SIMULATIONS 101 Electrical Spectrum Power dBm Frequency Hz Electrical Spectrum Power dBm Wilts Frequency Hz Fig IV 30 OFDM spectrum after the DAC s filter VPI The last signal analyzer in t
90. h Zehnder modulator VPI The material for the MZM has electrooptical properties by which the phase of the optical wave propagating inside it receives a phase modulation proportional to the applied electrical field Therefore the optical power Pout at the output of the MZM depends on the phase difference A between the two arms of the modulator which can be changed by varying the bias of the MZM Pour t Pin t d t Pin t cos A t AP t DA 11 15 Where d t is the MZM power transfer function and A t and A t are the phase changes in each arm caused by the applied modulation signal s t Figure 11 5 shows the Intensity Modulation schematic and transfer function for a MZM where the bias point is situated in the linear zone of the transfer function in order to obtain a linear intensity to optical power relationship IM This point is known as the quadrature point and is the most used in combination with DD Mach Zehnder Modulator Fig 11 5 IM with Mach Zehnder modulator By changing the bias of the MZM the phase of its two arms is shifted Hence the so called Optical Field Modulation mode can be achieved by setting the bias 28 FIBER BASED OFDM TRANSMISSION SYSTEMS of the MZM to the null point This is shown in Figure II 6 where the transfer functions of the optical intensity and optical field are represented and the drive voltage determines the type of modulation performed by the MZM Transmission
91. has been used for each subcarrier modulation with a 10 Gbps data rate The upper graph represents an OFDM signal generated with the same characteristics except for zero padding which has not been applied Fig IV 18 Gap generation by means of zero padding VPI It can be seen that the frequency gap due to zero padding has occupied half of the spectrum to transmit This will be the main drawback when using this technique though it is an alternative to the use of analogue components such as RF mixers performing the up downconversion functions If zero padding is applied on the central half of the input sequence of the IFFT the spectrum is compressed as explained in Chapter allowing the use of simpler filters to erase the aliases resulting from the sampling stage The resulting spectrum after this process is shown in Figure IV 19 Again only half of the IFFT inputs are going to be used by information symbols meaning a loss in bitrate efficiency On the other hand off the shelf DACs will be able to be used to obtain the analogue OFDM signal after the IFFT stage 88 FIBER BASED OFDM TRANSMISSION SYSTEMS LA electrical I and Q signals Electrical Spectrum n 8 LA 2 SE ES E a 3 s z o a El MM HAMM AL ili lli le 269 Frequency Hz Fig IV 19 Oversampling by means of zero padding VPI Any kind of zero padding will be extracted at the receiver after the FFT operations in the same way as it
92. has been used to represent the applied phase equalization array in radians for the 64 modulated subcarriers CHAPTER III VPI DEMOS 65 i ak T L NS T L 3 1 1 1 1 1 1 0 10 20 30 40 50 60 70 Fig 111 23 Phase equalization curve VPI It is thought that these coefficients have been experimentally extracted from a training sequence after identifying the optical channel properties and are only valid for the specific settings in the demo If for instance the length of fibre the bit rate or the QAM levels are changed a different sequence for the equalizer must be used which is not provided by the demo It will be seen that the custom simulations use a very similar equalizer shape that comes from the simplified fibre model in which chromatic dispersion is considered as the only relevant effect 111 3 4 Optical channel path The optical channel path is composed by an optical modulation stage the fibre link and a photodiode in direct detection configuration at the receiver Figure 111 24 shows the optical modulation stage where the two inputs of the MZM correspond to its driver connected to OFDM coder output and a laser at continuous wave CW mode Fig 111 24 Optical modulation stage VPI 66 FIBER BASED OFDM TRANSMISSION SYSTEMS The driver basically sets the optical modulation index relative to the half wave voltage of the MZM Since the used MZM module is set by default at the quadrature point
93. he RF upconversion galaxy will represent the upconverted OFDM signal spectrum Here the and Q components have been multiplied by a 7 5 GHz carrier and added with a 90 phase shift for the quadrature component Electrical Spectrum Input 1 SB Power dBm 8e9 Frequency Hz Electrical Spectrum Input 1 SB Power dBm 8e9 Frequency Hz Fig IV 31 Upconverted OFDM signal VPI 102 FIBER BASED OFDM TRANSMISSION SYSTEMS Once the coded OFDM signal is upconverted it has to be optically modulated by a MZM As explained in Chapter II the resulting spectrum will consist of an optical carrier which in this case is centred at 193 1 THz and two sidebands of the optical OFDM signal as shown in Figure IV 32 Optical Spectrum of DSB OFDM signal before filtering B 64 OFDM subcarriers Power dBm a Frequency relative to 193 1 THz GHz Optical Spectrum of DSB OFDM signal before filtering 64 OFDM subcarriers Power dBm Fig IV 32 Double sideband optical OFDM signal VPI An optical filter will be then in charge of removing the lower sideband so the single sideband SSB transmission configuration is achieved The resulting spectrum is represented in Figure IV 33 SSB Optical Spectrum after filtering Power dBm a Frequency relative to 193 1 THz Hz SSB Optica Spectrum after filtering Power dBm o Frequency relative to 193 1 THz Hz
94. he UnpackBlockEl modules as it can be seen in 6 from Figure 111 11 Once the electrical signal is sampled the number of samples needs to be reduced so just the correct amount of information symbols is represented on the constellation diagram CHAPTER III VPI DEMOS 55 As it was explained in the coder case this is because VPI needs the number of samples of the original bit sequence to be at least equal to the number of samples to be represented as an electrical signal As the coder internal sequence is organized in symbols not in bits it is supposed that this sequence is internally upsampled so it can be correctly processed by the software Thus two DownSample blocks 7 are used to provide the exact amount of information symbols to be represented by the next module The downsampling factor indicated in the Parameter editor of these blocks is set to factor SampleRateDefault BitRateDefault BitsPerSymbolQAM 11 6 As the SampleRateDefault parameter is set to 4 BitsPerSymbolQAM BitRateDefault for this demo in order to have a frequency simulation window that is 4 times larger than the required optical bandwidth of the optical OFDM signal the downsampling factor and also the internal upsampling factor of the coder will be 4 for any type of subcarrier modulation and bitrate The constellation diagram is plotted by the NumericalAnalyzer2D module 8 which also acts as an interface to the VPI Photonics Analyzer tool 111 2
95. he fibre length w is the subcarrier frequency and f is the second term order of the signal phase delay approximation in 11 7 However this equalization will be not enough to obtain the ideal received constellation as a constant phase shift will still affect the received symbols due 42 FIBER BASED OFDM TRANSMISSION SYSTEMS to the choice of the reference frequency for the fibre This issue will be dealt with in section IV X CHAPTER III VPI DEMOS 43 CHAPTER III VPI DEMOS Virtual Photonics Integrated VPI is a powerful tool that allows to simulate a wide range of optical transmission designs giving the possibility to create multiple configurations for a given transmission scenario Specifically the simulations described in this chapter are going to be performed by means of the VPI Transmission Maker application though it will be simply referred as VPI during this work VPI contains two demonstration scenarios which are very interesting regarding this work s purposes Those are the OFDM Generation and Detection demo Optical Systems Demos Modulation Multilevel and the OFDM for Long Haul Transmission demo Optical Systems Demos Long Haul These demos are going to be described in this chapter in order to get an idea of how to implement an optical OFDM transmission on a simulation environment The first demo simply deals with the generation and detection of an electrical OFDM signal so no optical transmission is considered
96. his module has 4 outputs and just one of them is connected to a numerical analyzer This output corresponds to the bit error rate value for the received sequence and is the only one which will be represented in this simulation As this module also expects a TimeWindow Bitrate sequence of electrical samples at its input the compensated sequence of demodulated bits is needed However this time the upconversion stage is not needed because the bitrate compensation is enough to provide the expected sequence length As in the EVM case the module offers the possibility to ignore the compensating bits so the following values are given to the IgnoreBits and Start TimeTolgnore parameters NumberOf BitsTol gnore TimeWindow BitRate tRate Bi x BpS floor rimewindow Bps ceil Ngg 1 0 StartTimeTolgnore TimeWindowBitRate 1 BitRate N BpS fio Bps ceil N_FFT 1 cr IV 12 CHAPTER IV CUSTOMIZED SIMULATIONS 95 These parameters will appear in the Parameter editor as long as the gnoreBits parameter is set to ApplyONce In order to assist the BER calculations a clock recovery module is previously inserted The customized sequence comparer module presented in section IV 1 6 can be also used to perform the BER calculations allowing the possibility to see which of the information bits has been wrongly received IV 3 4 Reference frequency choice and cyclic prefix extraction IV 3 4 1 Reference
97. ical OFDM is shown in Figure 1 16 where an OFDM signal is represented with different colours for each subcarrier It is true that null ISI could be achieved with the introduction of any temporal guard interval but only the cyclic prefix can guarantee null ICI This fact is mathematically demonstrated in P1 It is important to mention that the introduction of cyclic prefix entails the loss of orthogonality in the transmitted symbols though this will not be a problem as this cyclic extension will be eliminated in the receiver recovering the original orthogonality B7 16 FIBER BASED OFDM TRANSMISSION SYSTEMS Inter Symbol interference from neighboring OFDM symbol Chromatic Dispersion FFT size Cyclic prefix Fig 1 16 ISI because an insufficiently large CP P4 Another interesting effect can be observed in the OFDM signal spectrum when the temporal duration of the OFDM symbol is increased due to the CP insertion the corresponding sincs are narrower in frequency than before so their maximums don t match up exactly with their neighbours nulls and the resulting spectrum is not plain any more but it suffers from rippling This effect is dealt with in Annex B where the consequences of adding a CP on the signal spectrum are discussed In the simulations performed with VPI the cyclic prefix parameter will be determined by a percentage of the total number of symbols at the output of the IFFT block The typical val
98. ical filtering CHAPTER II OPTICAL OFDM 39 Once photodetected the electrical signal is downconverted to baseband in the opposite way as it was done at the transmitter before applying the FFT to ideally recover the original subcarriers Thus if the optical OFDM band is located close to the optical carrier in the frequency domain the intra mixing products are located in the same frequency range as the electrical OFDM signal leading to performance degradation Taking all this into account it can be said that the optical bandwidth requirements for direct detection optical OFDM are determined both by the OFDM band and the gap between the OFDM band and the optical carrier always omitting one optical sideband Typically the width of gap is equal to the width of the OFDM band in minimum 11 5 2 2 Coherent Optical OFDM Coherent optical OFDM CO OFDM represents the best performance in receiver sensitivity spectral efficiency and robustness against polarization dispersion but it requires the highest complexity in the transmitter design There are two main advantages coming from the combination of coherent optical communications and OFDM OFDM brings coherent systems computation efficiency and ease of channel and phase estimation and the coherent systems bring OFDM a much needed linearity in e o upconversion and o e downconversion since a linear transformation is the key goal for the OFDM implementation Moreover there is no need to cr
