Cost-effective optical transmission systems based on orthogonal frequency division multiplexing
Abstract
Orthogonal frequency division multiplexing (OFDM)is becoming increasingly popular in optical fiber applications because as data rates increase, the computational requirements involved in electronic dispersion compensation for serial modulation formats become impractical. Some investigations explain that OFDM can be used for the electronic compensation of chromatic dispersion and polarization mode dispersion in single-mode optical fiber systems and for mode dispersion in multimode systems. The main goal of this Master thesis is to study on one hand the OFDM systems and on the other, the optical transmission systems and also the combination of the two: optical OFDM systems. A general classification of the present proposals for optical OFDM implementations is presented and two of the identified schemes, those which lead to more cost-effective solutions, have been studied in deeper detail. These are based on conventional Intensity Modulation and Direct Detection (IM/DD) optical transmission systems. The first system relies on a RF up-conversion stage prior to the optical intensity modulation that allows to modulate the real and imaginary parts of the optical OFDM signal into the phase and quadrature components of an RF frequency, while the second involves imposing the Hermitian symmetry among the subcarriers in order to obtain an OFDM signal which is purely real. Starting from a built in demo of the software called Virtual Photonics Inc. (VPI) a practical investigation about OFDM optical systems has been done. This demo is called Long Haul transmission and implements the RF up-conversion optical OFDM scheme. This demo is only an example restricted to a specific scenario and offers little flexibility. That is why a new VPI simulation setup has been created by exploiting the Matlab interface provided by VPI where the OFDM coding and decoding have been developed in Matlab code and can be adjusted and modified to any scenario. Additionally, another VPI simulation setup has been developed which allows to impose the Hermitian symmetry among the subcarriers allowing for the obtention of a purely real OFDM signal to be directly Intensity modulated over an optical carrier. Results and comparisons of the outcome of both, our simulation setups and the VPI demo, are presented showing good agreement. Moreover, our setups have incorporated several improvements based on the investigation of optical OFDM systems carried out. Also, the functionalities of the software have been exploited to come out with user-friendly setups that allow any researcher in the field to carry out advanced simulations with little effort.
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MASTER THESIS TITLE:Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing MASTER DEGREE: Master in Science in Telecommunication Engineering & Management AUTHOR: Edurne Garcia Villar DIRECTOR: María Concepción Santos Blanco DATE: Monday 27th of June 2011
Title: Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing Author:Edurne Garcia Villar Director: María Concepción Santos Blanco Date: Monday 27th of June 2011 Overview Orthogonal frequency division multiplexing (OFDM)is becoming increasingly popular in optical fiber applications because as data rates increase, the computational requirements involved in electronic dispersion compensation for serial modulation formats become impractical. Some investigations explain that OFDM can be used for the electronic compensation of chromatic dispersion and polarization mode dispersion in single-mode optical fiber systems and for mode dispersion in multimode systems. The main goal of this Master thesis is to study on one hand the OFDM systems and on the other, the optical transmission systems and also the combination of the two: optical OFDM systems. A general classification of the present proposals for optical OFDM implementations is presented and two of the identified schemes, those which lead to more cost-effective solutions, have been studied in deeper detail. These are based on conventional Intensity Modulation and Direct Detection (IM/DD) optical transmission systems. The first system relies on a RF up-conversion stage prior to the optical intensity modulation that allows to modulate the real and imaginary parts of the optical OFDM signal into the phase and quadrature components of an RF frequency, while the second involves imposing the Hermitian symmetry among the subcarriers in order to obtain an OFDM signal which is purely real. Starting from a built in demo of the software called Virtual Photonics Inc. (VPI) a practical investigation about OFDM optical systems has been done. This demo is called Long Haul transmission and implements the RF up-conversion optical OFDM scheme. This demo is only an example restricted to a specific scenario and offers little flexibility. That is why a new VPI simulation setup has been created by exploiting the Matlab interface provided by VPI where the OFDM coding and decoding have been developed in Matlab code and can be adjusted and modified to any scenario. Additionally, another VPI simulation setup has been developed which allows to impose the Hermitian symmetry among the subcarriers allowing for the obtention of a purely real OFDM signal to be directly Intensity modulated over an optical carrier. Results and comparisons of the outcome of both, our simulation setups and the VPI demo, are presented showing good agreement. Moreover, our setups have
incorporated several improvements based on the investigation of optical OFDM systems carried out. Also, the functionalities of the software have been exploited to come out with user-friendly setups that allow any researcher in the field to carry out advanced simulations with little effort.