99. ied for easier filtering of the electrical OFDM signal with respect to its aliases before the e o conversion Two DAC s are used to convert the real and imaginary parts of the electrical OFDM signal from the digital to the analogue domain Subsequently an analogue electrical IQ mixer allows both parts of the complex OFDM signal to be sent as inphase and quadrature signals over the RF frequency carrier so that the signal can be modulated with a standard MZM 34 FIBER BASED OFDM TRANSMISSION SYSTEMS Intermediate frequency gt Aadnolex I freq gt 2 DAC bandwidth Actual data FFT size je BPF to eliminate A freq freq 2 BAC bandwidth Fig 11 15 RF upconversion based on Intensity Modulation schematic P4 1 5 1 2 Optical IQ modulation If an IQ MZM is used for the optical modulation of the electrical OFDM signal only one complex optical OFDM band is obtained so no optical filter is required at the transmitter end The resulting schematic for this technique is depicted in Figure 11 16 where the real and imaginary components of the OFDM signal are directly fed to the IQ MZM For simplicity oversampling is neglected e NEN Simplified OFDM transmitter Simplfiedc AL E o MEM freq 3 fJ 2 DAC bandwi M andw idth St AP a LL ro Af freq Fig 11 16 Optical IQ modulation schematic P4 This scheme provides the possibility of a full data IFFT input sequence
100. iers as before The input sequences of the IFFT are represented in the left side After performing the IFFT operation the sampled signal is obtained centre figures Note that twice the number of samples is used to represent that signal in the case of using oversampling The D A conversion carried out in the DAC is understood as temporal extrapolation frequency alias filtering of this sampled signal lll me LAA Sampling DTFT 0 2n Fig 1 14 Aliases moving away due to zero padding If the spectrums of these analogue signals are represented by applying the Discrete time Fourier transform DTFT it can be seen how the oversampled signal spectrum becomes narrower This narrowing effect is produced because the high frequencies are zero padded though the same quantity of information is still being added over the same bandwidth so the spacing between subcarriers is decreased This will cause a frequency separation between the maximum frequency of the OFDM signal and the minimum frequency of the subsequent alias Thus the requirements of the filter needed to recover the original signal will not be too high enabling the choice of a non expensive DAC for the system This technique will be applied in the simulations performed in chapter IV by using the same number of IFFT inputs for information symbols and for zeros CHAPTER OFDM BASICS 15 For instance a 128 IFFT FFT size will be used to apply the oversampling
101. il N FFT 14 CP NTS OFDM yyl CP yyl SP ceil N FFT CP 1 size yyl SP 1 CP symbols are extracted yyl FFT fft yyl CP N FFT The FFT is performed Zero Padding removal yyl QAM yyl FFT N FFT Nc 241 size yyl FFT 1 N FFT NC 2 yyl QAM yyl FFT 1 Nc 2 yyl FFT size yyl FFT 1 Nc 2 1 size yyl FFT 1 Mod Edu oo Equalization D 17e 6 SDispersion BW 5e9 Signal Bandwidth c 3e8 Speed of light frf 7 5e9 SReference frequency L 1000e3 SFibre link distance fo 193 1e12 Optical carrier frequency lambda c fo SWavelength ANNEX D MATLAB CODE 17 SLowery coefs 2 1203982e 001 2 1805440e 001 1 9621803e 001 2 1203336e 001 2 6253623e 001 2 8899551e 001 2 8514322e 001 3394620e 001 3 7314924e 001 4 0120419e 001 4 2135611e 001 1788445e 001 5 6894703e 001 6 2998440e 001 7 3253757e 001 8296186e 001 8 9312601e 001 9 5320192e 001 1 0216461e 000 1529878e 000 1 2464763e 000 1 3586995e 000 1 4649820e 000 5616805e 000 1 6995038e 000 1 8490457e 000 1 9557745e 000 0796425e 000 2 4095242e 000 2 5301500e 000 2 6837541e 000 7322297e 000 2 8382730e 000 2 8455154e 000 2 7563871e 000 6329964e 000 2 3774626e 000 2 1575748e 000 1 9194399e 000 7613838e 000 1 6535138e 000 1 5558741e 000 1 4912738e 000 3888316e 000 1 2861190e 000 1 1495645e 000 1 0487200e 000 3607302e 001 8 4476346e 001 7 6078367e 001 7 2272519e 001 5489735e 001 5 8596704e 001
102. ime Window 1 TimeWindow df 111 4 1 TimeWindow fmin gt 111 5 111 1 4 Custom modules 111 1 4 1 Creating and adding galaxies To create a new galaxy the user has to click on the File New option in the toolbar menu and a new schematic will appear At first it will be considered as a universe though it will automatically saved as a galaxy when input and output ports are used in the schematic These ports can be found in the Tree tab of the GUI pressing the TC Modules button and selecting the Wiring Tools category To add a customized galaxy module the option Insert Add module in the tool bar allows loading it into a universe or galaxy schematic by just selecting them from the corresponding location if known VPI modules can also be loaded in this way When adding an already existing galaxy to a schematic the user can choose between inserting a copy or a link of the mentioned galaxy Figure 111 4 shows the VPI message appearing in this case for a galaxy named RF Upconversion Add module RF Upconversion vtmg In order to use this package within the current schematic a link or a copy must be created in the schematic s Resources Folder Please select from the Following options Fig 111 4 Copy or link to an already existing galaxy VPI CHAPTER III VPI DEMOS 49 If the Copy option is selected VPI will copy the entire galaxy to the Resources folder in the schematic s Package Explorer and any ch
103. information symbols or QAM symbols within the OFDM transmission The possible ideal values for these symbols with a 4 QAM subcarrier modulation are 1 i 1 i 1 i and 1 i Figure IV 8 is an example of this configuration for a 4 QAM modulation of the OFDM subcarriers where a perfect constellation is received because of a transmission through an ideal channel 80 FIBER BASED OFDM TRANSMISSION SYSTEMS Fig IV 8 OFDM transmission through an ideal channel Note that a module has been inserted between the coder and decoder which function is to separate the real and imaginary parts of an incoming set of complex numbers If the decoded stream of bits is wanted at the OFDM decoder output in order to compare it with the original PRBS sequence for a BER study the CoSimOutputMxFit module should be used indicating the name of that variable in the decoder Matlab code in this case zz After that the UnPack M module should indicate the corresponding vector size so it can be available at the output of the module Then both the decoded and the original sequence can be compared through a BER estimator module provided by VPI or by means of the customized sequence comparer presented in section IV 1 6 IV 1 5 RF up downconverters These modules are in charge of performing the RF upconversion at the transmitter and the corresponding RF downconversion at the receiver The external appearance of both of them i
104. ion 1 5 a 2 D n egative Positive requencies omplex output Fig 1 21 RF upconversion P6 In this schematic oversampling is first used to shift the alias away from the OFDM signal and then the frequency upconversion is done to create a gap in the electrical spectrum The real and imaginary parts of the signal are separated after the IFFT stage and after its conversion to the analogue domain the complex baseband signal is obtained lower inset of the figure The real and imaginary parts corresponding to the in phase l and quadrature Q components of the signal are then passed through an electrical IQ mixer for its upconversion to an IF namely f For this purpose there must be a 90 phase shift between the locally generated carrier at IF frequency that multiplies the in phase component and the one multiplying the quadrature component Despite the increase in complexity of the analogue part entailed by the use of an RF upconversion stage the IFFT FFT size and the DAC bandwidths could be fully used to process useful data in order to lower the DAC requirements Alternatives exist to this configuration sometimes involving a tradeoff between reduced efficiency and lower complexity arrangements The following subsection is good example At the receiver the signal is downconverted by another IQ mixer with the opposite function returning the OFDM signal to baseband before extracting the CP and performing the FFT operat
105. ion 20 FIBER BASED OFDM TRANSMISSION SYSTEMS 1 3 2 Zero padding at the edges of the IFFT input sequence This is another way to create a gap between the OFDM signal and the DC component which allows avoiding the problems carried by the use of analogue mixers and oscillators As shown in Figure 1 22 zeros are added at the beginning and at the end of the IFFT input sequence The more zeros are added the larger will be the created gap though the bitrate efficiency will decrease Simplified OFDM transmitter t 0 DAC bandwidth FFT size freq Data Fig 1 22 Gap created by zero padding P4 In the same way as in the RF upconversion case this gap will serve as a guard band between the OFDM subcarriers and the optical carrier when optical modulation is applied This will be used to avoid unwanted mixing products both in emission when using IM modulation and at the receiver when using DD This form of zero padding can be used at the same time as the oversampling method when creating the input sequence for the IFFT obtaining a signal with remote aliases and a guard band close to DC though it can result in quite a reduction of the spectral efficiency Thus this trade off between low complexity of the receiver and spectral efficiency of the transmission will be decisive in the resulting configurations 1 4 General system schematic By putting together all the concepts explained until now the final appearance o
106. l xxl CP xx1 IFFT 1 N FFT ceil N FFT CP N FFT xxl IFFT y xxl CP zeros 1 TimeWindow BitRate BpS NTS casados As the effective bitrate will be smaller than the original bitrate if ZP or CP have been used we add zeros to compensate for this bitrate difference TimeWindow BitRate BpS NTS casados Qd NTB INFO BpS Nc ceil N FFT 1 CP length y test of symbol rate before and after IFFT disp CHECK OK else disp CHECK NOK end pS S Upsampler LPF in VPI y is a complex number oe ANNEX D MATLAB CODE 15 D 2 OFDM decoder SOFDM decoder z ofdm decoder y BpS Nc N_FFT CP function I Q I EVM Q EVM zz ofdm decoder simu y real y imag BitRate TimeWindow BpS Nc N FFT CP yrx complex y real y imag NTS OFDM floor length yrx ceil N FFT 14CP STotal number of OFDM symbols that it must be integer NTS QAM CP NTS OFDM ceil N FFT 14CP NTS INFO NC NTS OFDM NTB INFO NTS INFO BpS Total number of information bits NTS ZP N FFT Nc NTS OFDM NTS CP NTS OFDM ceil N FFT CP NTS_casados NTS_INFO NTS_ZP NTS CP yyl adc y Qbits yyl yrx 1 NTS_OFDM ceil N_FFT 1 CP Compensating seros are extracted 9 0 0 0 0 0 00 0 0 0 00 0 0 0 0 0 O Q O O O O O O O O O O O O O O O O O O O O O O O yyl is the parameter of analog signal Obits indicates the paramater of number of quantification bits Om
107. l zeros 1 BitRate TimeWindow BpS length yyl QAM serial Isalida I zeros 1 BitRate TimeWindow length 1 Osalida O zeros 1 BitRate TimeWindow length Q P I real yyl QAM serial Q imag yyl QAM serial I EVM I zeros 1 TimeWindow BitRate BpS length I Para EVM 18 FIBER BASED OFDM TRANSMISSION SYSTEMS Q EVM Q zeros 1 TimeWindow BitRate BpS length Q Para EVM yyl bits de2bi qamdemod yyl QAM serial 2 BpS Demodulation z yyl bits just output bits info zz yyl bits zeros 1 BpS length yrx length yy1 bits zero padding to complete the starting size
108. l smaller ones as shown in Figure l 1 Packets One big truck Many small trucks Fig 1 1 Data transported as a set of packets P18 Suppose that each small truck uses a different road where every available path has the same length and all the trucks drive at the same speed If an accident happens in one of the roads and it gets blocked part of the packets will not be received with the rest at the destination On the other hand if all the packets are transported by a big truck that drives on the same road where the accident happens the whole shipment will get stuck and will not arrive to destination For an OFDM signal transmission each small truck represents a subcarrier and the roads where data is going to be carried are an analogy of the different frequencies at which each subcarrier is going to be transmitted Moreover each packet containing goods represents the modulated portion of data to be carried by a subcarrier which is called an information symbol CHAPTER OFDM BASICS 5 Then continuing with the analogy it should be more difficult to drive a big truck than a smaller one meaning that transmission impairments will have a bigger impact on the single carrier signal since in the transmission case it will have to be transmitted at a higher data rate On the other hand for a transport company it is more expensive to contract N small trucks than a big one In the transmission case this is equivalent to the difference b
109. lculate the spectrum values at those points corresponding to the maximum of individual subcarriers Then the received subcarriers can be demodulated through an FFT operation without interference and without the need for analogue filtering to separate them which makes OFDM not only efficient but also easy to implement in practical transmission systems Hence it can be said that the modulated OFDM signal can be obtained by performing the IFFT operation to the symbols to transmit and then using a DAC to convert the digital signal into an analogue signal at a sampling rate Ts Ideally this D A conversion should convolve each temporal sample by a sinc function This ideal shaping is translated into a perfectly rectangular filter that removes the alias in the frequency domain as shown in Figure l 7 Transfer function Gif b EC Se Symbol Rat 2 Fig 1 7 Ideal filter at the DAC VPI 10 FIBER BASED OFDM TRANSMISSION SYSTEMS Where fy is the Nyquist frequency which will be the highest frequency component of the OFDM signal This ideal filter will remove the alias generated due to the sampling process leaving the fundamental signal untouched The contribution of the different sinc pulses at each of the samples of the OFDM symbol results in a perfect square pulse of the OFDM symbol and each of the subcarriers would be represented by a perfect sinc function in the frequency domain Figure 1 8 shows a very basic schematic for an
110. les such as BER Estimators Clock Recovery modules and the Channel Analyzer e SampleRateDefault it specifies the sampling frequency when working in Block Mode It is defined as the number of samples taken by second and determines the maximum frequency that can be simulated e BitRateDefault it defines the transmission bit rate by setting the BitRate parameter of emitters bit generators etc to BitRateDefault 111 1 3 2 Restrictions on Global Parameters As VPI works with the FFT algorithm when working with periodic signals a series of restrictions have to be considered First the number of samples by Time Window has to be a power of two This condition sets a limitation when selecting the Time Window and the Sample Rate as expressed in 111 1 samples Time Window Sample Rate 2 111 1 Additionally the time resolution has to be considered given by 111 2 This will determine the maximum allowed simulation frequency given by 111 3 1 B SampleRateDefault 111 2 48 FIBER BASED OFDM TRANSMISSION SYSTEMS 1 X SampleRateDefault m max lt 3d 3 111 3 Finally the frequency resolution will be given by Expression Ill 4 A proper selection of the Time Window is required in order to obtain a correct signal frequency spectrum At the same time the Time Window determines the minimum allowed simulation frequency given by 111 5 since the period of the simulated signal T always has to be smaller than the T
111. mOutputOpt Fig 111 10 Cosiminterface interconnection for optical signal processing VPI This way an optical signal generated with VPI modules could be processed by one of the mentioned programming software which allows the user to modify the signal parameters and extract them in a customized way The Cosimlnterface module will be the key to the performed simulations in the next chapter acting as an interface for VPI to access the Matlab codes programmed for this work which contain the OFDM coder and decoder functions 111 2 OFDM Generation and Detection Demo 111 2 1 General schematic The next figure shows the universe schematic view for the OFDM Generation and Detection demo provided by VPI in Optical Systems Demos Modulation Multilevel in the left panel labels Fig 111 11 OFDM Generation and Detection VPI CHAPTER III VPI DEMOS 53 The goal of this section as well as the following one is to learn from each demo towards a new definition of a simulation setup for optical OFDM systems In this case a complex baseband OFDM signal is generated in an OFDM coder 1 connected to the OFDM decoder 5 by means of VPI wires so the received signal is directly detected without any transmission channel between transceiver and receiver This means an ideal channel transmission Also two visualizer modules 4 8 can be seen which function is to extract the relevant results from the simulation Before
112. mentioned equalization coefficients are properly indicated in the PEW The situation of the constellation points results in an EVM of 0 177 obtaining an obvious improvement with respect to the previous results Fig 111 28 Equalized received constellation VPI It is worth mentioning that the expected constellation should have the form of a typical 4 QAM Instead a 45 rotation is found This point will be studied in more detail when describing the results for the customized simulations As it has been said before the equalization coefficients used in this demo can only be used for a 1000 km transmission distance This will not happen in the simulations performed in the next chapter where an ideal equalization only based on the effect of chromatic dispersion is used for any distance obtaining the corresponding equalized constellation diagram What this result also shows is that for the default fibre and laser parameters considered indeed chromatic dispersion is the main effect to equalize Also no significant effect can be seen when applying cyclic prefix to the sequence meaning that the received constellation diagram in Figure 111 28 will have the same appearance for any CP value apart from the fact that less information symbols are going to be represented as more cyclic prefix is added A possible explanation for this issue would be an incorrect procedure of the cyclic prefix extraction at the receiver as explained in section
113. ments could cause problems with frequency synchronization and inphase I and quadrature Q balance in a real system ANNEX C DIRECT DETECTION OPTICAL OFDM TRANSMITTER CONFIGURATIONS 11 As this is the configuration that has been performed in the simulations presented in Chapter IV it is interesting to know the theoretically expected form of the spectra at each point so it can be compared with the experimental results From left to right Figure C 5 shows the obtained spectra at the following points of the scheme 1 Baseband OFDM signal and its aliases after the DACs The dotted line represents the subsequent RF filtering used to remove images 2 OFDM signal after the RF upconversion stage 3 Filtering the optical lower sideband after the e o conversion p LSA USB p P x 1 E O a ININL 10 5 5 10 Guz 10 5 510 Gu 5 0 5 10 c Fig C 5 Spectra at each point of the scheme P6 C 5 Colourless transmitter Another option would be to use the scheme depicted in figure C 6 where a complex IQ modulator is the input of the and Q components of the OFDM signal Only one optical single sideband is generated by using a signal and its Hilbert transform to drive the optical I Q modulator 0 Xo lo EM BE N 2 1 219 o Xu 613 0 pI S Fiber Link a Fig C 6 Colourless transmitter configuration P6 A Hilbert transform can be generated simply in an OFDM transmitter by setting half of the IFFT inputs to zero
114. mit an optical carrier with the required gap to the OFDM band in addition to the modulated subcarriers This leads to a spectral efficiency of nearly twice the one in DD OFDM for any type of subcarrier modulation 11 6 Equalization In order to obtain an OFDM signal without errors at the receiver the use of cyclic prefix is essential This will eliminate ISI when a temporal dispersion affects the channel However the effect of chromatic dispersion causes the information symbols to still be affected by amplitude and phase changes when arriving to the receiver as shown in Figure 11 26 H H Phaseo Phased Phase 120 OEI Ta Phase 120 FFT size Fig 11 26 Phase distortions on the received constellation P4 Consequently an N level equalizing stage has to be introduced right after the FFT operation at the receiver in order to correct the phase and amplitude levels where N is the number of received subcarriers The design parameters for this stage should be obtained through a channel estimation which is usually performed with training sequences These sequences are added by using pilot subcarriers in each OFDM symbol so the channel transfer function can be approximated As the design of training sequences is beyond the scope of this work the required phase compensation for each OFDM symbol will be calculated based on the dispersion model suffered by each subcarrier see section II X p 3Bzw L 11 19 Where L is t
115. mpling instants and hence no ISI However this ideal filter is not realizable A practical extension is a raised cosine characteristic fitted to the ideal low pass filter which is a commonly used pulse shape in OFDM Its transfer function is given by expression l 5 a gt G f 1 S For 2 f gt ep os 1 sim 5 w1 7 05 For 0 lt f lt Here T is the symbol period and a is the roll off factor defined as the ratio of excess bandwidth above fy When a 1 the bandwidth is doubled over the bandwidth when a 0 The impulse response of the raised cosine filter used in CHAPTER OFDM BASICS 13 VPI for a 0 and a 0 5 is shown in figure 1 12 Note that the length is reduced at the expense of increased bandwidth 0 05 1 1 5 2 25 3 35 4 time us Fig 1 12 Impulse response for the raised cosine for a 0 and a 0 5 VPI 1 2 2 2 Oversampling by means of zero padding Before giving the OFDM signal its corresponding shape the values at the output of the IFFT representing the analogue signal to transmit have to be sampled by the DAC By sampling them at a rate of 1 T the aliases produced by the sampling process would be right next to the main OFDM signal making it impossible for any practical filter to separate them However padding the correct positions of the IFFT input sequence with zeros can help to shift the aliases away from the OFDM signal as shown in Figure 1 13 This technique will be r
116. mpling rate required by VPI obtaining at the output the electrical samples that represent the analogue OFDM signal Note that the OFDM coder has two outputs which are not only connected to the decoder but also processed by the PulseRaisedCosQAM modules 3 serving as pulse shaping filters As it was explained in Chapter I the most suitable impulse response for an OFDM signal is the square root raised cosine approach so the squareRootRaisedCosine option should be selected as the Nyquist response parameter for these blocks Once this type of filtering is applied both parts of the signal are ready to be represented so the SignalAnalyzer module 4 is used as an interface to the VPI Photonics Analyzer tool where the signal will be displayed The results of this representation will be described in Section III 2 4 At the receiver side the decoder module performs the opposite operations carried on in the coder module providing the electrical samples representing the real and imaginary parts of the decoded complex information symbols These parts are going to be fed to another kind of analyzer 8 which will plot the received constellation based on the received information symbols But before that as both inputs and outputs of the decoder belong to the electrical type the electrical samples of each branch have to be transformed into floating type values that will represent samples of the electrical OFDM signal This function is carried on by t
117. mporal window of 819 2 nanoseconds These parameters must be taken into account when processing the input bit sequence in the Matlab code so they will be declared as cosimulation input parameters as shown in the next section IV 1 1 2 Coding parameters This schematic category contains the parameters affecting the coder and decoder modules which are listed below e BpS Number of bits used to represent each QAM symbol The most typical values are 2 and 4 giving rise to a 4 QAM and a 16 QAM modulation respectively e Nc Number of information subcarriers entering the IFFT operation also exiting the FFT The symbols representing each subcarrier will be modulated in an X QAM where X depends on the BpS parameter e N FFT Total number of inputs of the IFFT stage also FFT This parameter determines the quantity of oversampling by means of zero padding added to the transmission For instance a 32 input IFFT with Nc set to 16 means that half of the IFFT the 16 central positions is padded with zeros e CP Cyclic prefix relative to the OFDM symbol length ranging from 0 to 1 Typical values of CP in a real OFDM transmission range from 10 to 20 so this parameter should be given a value between 0 1 and 0 2 1V 1 1 3 RF galaxies parameters As the OFDM signal will be up downconverted in the optical OFDM simulations the RF galaxies category will be created to hold the parameters concerning the electrical up downconversion Tho
118. nctions can be found in Annex D IV 1 Custom modules and Matlab code implementation IV 1 1 Parameter settings Before getting into the operation of the customized modules it is important to understand the parameters that will be used by them Some of these parameters have already been defined in the last chapter so this section will focus on the reasons why determined values are assigned to the parameters IV 1 1 1 Fulfilling VPI restrictions Expression 111 1 in the previous chapter indicates that the product of the simulation time window and the used sampling rate must be a power of 2 Another simple rule to avoid problems when running a simulation in VPI is that the product of the time window and the bitrate is also set to a power of 2 A good way to meet these rules is to first decide on a bitrate and then set the SampleRateDefault parameter so that the ratio SampleRateDefault BitRateDefault is a power of 2 Also the TimeWindow parameter should be set to equal the number of bits in a simulated block dived by the bitrate The number of bits has to be a power of 2 Following these tips the parameter values for the customized simulations will be e BitRateDefault 10e9 bps e SampleRateDefault 4 BithateDefault 40e9 Hz e TimeWindow 8 1024 BitRateDefault 819 2 nsec CHAPTER IV CUSTOMIZED SIMULATIONS 71 Thus the simulated sequence will consist of a block of 8 1024 8192 bits transmitted at 10 Gbps resulting in a te
119. nd the four parameters belonging to the Coding parameters category Apart from that the bit sequence coming from the PRBS generator should also be declared a detailed description of this process can be found in the next subsection Thus for an output data vector y if prbs represents the incoming bit sequence the main function for the OFDM coder Matlab code will be function y ofdm coder prbs TimeWindow BitRate BpS Nc N FFT CP IV 1 In a similar way to the VPI coder module the first thing that the ofdm_coder function does is to calculate the required number of bits to represent the OFDM signal according to the indicated parameters It starts by calculating the number of OFDM symbols that can be contained in the sequence taking into account the CP and zero padding overheads This is calculated as NTS OFDM floor length x1 BpS ceil N_FFT 14CP IV 2 Where x7 is a previously defined vector containing the whole input sequence as expressed below xl prbs 1 TimeWindow BitRate IV 3 Once the total number of OFDM symbols is calculated since each OFDM symbol contains Nc information symbols the number of QAM information symbols NTS INFO as well as the total number of bits representing the OFDM signal NTB INFO are obtained NTS INFO NTS OFDM Nc NTB INFO NTS INFO BpS IV 4 CHAPTER IV CUSTOMIZED SIMULATIONS 73 Because the number of OFDM symbols may not exhaust the whole input sequence a determin
120. ng at the input IFFT sequence as explained in Chapter The amplified spontaneous emission ASE inherent to the laser is unpolarized and is band limited by an optical filter extending from By below the carrier f to By above it being present in both the lower and the upper sideband zones The useful components in the electrical spectra that is the OFDM subcarriers are the different terms which result from the mixing of the OFDM sideband and the optical carrier Figure 11 19 shows the optical spectra of the contributions to this mixing and the resulting electrical spectra after downconversion D Wanted Electrical Subcarriers lo mE gt RZ Carrier x Subcarriers Fig 11 20 Useful components in the electrical spectra P13 When a frequency guard band is used Byap gt Bsc all of the results of the mixing products between OFDM subcarriers will fall out of band not degrading performance This way the unwanted out of band noise will be avoided wanted Mixing Products MIL gt ha Subcarriers Un Bsc Fig 11 20 Unwanted out of band noise P13 However other undesired mixing products resulting from the square law detection will fall inside the OFDM band Those are called the unwanted inband terms and correspond to the products resulting from optical carrier x noise OFDM signal x noise and noise x noise as depicted in Figure 11 21 Noise from both sidebands will be detected unless a narrow optical filter is
121. nonononnnnnnnnnnnnno nono nnnnnncnnanonannos 55 111 2 3Simulation results vii AAA a 56 111 3 OFDM for Long Haul Transmission DeMO cccononococnnononononononononononnnnnnannnnnnoncnnanannonnnnnnnnos 60 111 3 1 General schematis isiro aai a iaiiaeeeai AEE iE i 60 111 3 2 Inside the OFDM transmitter module eene 61 111 3 3 Inside the OFDM receiver module sees 63 111 3 4 Optical channel path ccccccccccecssssssnsecececscsesesseaeeececssesseseaeseeeeesesseasaeeeesesseeseaaeas 65 IIl 3 5 Simulation tesults 5 tt iot torte A da A erint 67 CHAPTER IV CUSTOMIZED SIMULATIONS ssessseseseseeeeee ener entrent enne sense nennen nennen 70 IV 1 Custom modules and Matlab code implementation eese 70 IV 1 4 Parameter settings tte teet tee ici e tease ele 70 IV 152 Code str ctUre pci reete Ren segete e RETE aaia ERREUR E Sev eius 72 IV 1 3 OFDM Coder eee t Le Re ee RES nee RUE nae ene dn na e SEI Ree asii dee 76 IV 1 4 OFDM DeCOGet tr eer RR e P eet t d et a eats 78 IV 1 5 RF up downconverters cccccessceeseceesceceseeecssececsseceseeecsseeecsaececseecsseeecsuececsseceeseeenas 80 IV 1 6 Sequence comparer ciriciri iiia aii anne iiaa aaaea kiaia a aanak 82 IV 2 Electrical OFDM Generation and Detection esseseeeeeeeeeeneneennnen en 83 IV 2 1 Universe Schematic siiki arrie unaia enne nnne a aa nennen 83 IV 2 2 RAW transmlissi
122. ntributions between harmonics to cancel as shown in Figure 11 12 Fibra y oo fi ati MO EB Wo Wo RF Wo Wo RF Fig 11 12 Conventional IM DD transmission system with an ideal fibre However a monomode fibre will introduce variations over the transmitted optical signal due to chromatic dispersion which will cause a different phase delay to each spectral component of the signal being transmitted through the fibre Thus these effects in direct detection configuration will not allow a complete cancellation of the harmonics and a nonlinear distortion will appear at the receiver end as shown in Figure 11 13 32 FIBER BASED OFDM TRANSMISSION SYSTEMS y 4 Detector 4 OX um Y Wo Wo RF RF 2RF IRF Fig 11 13 Transmission system for a dispersive fibre In an intuitive mode the nonlinear effect can be thought of as set of spectral components which spreads out at the transmitter end and it is not able to fold back in the receiver end to just one spectral component because the spectral components are different and do not match up between them any more 11 5 Optical OFDM transmission systems One way to categorize OFDM generators would be to classify them depending on the type of subcarrier generation This would give rise to two different transmitter categories analogue and digital generation While the first one requires a complex integrated modulation the latter allows a simple optics design with flexible and
123. o o eo e e d e o o eo e e t e o eo e e o o o t wt eo ACRONYMS ADC Analogue to digital converter ASE Amplified spontaneous emission BER Bit error rate CO D Coherent detection CP Cyclic prefix DAC Digital to analogue converter DD Direct detection DFT Discrete Fourier transform DMT Discrete multitone DTFT Discrete time Fourier transform EVM Error vector magnitude FDM Frequency division multiplexing FFT Fast Fourier transform GDD Group Delay Dispersion GUI Graphical user interface ICI Intercarrier interference IDFT Inverse discrete Fourier transform IF Intermediate frequency IFFT Inverse fast Fourier transform IM Intensity modulation ISI Inter symbol interference LO Local oscillator MZM Mach Zehnder modulator OFDM Orthogonal frequency division multiplexing OSSB Offset single sideband PEW Parameter editor window PRBS Pseudo random bit sequence QP Quadrature point SER Symbol error rate SSB Single sideband QAM Quadrature amplitude modulation VPI Virtual Photonics Inc e p Escola Polit cnica Superior de Castelldefels UNIVERSITAT POLITECNICA DE CATALUNYA ANNEXES TITLE Fiber based Orthogonal Frequency Division Multiplexing Transmission Systems MASTER DEGREE Master in Science in Telecommunication Engineering 8 Management AUTHOR Eduardo Heras Miguel DI
124. ong Haul Transmission demo The other difference is the use of the upsampling modules for both parts of the signal This operation inserts a given number of samples according to the factor parameter in order to compensate for the difference between the number of samples of the original sequence and the number of samples of the coded OFDM sequence which is going to be converted into electrical values in the next stage In this case the and Q sequences are represented by a vector of BitRate TimeWindow BpS values while the original sequence is formed by BitRate TimeWindow samples so the upconverting factor should be set to no less than the value of BpS This will produce new samples usually zero valued that will be allocated between the original samples as indicated in the Parameter editor The downconverter schematic is depicted in Fig IV 11 where each downsampling module is set with the same factor value as the upsamplers used in the RF upconversion The downsamplers are used in order to recover the exact number of samples representing the received symbols including the ones used for zero padding cyclic prefix and if any the ones used for symbol rate compensation 82 FIBER BASED OFDM TRANSMISSION SYSTEMS M MullipiyE iseddos KEI le ncSineBl Fork Multiply Fig IV 11 RF downconverter schematic VPI The parameters that have to be created for both the up and downconverter galaxies are those belonging to th
125. oramtion symbols NTB INFO NTS INFO BpS Total number of information bits NTS ZP N FFT Nc NTS OFDM Total number of symbols due to zero padding NTS CP NTS OFDM ceil N FFT CP Total number of symbols due to CP NTS casados NTS INFO NTS ZP NTS CP Total number of symbols to transmit Ideally it should be TimeWindow BitRate BpS but it may not cover the whole sequenc xx1 x1 1 NTB_INFO Vector containing the information bits to transmit o The QAM symbol sequence is built with the information bits to transmit a vector xxl QAM of size NTS INFO 14 FIBER BASED OFDM TRANSMISSION SYSTEMS xxl QAM qammod bi2de reshape xx1 BpS NTS_INFO 2 BpS The OFDM INFO symbol sequence is built with the previous QAM sequence xxl OFDM INFO reshape xxl QAM Nc NTS OFDM Zero padding is inserted to obtain a matrix of size N FFT x NTS OFDM if mod N FFT 2 mod Nc 2 xxl OFDM ZP zeros N FFT Nc 2 NTS OFDM xxl OFDM INFO zeros N FFT Nc 2 NTS OFDM Gap generation by means of zero padding xx1 OFDM ZP xxl_ OFDM INFO 1 Nc 2 zeros N FFT Nc NTS OFDM xxl OFDM INFO Nc 2 1 Nc Oversampling else disp Both N FFT and Nc must be even or odd integers end oo IFFT is applied xxl IFFT ifft xxl OFDM ZP N FFT oe sborder ofdm symbols change to zero oo oe mk diag 0 zeros 1 NTS OFDM 2 0 oe oe xxl IFFT xxl IFFT mk oo Cyclic prefix is added to each OFDM symbo
126. order to apply oversampling by means of zero padding The input bit sequence will be formed by a block of 8 1024 8192 bits BER_seg_seg vtmu Parameter Editor x Name BER seg seg vtmu E usss ID BER seg seg vtmu E ERE v x BE mg Name Value Player Show RF galaxies fl CarrierFrequency F Phase f Rollo 1 Coding Parameters i 8 amp 5 f cP il Ne i N_FFT Global F TimeWfindow 8 1024 Bit Rate Default E InBandNoiseBins OFF E Boundary Conditions Periodic E Logicallnformation ON ff Sample Mode Bandwidth 1280e8 Sample Mode Center Freque 193 1612 F Sample Rate Default 4 BitRate Default F BitRate Default 10e9 3 DesignRules Scheduler Player ogoooggso OOOO OOO Fig IV 23 Parameter editor of the universe schematic VPI The quantity of cyclic prefix present in the sequence will also be modified in order to see the effects on the received constellation 92 FIBER BASED OFDM TRANSMISSION SYSTEMS IV 3 2 Custom modules modifications If the EVM and BER values are to be calculated a logical channel has to be added to the scenario This is why RF upconversion galaxy in Figure IV 22 has two input ports one for the coded OFDM sequence and another for the original sequence coming from the PRBS generator As shown in Figure IV 24 a LogicAdd Channel module has been inserted in the right bottom of the RF upconversion galaxy The ChannelLabel paramete
127. os The last of them shows the Matlab code used in the simulations 4 FIBER BASED OFDM TRANSMISSION SYSTEMS CHAPTER OFDM BASICS 1 1 General idea Frequency Division Multiplexing FDM is a technique where the main signal to be transmitted is divided into a set of independent signals which are called subcarriers in the frequency domain Thus the original data stream is divided into many parallel streams or channels one for each subcarrier Each subcarrier is then modulated with a conventional modulation scheme and then they are combined together to create the FDM signal In an FDM transmission the receiver needs to be able to independently recover each of the subcarriers and therefore these signals need to fulfil certain conditions For instance they can have nonoverlapping spectra so that a bank of filters tuned to each of the different subcarriers can recover each of them independently However practical filters require guard bands between the subcarrier bands and therefore the resulting spectral efficiency is low If the subcarrier signals fulfil the orthogonality condition which will be introduced by expression 1 2 their spectrum can overlap improving the spectral efficiency This technique is known as orthogonal FDM or OFDM To see the main advantages offered by OFDM it is useful to think about a set of packets which are transported in a truck The whole set of packets can either be carried by one big truck or by severa
128. owever this is not realizable in practice so a raised cosine characteristic is fitted to the ideal low pass filter as a practical solution Thus a roll off factor will be defined as the ratio of excess bandwidth above the maximum frequency of the signal to be represented Figure IV 17 represents the real and imaginary components of a baseband OFDM signal transmitted at 10 Gbps where a square root raised cosine Nyquist response with different roll off factors has been applied for its representation The upper figure represents the and Q components after passing through an ideal filter a 0 and in the lower case a roll off factor of 0 2 has been applied Note that the excess bandwidth is approximately 360 MHz for this case Fig IV 17 Filtered OFDM signal with roll off factors of 0 and 0 2 VPI The roll off factor in the lower case will be applied in every of the following simulations serving as an approach to a real OFDM system CHAPTER IV CUSTOMIZED SIMULATIONS 87 IV 2 4 Zero Padding In Chapter it was seen that there are two ways of using zero padding at the input sequence of the IFFT zeros can either be inserted at the middle of the sequence oversampling or at the edges creating a frequency gap with respect to the optical carrier The results of applying zero padding to half of the IFFT inputs at the edges in the generation of an OFDM signal can be seen in the lower graph of the next figure where 4 QAM
129. performed in the Electrical OFDM Generation and Detection scenario giving rise to the constellations depicted in the next figure Received constellation DEAR E Received constellation DR received constellation received constellation Fig IV 21 Received constellations for a 4 QAM and a 16 QAM modulation VPI Note that contrary to VPI demos no points are plotted in the 0 0 position of the constellation This is because the customized OFDM decoder module extracts the precise number of information symbols to plot the constellation diagram The variables used for this purpose are the uncompensated and Q received components of the signal as explained in section IV 1 2 90 FIBER BASED OFDM TRANSMISSION SYSTEMS IV 3 Optical OFDM IV 3 1 Universe schematic An optical OFDM testing scenario has been created based on the OFDM for Long Haul Transmission demo described in Chapter Ill The universe schematic is shown in Figure IV 22 where the OFDM coder and decoder galaxies with their corresponding RF up downconversion stages appear again as the OFDM signal transmitter and receiver respectively versal iber Fad vung ip 0 080 m M pn fem Fig IV 22 Optical OFDM system scenario VPI This scheme corresponds to the RF upconversion based on Intensity Modulation configuration described in section 11 5 1 1 which is the same as in VPI s demo though this time oversampling is applied to the OFDM coder
130. r before driving the single input optical modulator though another DAC is required after the IFFT output serialization stage Because of the frequency upconversion there is no need to use Hermitian symmetry to cancel the imaginary component of the signal so one DAC is needed to process the real part of the OFDM signal and another for the imaginary part that is inphase and quadrature respectively Figure C 4 shows the scheme for this configuration an Electrical Spectrum x m Parallel to Serial Fiber Link Negative Positive Frequencies Complex output Alias Optical Spectrum Bit Rate Sample Rate 1 4 QAM Fig C 4 RF upconversion configuration P6 Thus the width of the guard band is not determined by nulling the OFDM inputs but by the RF frequency and so all subcarriers except the dc subcarrier can be used to carry data if the DAC filter is good enough However in the scheme depicted in figure C 4 trigonometric interpolation is used in order to shift the alias away The analogue upconversion allows flexible placement of the signal spectrum relative to the optical carrier and the RF frequency is independent of the DAC sample rate As in the previous designs an optical filter is used to suppress one sideband For a given data rate this design requires a DAC sample rate of approximately one quarter that of the first design but the addition of analogue mixers with such high frequency and bandwidth require
131. r Down lad Reset to Default Fig 111 7 Create Schematic Parameter option VPI In order to make the parameters management easier the highest level parameter should be the only one indicating the value used for the simulation while the lower level ones should just indicate its name in the Value field However this field can be given another value if a module belonging to a lower level has to work with other characteristics than those of the higher level ones CHAPTER III VPI DEMOS 51 Ill 1 4 3 Cosimulation Cosimulation is a technique in which some part of the simulation is handled by an application other than the VP Transmission Maker simulator It allows three different programming languages to interact with VPI Matlab Phyton and C C This technique has played a very prominent role in this Master Thesis as it has been used to build a complete optical OFDM simulation tool by the combination of the Matlab programming for the OFDM coding and decoding and VPI modules for the simulation of the RF and optical paths The main module to carry out the cosimulation is called the Cosimlnterface module and it is represented in Figure 111 8 Fig 111 8 Cosiminterface module VPI To execute a programming code the code file must be attached to the nput folder of the schematic containing the Cosiminterface module and its main function which name must be the same as the code file name has to be indicated in the RunCommand par
132. r of this module must be the same for the modules in charge of performing the EVM and BER calculations Amplkude Sau Frequency CarrkerFraquency Hz Fig IV 24 RF upconversion module with a logical channel VPI Another modification has been introduced in the OFDM decoder module in order to obtain the 5 output configuration mentioned in section IV 1 2 Figure IV 25 shows the resulting schematic for the OFDM decoder galaxy where the and Q components of the downconverted OFDM signal at the input of the module give rise to 5 different sequences at its outputs e The symbol rate compensated and Q components of the decoded OFDM signal upper ports are used to calculate the EVM e The uncompensated parts middle ports are fed to a 2 dimension numerical analyzer to plot the received constellation diagram see Figure IV 26 e The bitrate compensated decoded sequence lower port will be used for the BER calculation CHAPTER IV CUSTOMIZED SIMULATIONS 93 gt BS gt Bi interfaceType Matlab oSiminputhtxF it rM nputimtxFit p A MxF it LinPk M Fig IV 25 OFDM decoder galaxy schematic 5 output configuration VPI IV 3 3 Error Vector Magnitude and Bit Error Rate measuring Figure IV 26 is a zoomed version of the universe schematic where modules taking part in the EVM and BER measuring are viewed in detail Fig IV 26 EVM and BER measuring VPI As in VPI s demo
133. r schematic with four ports one for the input and output of each part of the signal CHAPTER IV CUSTOMIZED SIMULATIONS 79 Le ap CoSiminputMxr it A p A gt E gt InterfaceType Matlab Cosiminpuimxr It CosimOutputhtxF It Fig IV 7 Internal view of the OFDM decoder For each signal component the incoming values are inserted into a matrix with the same size as the one created at the coder output 1 row x BitRate TimeWindow BpS columns Then the real and imaginary parts are named y real and y imag by the CoSimlnputMxFlt modules and they are fed to the CoSim module where both variables are going to be an input to the main code function along with the galaxy parameters As in the coder case once the Matlab file is inserted into the nput folder of the scenario the main function of the decoder code must be indicated in the RunCommand parameter of the CoSim module so the desired output values are extracted from the code when its execution is finished It has been decided that the output of the CoSim module should be the received inphase and quadrature components of the signal so after the proper resizing they can be represented in a numerical analyzer as the received constellation points Thus the extracted variables will be inserted into a 1xN matrix where N has the following size N floor TimeWindow BitRate BpS ceil N_FFT 1 CP IV 8 This size corresponds to the number of
134. ransmitter parameters VPI e ChannelLabel indicates the name of the logical channel It must be the same for all of the modules using the original sequence that was added to the LogicAddChannel module e CarrierFrequency Indicates the RF frequency at which the baseband OFDM signal will be upconverted This value is set from the schematic parameter so it will also affect the RF downconversion stage of the OFDM receiver galaxy CHAPTER III VPI DEMOS 63 The main category in this PEW is the Physical category which contains the QAM OFDM Signal subcategory At the same time QAM OFDM Signal is divided into other subcategories such as the PRBS generator DAC RF and Filter As these smaller categories are declared as galaxy parameters they can be edited from the main schematic by double clicking on the module without the need to look inside and change them on the corresponding module The same can be applied to the OFDM receiver galaxy 111 3 3 Inside the OFDM receiver module Once again the OFDM receiver module will perform the same operations as the transmitter in a reversed order First of all the signal is downconverted by multiplying it by the same RF frequency as before and applying a 90 phase shift to the quadrature component as shown in Figure 111 21 RF up conversion Pulse shaping OFDM decoding Fig 111 21 Schematic of the OFDM receiver module VPI After that both components pass through
135. reasing until one cycle for the last subcarrier k 2 N 1 Such property is represented in figure A 2 l fih g j crete abria IF 0 b E Duende Time nisem Duet Tine hoem d e f NIE 2 Doce Tin hd Fig A 2 Discrete time domain signal for individual subcarriers for d k 2 N 2 Nyquist term e k N 2 and f k N 1 P1 ANNEX A INSIGHT INTO THE OPERATION OF AN OFDM SYSTEM 3 In mathematical analysis a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign fx f A 2 For all x in the domain of f This definition extends also to functions of two or more variables For instance in the case that fis a function of two variables it will be Hermitian as long as f Cx 7x2 f x1 X2 A 3 For all pairs x1 x2 in the domain of f Taking this and the basic properties of the Fourier transform it follows that e The function f is real valued if and only if the Fourier transform of f is Hermitian e The function f is Hermitian if and only if the Fourier transform of f is real valued Now knowing that in a complex valued IFFT the first half of the rows corresponds to the positive frequencies while the last half corresponds to negative frequencies it can be deduced that Hermitian symmetry will be achieved by inserting the complex conjugate of the first half of the IFFT
136. rent transmitter configurations can be designed for a DD OOFDM system depending on the subcarrier modulation input sequence of the IFFT complexity of the used components etc In P6 various experimental demonstrations have been performed giving rise to four basic transmitter configurations that mainly depend on the input sequence of the IFFT Thus each transmitter will have different degrees of optical complexity depending on the required components though a single photodiode DD photoreceiver is used in all the scenarios so no laser is required A colourless transmitter is also introduced where there is no need of optical filter to suppress one optical sideband The CP insertion is not considered in the figures but it should be added to all of them at the output of the IFFT before the data serialization In all of the upcoming scenarios an optical single sideband OSSB OFDM signal and a component at the optical carrier frequency are transmitted Usually a frequency guard band separates the OFDM signal from the optical carrier and the signal is received by detecting the carrier signal mixing products described in Chapter Il To provide the optimum noise performance the transmitter optical modulator should be biased for equal carrier and sideband powers as this provides the peak electrical SNR and lowest BER for a given OSNR C 1 Real drive signal This is a simple configuration where half of the input sequence of the IFFT is forme
137. rmation symbols at least one symbol is also represented in the centre of the diagram circle in 0 0 This is because VPI organizes the sequence to be transmitted by first calculating the required information symbols according to the bits per symbol and cyclic prefix parameters discarding a number of bits from the original sequence which will be occupied by the bits representing the required cyclic prefix quantity If the resulting number of OFDM symbols does not cover the whole sequence VPI fills it with zeros to compensate for any differences between the effective and transmitted data rates and symbols in 0 0 are represented as long as those padded zeros are not previously extracted This is another point to be improved by the upcoming custom simulations The transmitted signal spectrum will be represented by means of a signal analyzer for both the real and imaginary components of the OFDM signal As negative frequencies do not exist for a real system a complex baseband OFDM signal like the one which is being generated will be represented as in Figure 58 FIBER BASED OFDM TRANSMISSION SYSTEMS 111 15 where the real and imaginary parts in green and blue respectively are superimposed B Imaginary SB A At Pal Power dBm A i Fig 111 15 Superimposed OFDM signal spectrum VPI sh Frequency GHz Because of this superimposition of the signal just half of the OFDM bandwidth will be represented The OF
138. rmstrong Brendon J C Schmidt Dhruv Kalra Himal A Suraweera and Arthur J Lowery Performance of Asymmetrically Clipped Optical OFDM in AWGN for an Intensity Modulated Direct Detection System Monash University 2007 P18 Charan Langton Orthogonal Frequency Division Multiplex OFDM tutorial Intuitive Guide to Principles of Communications 2004 P19 C Liu and F Li On spectrum modeling of OFDM signals for digital broadcasting in Proc ICSP 2004 pp 1886 1889 P20 S Talbot and B Farhang Boroujeny Spectral Method of Blind Carrier Tracking for OFDM IEEE transactions on signal processing vol 56 7 2008 P21 M Ivrlac and J Nossek nfluence of a Cyclic Prefix on the Spectral Power Density of Cyclo Stationary Random Sequences ed Springer Multi Carrier Spread Spectrum 2007 Websites W1 Wikipedia W2 EE Times http www eetimes com electronics news 4139996 IEEE 802 1 1a Speeding Up Wireless Connectivity in the Home W3 Blinkdagger Matlab blog http blinkdagger com matlab matlab fft and zero padding W4 Wikitel http es wikitel info wiki OFDM W5 Intuitive Guide to Principles of Communications http www complextoreal com W6 VPI Photonics official website http www vpiphotonics com d e e e Y o Y t eo eo e o e e Y e t eo e o eo e e e e o eo e e e e
139. romatic dispersion is a deterministic distortion given by the design of the optical fibre It leads to a frequency dependence of the rate at which the phase of the wave propagates in space optical phase velocity and its effect on the transmitted optical signal basically scales quadratically with the data rate P2 This frequency dependence of the phase can be easily identified by describing a pulse propagating through a monomode optical fibre in the frequency domain Xout w Xin w e JPW 11 1 Where X w represents the Fourier transform of the transmitted signal Xout w is the Fourier transform of the received signal and f w corresponds to the phase constant of the fundamental propagating mode Because of the frequency dependence of the main limiting effect considered in expression ll 1 will be chromatic dispersion Other phenomena such as losses or nonlinearities will be not considered though their effects in fibre propagation can be added afterwards The consideration of dispersion as the main limiting effect in an optical transmission has been shown to be a good approach in a broad variety of practical applications but more importantly allows the simplification of its study In an ideal case the phase constant e 8 2 in 11 1 has a linear dependency with frequency meaning that all the spectral components undergo the same phase delay which is the same as saying that they travel at the same velocity CHAPTER II OPT
140. rows into the second half as depicted in Figure A 3 Fig A 3 Use of Hermitian symmetry at the IFFT input sequence P6 This way the imaginary component is cancelled and the output values of the IFFT will represent a real valued OFDM signal A IBER BASED OFDM TRANSMISSION SYSTEMS ANNEX B CYCLIC PREFIX EFFECT ON THE OFDM SIGNAL SPECTRUM One answer to the question What s the cyclic prefix used for could be to deceive the channel Evidently a linear convolution operation is carried out in the channel however a circular convolution would be of more interest because this would provide a purely multiplicative effect in the transformed domain eliminating inter carrier interference ICI as explained in B7 Apart from that the cyclic prefix incorporation avoids block to block or OFDM symbol interferences which means null inter symbol interference ISI As long as the cyclic prefix duration is equal or longer than the channel s impulse response the effect of one block over the previous one will be limited to its cyclic prefix corruption without damaging the information part The introduction of any temporal guard interval would achieve this null ISI characteristic but only the cyclic prefix can guarantee null ICI However this elegant way of avoiding ISI comes of course at the price of reduced bandwidth efficiency since the cyclic prefix adds redundancy to the signal Besides this loss in efficiency the cyclic prefi
141. rtions caused by the transmission path The Parameter editor of the schematic is shown in Figure IV 15 where the names of each parameter and category correspond to those of the coder and decoder so they can be changed from there instead of having to do it once for each module Electric ytmu Parameter Editor Es Name Electric vtmu t sess ID Electric vtmu GDr eee Name E Coding Parameters i Bps f cP Fal Time Window 8 1024 Bit Rate Default amp InBandNoiseBins OFF Boundary Conditions Periodic S Logicallnformation ON Fal Sample Mode Bandwidth 1280e8 l Sample Mode Center Freque 193 1612 Fal Sample Rate Default 4 BitRate Default F BitRate Default 10e9 DesignRules Scheduler Player OOOOOOOO OK Cancel Apply Fig IV 15 Parameter editor of the universe schematic VPI CHAPTER IV CUSTOMIZED SIMULATIONS 85 In order to see the theoretical concepts described in Chapters and II applied in a simulation scenario the next subsections show different tests which have been performed in this scenario so the effects of changing any of the parameters in an OFDM transmission can be observed The signal analyzer connected after the pulse shaping modules will be used to display the spectrum of the electrical OFDM signal in every performed test After that the ideally received constellations for a 4 QAM and a 16 QAM types of OFDM coding are shown where the zero valued
142. s defined in the universe PEW any change in its value from this level will be applied to both modules belonging to the galaxies CHAPTER III VPI DEMOS 47 On the other hand if the value of this parameter is changed directly from the pulse shaping star inside the coder it will only affect this module leaving the one inside the decoder untouched This feature will be used in the customized simulations presented in the next chapter when a simultaneous change is desired for any parameter of both the OFDM coder and decoder modules Thus two types of parameters can be defined global parameters which affect to all the modules within a simulation lower levels included and the specific ones belonging to a single module 111 1 3 1 VPI global parameters Besides the parameters that can be defined by the user to be used by all the modules in a simulation VPI provides a set of already defined global parameters which are very important for the correct and efficient operation of the simulator The most relevant for this work s purpose are e TimeWindow this parameter sets the period in which a block of data is represented This time will inevitably fix the spectral resolution of the simulated signals setting i e the resolution of spectral displays e Logicallnformation This is a tool used by VPI to send information between modules within the same simulation It removes the need for sneak wires between the transmitters and some modu
143. s going to be created in a category called RF galaxies New categories can be created for a better organization of the parameters appearing as expandable folders as in Figure III 5 The Create category button in the same figure a yellow folder icon to the left of the Create parameter button allows to create a new category To insert a parameter into a category it just has to be dragged into the corresponding folder Any parameter can be shared by modules belonging to different simulation levels as long as it has the same name for every module containing it When creating a new simulation scenario where modules of different levels will share some parameters the usual and easier procedure is to create parameters in the lower level and then expand them to the upper levels This expansion of a parameter is done by right clicking on the created parameter and selecting the Create Schematic Parameter option as shown in Figure Ill 7 This way the parameter and its corresponding category will be automatically created in the upper level with the same settings FuncSineEl_vims1 Parameter Editor Name FuncSineElwvtms E ID FuncSineEl vtmsi C Show 1D y e E ES s 2 Ope ptg Name Value Unit Sh 2 Physical AAA F Amplitude 5 Frequency f Phase Bias Enhanced 5 AgddLogicallnfo 5 OutputDataType E Boundary Conditions Periodic Active On Create Schematic Parameter Move Paramete
144. s regarding orthogonal frequency division multiplex OFDM has been carried out The goal of this study has been the adaptation of these concepts into the special characteristics offered by optical systems Thus the following step has been to study the most relevant features of optical communications such as the type of modulation and demodulation systems and the optical filter and fibre parameters Some of these concepts are not usually referred in the current bibliography of optical OFDM though they are the basis for creative contributions to the subject Hence this has been the main reason why the first two chapters of this document have been dedicated to highlight the main aspects concerning the use of OFDM in optical transmissions hoping that they serve as a reference for future studies of the subject The different combinations of electrical generation of the OFDM signal and the optical modulation and reception categories give rise to several transmission systems able to implement an optical OFDM communication The most relevant ones for this work s purpose have been described in detail before introducing the simulation environment The software Virtual Photonics Inc Transmission Maker VPI has been used as the tool to contrast all the acquired knowledge on optical OFDM in a simulation scenario Two built in demonstration simulations offered by VPI have been tested in order to understand the role of each parameter within the system
145. s shown in Figure IV 9 where the RF upconversion module is connected to the OFDM coder and the RF downconverter outputs are fed to the decoder module as the received and Q components of the baseband OFDM signal TEE Fig IV 9 RF up downconverters connected to the OFDM coder and decoder Their internal structure is very similar to those of the OFDM transmitter and receiver modules used in the Long Haul Transmission demo CHAPTER IV CUSTOMIZED SIMULATIONS 81 However it is important to notice a couple of differences between the RF upconversion stage in VPI s OFDM transmitter and the customized RF upconversion module which internal schematic is shown below cos gt gt id factor expr SampleRateDefault BitRateDefautt BpS SymbolRate ias Hz Fork Amplitude 5 a u Frequency CarrierFrequency Hz E gm na itt Phase Phase degs cos gt gt gt gt O gt HP MultiplyEl PulRaisedC s factor expr SampleRateDefault BitRateDefault J BpS SymbolRate BitRateDetault BpS Hz Fig IV 10 RF upconverter schematic VPI As it can be seen from Figure IV 10 the input sequence corresponding to the coded OFDM baseband signal is separated by the ComplexToRect module into the real values of the and Q components of the signal This operation is internal to VPI s OFDM coder so this module is not used in the L
146. same constellation form as in the Long Haul demo is obtained as shown in the right graph in Figure X A The EVM for this case is 0 186 For the next figures a 55 phase shift has been applied in the equalizer code in order to show a squared constellation Thanks to it the obtained BER values for all of them are approximated to O by VPI as all of the symbols fall within the corresponding quadrant of the diagram If the cyclic prefix is used for the transmission and extracted as in expression IV 24 a notorious improvement in the symbol dispersion is obtained This is shown in the next figure where the right graph represents the constellation diagram when a CP of 20 has been added to the transmission over another one where no CP was used left Numerical UE 23 Numerical Fig IV 40 Dispersion improvement by using CP VPI CHAPTER IV CUSTOMIZED SIMULATIONS 107 In this case the EVM improves from 0 186 to 0 115 even going beyond the 0 177 EVM value obtained in the VPI demo with the same parameters Figure IV 41 shows how the use of oversampling by means of zero padding also achieves an improvement in the received constellation form The left graph shows the resulting constellation when a 2xoversampling configuration is used without CP 128 IFFT inputs for 64 information subcarriers Numerical Numerical Fig IV 41 Constellation with zero padding without left and with right CP VPI This configura
147. se the local oscillator is placed in the middle of the OFDM signal Essentially this implementation is the reverse of the transmitter using the optical IQ mixer in Figure 11 18 Thus it shares the same advantages and disadvantages the FFT size and ADC bandwidths can be used for data modulation if no oversampling is applied and few electronic components are used though it requires two ADCs and the IQ MZM at the transmitter side has three bias voltages that need to be adjusted On the other hand the heterodyne reception setup can be considered as a variant of the DD receiver in Figure 11 22 where an electrical IQ mixer was used to process the real and imaginary parts of the OFDM signal Here the local oscillator is placed left or right of the OFDM signal as depicted in Figure 11 25 fi Simplified OFDM receiver 2 DAC bandwidth 0 5 L 1 1 ids i 1 1 Actual data freq i Laser local oscillator freq Fig 11 25 Heterodyne CO OFDM receiver P4 This setup shares the same advantages and disadvantages with the homodyne one so its use will depend on the chosen transmitter configuration CHAPTER II OPTICAL OFDM 41 As explained in Chapter the electrical IQ mixer at the receiver can be substituted by a larger FFT block to implement the required operations The optical bandwidth requirements for CO OFDM are much lower compared to DD optical OFDM because there is no need to trans
148. se are e CarrierFrequency As in VPI s demos this parameter indicates the RF frequency at which the baseband OFDM signal will be upconverted at the transmitter and then downconverted at the receiver e Phase Value of the phase shift in degrees to be applied by the PhaseShift module as explained in the last chapter e RollOff The ratio of excess bandwidth above the filters cut off frequency The Nc and N_FFT parameter values must be even so the IFFT input sequence is properly allocated 72 FIBER BASED OFDM TRANSMISSION SYSTEMS Any change in these parameter values from the universe s PEW will affect both the upconverter and downconverter modules so just one change is required for it to be effective in the modulator and demodulator This is an added feature with respect to the VPI demos where the change of the value on any of the above parameters needs to be made in both the modulator and demodulators PEWs IV 1 2 Code structure In this section the basic structure of the Matlab code is explained describing the order in which the operations are carried out inside the coder and decoder modules The specific code sentences used to process data will be inserted during the following subsections in order to provide an easier understanding for the use of each new module and code sentence The Matlab code for the OFDM coder module will need to process 6 parameters those are the TimeWindow and BitRate global parameters a
149. similar to the one represented in Figure IV 30 Electrical Spectrum Power dBm 2e9 Frequency Hz Electrical Spectrum Power dBm Fig IV 36 Downconverted electrical OFDM signal VPI However by comparing Figures IV 30 and IV 36 a considerable decrease in the received power level can be observed This is why an amplification stage is usually placed at the receiver so an amplifier module has been inserted at the input of the RF downconversion galaxy see Figure IV 11 After the RF downconversion stage the resulting OFDM signal is fed to the OFDM decoder where the representation of the received constellation diagram and the calculation of the EVM and BER values will account for the quality of the transmission These parameters are dealt with in the following section IV 3 6 Simulation results Il Decoded signal In this section the results of the received constellation diagram EVM and BER values are going to be described for different transmission parameters such as the use of cyclic prefix or the fibre link distance First the reliability of the system has been tested without the optical link and also without the optical modulation and demodulation stages so the HF up downconversion modules were linked with VPI wires The squared constellation in Figure IV 37 proves that the OFDM decoder is able to recover the original transmitted symbols after going through frequency upconversion and downconversion stages
150. st of the dispersion caused by a multipath channel remains within the guard interval It will also be explained later that in the guard time the OFDM symbol is cyclically extended to avoid generating ICI In single carrier systems ISI occurs and can only be compensated by using complex equalizers at the receiver Ina multicarrier system no equalization to overcome ISI is required and only the amplitude and phase of each subcarrier need to be corrected according to the channel frequency response This is simply done by one complex valued multiplication per subcarrier which is in fact a single tap equalization 1 2 Digital generation of subcarriers 1 2 1 Fast Fourier Transform Following the last section s analogy the more trucks are used to transport the load the fewer packets are going to be carried by each one the easier it is for each truck to complete the journey and the less load is going to be lost in case of an accident Then it can be said that in an OFDM transmission a large number of subcarriers is desirable so that the minimum possible quantity of data is lost in case of any non ideality occurring in the transmission channel This effect is shown in Figure 1 6 S ubcarriers effected by fades T T N A f AN Re sponse A VYY j of channel d EE d Fig 1 6 OFDM subcarriers affected by a fading channel P18 However creating an OFDM signal with a large number of subcarriers following the analogue method
151. stems such as ADSL s t is a real signal so the input vector to the IFFT is constrained to have Hermitian symmetry By using this technique the imaginary component of the IFFT output is canceled Because the IFFT simultaneously performs modulation and multiplexing there is no point in the transmitter or receiver where an individual time domain subcarrier can be observed as they are only present in the frequency domain Still in a linear channel this approach would be very useful to describe the overall system hence a single subcarrier will be tracked through the processing of the IFFT operation for some different cases so it can be seen how to achieve Hermitian symmetry for baseband systems In order to simplify the explanation only one symbol will be considered without the use of cyclic prefix CP Also from Chapter I it can be deduced that the mth discrete time domain component associated with the Ath subcarrier of a given OFDM symbol is Ss ad Ere vum Jw CkEXP v for 0 lt m lt N 1 A 1 Thus fixing values for the symbol ck and the number of subcarriers N the discrete signal can be plotted for each subcarrier k A symbol value of cx 1 for 32 subcarriers has been chosen in P1 to represent individual discrete time domain subcarriers as it can be seen on Figures A 1 and A 2 where the real and imaginary components of the OFDM signal are represented in the upper and lower parts of each graph respectively For k 0 the top s
152. subcarrier must be separated from its neighbours by exactly 1 T so each subcarrier within an OFDM symbol has exactly an integer number of cycles in the interval T and the number of cycles differs by exactly one as depicted in Figure 1 3 This way orthogonality between subcarriers is achieved This property can be explained for any couple of subcarriers by the following expression o T 2 COS COS If m and n are different natural numbers the area under this product over one period is zero The frequencies of these waves are called harmonics and for them the orthogonality condition is always fulfilled dt 0 MEN 1 3 Fig 1 3 Time domain subcarriers within an OFDM symbol W2 Figure 1 3 shows three subcarriers from one OFDM symbol in a time domain representation In this example all subcarriers have the same phase and amplitude but in practice the amplitudes and phases may be modulated differently for each subcarrier In expression 1 1 the OFDM symbol is ideally multiplied by a square pulse P t which is one for a T second period and zero otherwise The amplitude spectrum of that square pulse has a form sinc mft which has zeros for all frequencies f that are an integer multiple of 1 T Then as shown in Figure 1 4 an OFDM symbol spectrum consists of overlapping sinc functions each one representing a subcarrier where at the frequency of the kth subcarrier all other subcarriers have zeros CHAPTER OF
153. technique when the information is coded into 64 OFDM subcarriers 1 2 3 Cyclic Prefix As mentioned before by dividing the data stream into N subcarriers the symbol period is made N times longer which also reduces the delay spread or chromatic dispersion relative to the symbol time To avoid interferences between OFDM symbols meaning null ISI and also eliminate ICI a guard time is introduced for each OFDM symbol after the IFFT which is cyclically extended within this guard time as shown in Figure 1 15 This cyclical extension is called the cyclic prefix CP Amplidutde 2 x N 2 p DY ON Fig 1 15 Cyclic prefix in an OFDM symbol time domain sequence P4 Due to the insertion of this prefix the symbol duration is extended without transmission of additional data leading to a reduction of the net bitrate by a factor of sfr disi where tcp is the extension of the symbol period due to the cyclic prefix However the simple equalization resulting from the elimination of both ISI and ICI from the received signal is a major advantage which deserves giving up a bit of transmission efficiency As long as the cyclic prefix duration is equal or longer than the maximum delay caused by the channel impairments the effect of one symbol over its neighbours will be limited to its cyclic prefix corruption without damaging the information part The effect of a cyclic prefix length shorter than the drift caused by chromatic dispersion in opt
154. the BER El mQAM module is used to calculate the EVM of the received constellation This module expects and Q sequences of electrical samples with length TimeWindow Bitrate so the received information symbols have to be first compensated in Matlab adding zeros to the sequence and then upsampled by a factor equal to the BpS parameter before converting them into electrical samples Despite offering clock recovery and amplitude and phase correction of the received symbols the EVM calculation performed by the BER_El mQAM 94 FIBER BASED OFDM TRANSMISSION SYSTEMS module would not be correct if the compensating symbols were taken into account For that purpose the IgnoreSybols parameter of this module should be set to ApplyOnce and then the X NumberOfSymbolsTolgnore and StartTimeTolngore parameters should be set to BitRate NumberOfSymbolsTolgnore TimeWindow oa n floor TimeWindow BitRatebBpS cei N FFT 14 CP StartTimeTolgnore BitRa 1 BitRate BpS N floor TimeWindow te Bps ceil Nggrz 1 cP IV 11 This way the number of symbols to ignore is indicated to the module as well as the time when it should start ignoring them By giving these parameters the values in expression IV 12 the zero valued symbols used for the symbol rate compensation are going to be omitted from the calculations The module in charge of performing the BER calculations is the BER OOK Stoch star As shown in Figure IV 22 t
155. the first visualizer on the left in the figure two pulse shaping modules 3 will generate a Nyquist response from an incoming electrical impulse The transmission is initiated in a PRBS or pseudo random bit sequence generator 1 According to the module s definition in the Reference Manual right click on the module and select the Help option the output of this module is a sequence of random integer numbers forming a vector of size TimeWindow Bitrate that will be fed to the coder See the Reference Manual in W6 for more details about the characteristics of this random sequence and the available types of sequence to select from the PRBS Parameter editor window Despite not being able to see the internal structure of the OFDM coder galaxy its operation principles can be guessed based on the acquired concepts during the investigation prior to the realization of this chapter For an M QAM modulation an OFDM coder in its simpler form omitting zero padding and cyclic prefix overheads would first pack the bit sequence coming from the PRBS into log M sets assigning one QAM symbol to each set Thus the parameter BitsPerSymbolQAM from the schematic s PEW allows changing the M factor for the QAM modulation as shown in Figure 111 12 OFDM Generation and Detection vtmu Paramet Name OFDM Generation and Detection vtmu E ID OFDM Generation and Detection vimu z 5 8 wee Name Value Unit Pl Sh QAM OFDM E
156. the modules offered by VPI to declare or extract any variable from a Cosimulation operation do not work with integer numbers but only with electrical or optical signal samples complex numbers or floating point values Once converted the Pack M module produces an MxN matrix with the floating point entries filling the first row from left to right using the first N input values In this case the main interest is to create a vector to be processed by the Matlab code so the parameters indicated to the module will be 1 row and Bitrate TimeWindow columns i e the whole input sequence of bits Next the floating point vector is processed by the CoSim nputFit module which declares a floating point input variable to the CoSim block It is important to remember that the name of this variable has to match with the one being used in the Matlab code so the parameter name for this module must be prbs The CoSim module will then access the Matlab code providing the values for the 6 input variables As explained in Chapter lll this is simply done by indicating the code s main function name in the RunCommand parameter not forgetting to attach the Matlab file to the nput folder of the galaxy schematic The CoSim module output is connected to another module which indicates the desired variable to extract from it once the cosimulation has been performed Since the output signal of the OFDM coder is a complex vector where each value represents one symbol
157. tion allows a slight improvement in the calculated EVM giving a value of 0 112 at the cost of reduced transmission efficiency If a CP of 20 is added to this configuration the best value of EVM is achieved 0 095 though less than 30 of the bits are used to represent information Note that fewer points are represented as more overheads are used This is because the OFDM coder discards information bits in order to allocate the desired CP and zero padding quantity as explained in section IV 1 The following figure represents the received constellation diagrams for two different link distances In the left side the constellation after a 500 km transmission is shown while in the right graph the OFDM signal has been transmitted over a 2000 km loop In the used configuration oversampling and a CP of 1096 have been applied The phase shifts due to the selected reference frequency are not compensated 108 FIBER BASED OFDM TRANSMISSION SYSTEMS Numerical Numerical Fig IV 42 Received constellations for 500 km left and 2000 km right VPI Although the phase shift is not compensated the EVM value is worse as the distance increases and less dispersion can be appreciated by looking at the graphs In this case EVM values are 0 076 for 500 km and 0 131 for 2000 km CHAPTER V CONCLUSION AND FUTURE LINES 109 CHAPTER V CONCLUSIONS AND FUTURE LINES V 1 Conclusions In this Master Thesis a revision of basic concept
158. trial television DTT and digital radio broadcasting in much of the world OFDM is also the basis of most DSL standards though in this context it is usually called discrete multitone DMT because of some minor peculiarities Despite the important advantages that OFDM provides and its widespread use in wireless communications it is only during the last years that it has been considered for optical communications P1 The lack of interest in optical OFDM in the past is partly because of the fact that the silicon signal processing power had not reached the point at which sophisticated OFDM signal processing could be performed in a CMOS integrated circuit and partly because the demand for increased data rates across long fibre distances is quite recent Another important obstacle has been the fundamental differences between conventional OFDM systems and conventional optical systems Table 1 summarizes these differences Table 1 Typical OFDM system vs typical Optical system P1 Typical OFDM Bipolar Info carried on LO at receiver Coherent system electrical field reception Typical Optical Unipolar Info carried on No LO laser Direct system optical intensity at receiver detection In typical non optical OFDM system the information is carried on the electrical field and the signal can have both positive and negative values bipolar At the receiver there is a local oscillator LO and coherent detection is used
159. trum is centred The analysis about how and why to choose the reference frequency precisely equal to that value and the derived implications is carried out in section IV 3 4 At the receiver after DD and decoding chromatic dispersion is compensated by correcting the phase of each sub carrier separately The equalized phase offsets correspond to the relative accumulated dispersion values experienced by each sub carrier during its transmission through optical fibre 11 3 5 Simulation results A list of the parameters used for this demo can be found below These will be the basis from where the simulations in the following chapter have been done If different values for any of these parameters are used it will be explicitly stated BitRateDefault 10e9 bps TimeWindow 8 1024 BitRateDefault seconds SampleRateDefault 4 BitRateDefault samples second BitsPerSymbolQAM 2 NumberOfCarriers 64 CyclicPrefix 0 2 CarrierFrequency 7 5 GHz Reference frequency 193 1 THz CarrierFrequency As the equalization coefficients represented in Figure 111 23 are only calculated for the dispersion parameters shown in Figure 111 24 in a 1000 km transmission distance 10 loops any change in the fibre Physical parameters will distort the form of the received constellation With this once the simulation is executed the VPI Photonics Analyzer tool will display the received optical spectrum the received constellation diagram and its corresponding
160. ubcarrier in the parallel inputs of the IFFT the samples have a constant value This can be easily deduced from Expression A 1 where the exponential will not change its value through any discrete index m This will represent the DC term in the baseband signal and the component at the carrier frequency in wireless and optical systems where the OFDM signal is upconverted to a higher frequency For k 1 the sequence represents the samples of one cycle of a sinusoid of frequency 1 Ts where Ts is the symbol period not considering the CP For k 2 the baseband frequency has been doubled and the samples now give two cycles of a sinusoid 2 FIBER BASED OFDM TRANSMISSION SYSTEMS gpl t Ni ESI n 0 2 Discrete Time ndo m x Dios Tine rom m di A de d v Y 7 y 3 Dew Tem edes m n Cuecroto Time nde m a b c Fig A 1 Discrete time domain signal for individual subcarriers for a k 0 b k 1 and c k 2 P1 It can also be observed that the imaginary component has a constant phase delay over the real one which will be the key to eliminate it from the signal so a real valued signal can be transmitted Because of the circular property of the FFT and IFFT P1 the represented sinusoid will increase its number of cycles for each subcarrier increasing K until the N 2h term also called the Nyquist term where the signal is critically sampled From there the number of cycles starts dec
161. ues for a cyclic prefix in an OFDM system range from 10 to 20 In view of all the above the final schematic for the OFDM signal generation could be represented by the one in Figure 1 17 where oversampling by means of frequency zero padding and a temporal cyclic prefix are added in the following order Add 0 x Cyclic Prefix N A Symbols Parallel To Serial R Complex sum Parallel Zero IFFT Output DAC s t 2 z 11010001 Mapping Padding N 4 Symbols Fig 1 17 OFDM signal generation schematic CHAPTER OFDM BASICS 17 At the receiver end zero padding and cyclic prefix are extracted in the opposite order in which they were inserted at the transmitter as shown in Figure 1 18 Extract 0 x Cyclic Prefix N 4 Symbols OMM i Extract R laut Zero Serial P Padding Demap 11010001 N A mag Fig 1 18 OFDM signal reception schematic Now that the electrical OFDM signal is ready to be transmitted it needs to be re modulated over an optical carrier to be transmitted through an optical channel For this purpose different methods of optical modulation and detection are presented in Chapter ll but before that Section 1 3 will serve as an introduction to the used method in the optical OFDM simulations 1 2 4 Mapping and demapping It has been said before that the bit stream coming from the signal source needs to be converted into many parallel data pipes each mapped onto correspondin
162. w 6 wo Y w wo Wpp IV 15 Where Y w represents the spectrum of the OFDM signal Thus the spectrum of the output signal is Xour w ES H o Xiy 0 E w Wy eX ores Y w Wo Wap eit ref IV 16 If the reference frequency is set to the optical carrier frequency wref wo Xoyr w w wo Y w wo Wrp e x0 00 IV 17 On the other hand if the RF frequency is considered as the reference frequency Wrer wrr the output signal is Xour w Sw ePX RP w 0 Wap eit otorF IV 18 The delay for the pulse in IV 17 is given by e x 92 and the phase shift in IV 18 appears due to the e kF term In order to provide these values the temporal expressions should be calculated CHAPTER IV CUSTOMIZED SIMULATIONS 97 The photodetected current can be described as a function of its responsivity multiplied by the square of the received signal modulus ip R Xout t IV 19 Thus the delay t for the pulse and the phase shift affecting the constellation can be calculated from the estimation of the temporal expressions for each of the above choices of the reference frequency respectively as DLcf xou COL 1 Yo t tear Ta TE TDLc fo Ixouc 1 Yo 6 9022 Ag rad ffr IV 20 Where D is the amount of CD to be compensated s m L is the fibre link distance c is the speed of light and Yp is the
163. was inserted recovering the original spectrum IV 2 5 Cyclic Prefix The effect of a change in the OFDM spectrum due to an increase of the cyclic prefix proportion can be seen in Figure IV 20 where in the upper figure a CP corresponding to 25 of the OFDM symbol length has been applied while in the lower one no CP is used For a better appreciation of the spectrums only one component of the signal has been represented the real one El electrical I and Q signals f ry Electrical Spectrum 1 589 Frequency Hz Electrical Spectrum 1 5e9 Frequency Hz Fig IV 20 No CP vs CP 25 of the OFDM symbol length VPI CHAPTER IV CUSTOMIZED SIMULATIONS 89 By inserting CP into the OFDM sequence a ripple can be appreciated in the OFDM signal spectrum This is because the sincs representing the subcarriers are narrower in frequency than before so their maximums don t match up exactly with their neighbours nulls This effect was referred in Chapter anda more detailed description of it can be found in Annex B IV 2 6 Received Constellation In an ideal channel condition X points will be represented in the received constellation diagram for an X QAM modulated OFDM signal This is because there is no distortion causing any phase or amplitude error in the reception of symbols so all of them are represented exactly in their theoretical location In this case a 4 QAM and 16 QAM modulation transmissions are
164. witt Orthogonal frequency division multiplexing using baseband optical single sideband for simpler adaptive dispersion compensation Opt Fiber Commun Conf 2007 REFERENCES 113 P10 W R Peng Wu V R Arbab et al Experimental demonstration of a coherently modulated and directly detected optical OFDM system using an RF tone insertion Opt Fiber Commun Conf 2008 P11 W R Peng Wu V R Arbab et al Experimental demonstration of 340 km SSMF transmission using a virtual single sideband OFDM signal that employs carrier suppressed and iterative detection techniques Opt Fiber Commun Conf 2008 P12 Arthur Lowery L B Du and Jean Armstrong Performance of optical OFDM in ultralong haul WDM lightwave systems Journal of Lightwave Technology 2007 P13 B J Schmidt Arthur Lowery and Jean Armstrong Experimental Demonstrations of Electronic Dispersion Compensation for Long Haul Transmission Using Direct Detection Optical OFDM Journal of Lightwave Technology 2008 P14 Ivan B Djordjevic PMD compensation in fiber optic communication systems with direct detection using LDPC coded OFDM Optics Express 2007 P15 J Zhang et al A novel automatic PMD compensation scheme based on DSP in optical fiber communication systems IEEE International Conference on Information Communications and Signal processing ICICS 2009 P16 J M Kahn and J R Barry Wireless infrared communications Proc IEEE vol 85 1997 P17 Jean A
165. x is responsible for another loss in performance because it also affects the spectral power density of the transmitted signal such that a ripple is introduced inside the main frequency band as shown in one of the simulated results depicted in Figure B 1 Electrical Spectrum 12 5l 215 l mul MN 1 1668 5e8 1e9 1 5689 1 8469 Frequency Hz Power dBm i Fig B 1 Zoomed ripple in the OFDM band for a high quantity of CP VPI This ripple is originated due to an increase of the temporal duration of the transmitter functions when using CP the sincs forming the OFDM spectrum are narrower in frequency than before so their maximums don t match up exactly with their neighbours nulls and the resulting spectrum is not plain any more but it suffers from rippling ANNEX B CYCLIC PREFIX EFFECT ON THE OFDM SIGNAL SPECTRUM 5 In P19 it is mathematically demonstrated that the power spectrum density PSD of an OFDM subcarrier is only affected by the symbol rate and the pulse shaping window no matter what other parameters are in the system Thus a single subcarriers PSD can be plotted as a function of different OFDM symbol lengths T in number of samples as it is done in Figure B 2 Note that as T increases the spectrum becomes narrower 1 T 16 T 20 T 32 0 9 0 8 0 7 0 6 0 5 0 4 Normalized Amplitude 0 3 0 2 0 1 0 a Ls ENZA 0 2 0 15 0 1 0 05 0 0 05 0
166. xer Bias A Real Bias C Optical Optical Optical input output Carrier p Output m Imag t Electrical gt eae 90 phase shift Fig 11 8 IQ Mach Zehnder modulator P4 Thus an IQ MZM in its bias null point is used so that the envelope of the electrical field of the optical modulated signal is proportional to the information signal The main disadvantage of this type of modulation is that the IQ MZM has three bias voltages that need to be precisely adjusted This way the optical IQ signal is directly obtained For a complex OFDM signal the output results in just one optical band see Figure 11 9 overcoming the problems caused by the double sideband spectrums in the last configurations freq Fig 11 9 Complex signal at the output of an IQ MZM P4 11 3 Why optical single sideband The main disadvantages caused by the double sideband spectrum appearing at the output of a standard MZM are e For complex modulations the information carried by the phase is lost e For both direct and coherent detection it reduces the obtainable spectral efficiency e Specifically for direct detection the duplicated sideband causes fading in presence of chromatic dispersion 30 FIBER BASED OFDM TRANSMISSION SYSTEMS Thus double sideband OFDM will only be considered for low cost applications where chromatic dispersion is not present or at least is not a limiting factor as in free space communications or access networks In the

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