ÍNDEX 0 INTRODUCTION ........................................................................................ 1 1 CHAPTER I. OFDM SYSTEMS ................................................................. 3 1.1 OFDM basic concepts ....................................................................................................... 3 1.2 Digital OFDM systems ....................................................................................................... 8 1.2.1 Pulse shaping ....................................................................................................... 11 1.2.2 Oversampling by means of zero padding ............................................................. 12 1.2.3 Cyclic Prefix .......................................................................................................... 13 2 CHAPTER II. OPTICAL CHANNEL ......................................................... 17 2.1 Chromatic dispersion ...................................................................................................... 17 2.2 Optical modulation techniques ...................................................................................... 19 2.2.1 Direct modulation laser (DML) .............................................................................. 19 2.2.2 Mach-Zehnder Modulator (MZM) ......................................................................... 21 2.3 Optical demodulation techniques .................................................................................. 24 2.3.1 Direct Detection .................................................................................................... 24 2.3.2 Coherent Detection ............................................................................................... 25 2.4 Equalization and Reference frequency ......................................................................... 26 2.4.1 Equalization concept ............................................................................................ 26 2.4.2 Reference frequency ............................................................................................ 27 2.5 VPI basic concepts .......................................................................................................... 30 2.5.1 Hierarchical organization ...................................................................................... 30 2.5.2 Simulation parameters .......................................................................................... 31 2.5.3 VPI interfaces ....................................................................................................... 33 3 CHAPTER III. OPTICAL OFDM SYSTEMS ............................................. 37 3.1 Optical OFDM modulation techniques .......................................................................... 37 3.1.1 RF upconversion based on intensity modulation.................................................. 39 3.1.2 Optical IQ modulation ........................................................................................... 40 3.1.3 Hermitiansymmetry ............................................................................................... 41 3.2 Optical OFDM demodulation techniques ...................................................................... 42 3.2.1 OFDM Direct Detection ........................................................................................ 42 4 CHAPTER IV. OFDM FOR LONG-HAUL TRANSMISSION DEMO ........ 47 4.1 General idea ..................................................................................................................... 47 4.2 Modulation galaxy ........................................................................................................... 48 4.2.1 Modulation Galaxy parameters............................................................................. 50 4.3 Demodulation galaxy ...................................................................................................... 50 4.3.1 Demodulation Galaxy Parameters ....................................................................... 52
4.4 Optical Channel ............................................................................................................... 53 4.4.1 Optical modulation stage ...................................................................................... 53 4.4.2 Fibre link ............................................................................................................... 54 4.4.3 Photodiode in direct detection configuration ........................................................ 54 5 CHAPTER V. CUSTOMIZED DEMO ....................................................... 57 5.1 General scenario.............................................................................................................. 57 5.1.1 Long-Haul Transmission demo versus Customized demo ................................... 58 5.1.2 Global parameters ................................................................................................ 59 5.2 Transmitterand receiver galaxies .................................................................................. 60 5.2.1 Transmitter galaxy ................................................................................................ 60 5.2.2 Receiver galaxy .................................................................................................... 61 5.3 OFDM basics results ....................................................................................................... 61 5.3.1 Normalization ........................................................................................................ 61 5.4 New improvements .......................................................................................................... 64 5.4.1 Ber calculation ...................................................................................................... 64 5.4.2 Equalization implementation ................................................................................. 65 5.4.3 Cyclic prefix implementation ................................................................................. 68 5.4.4 Zero padding implementation ............................................................................... 70 6 CHAPTER VI. HERMITIAN SYMMETRY DEMO ..................................... 73 6.1 General scheme ............................................................................................................... 74 6.2 Transmitter galaxy ........................................................................................................... 74 6.2.1 Zero padding insertion .......................................................................................... 76 6.3 Receiver galaxy................................................................................................................ 77 6.3.1 Zero padding extraction ........................................................................................ 77 6.4 Final results ...................................................................................................................... 78 7 CONCLUSIONS AND FUTURE LINES ................................................... 81 7.1 Conclusions ..................................................................................................................... 81 7.2 Future lines ...................................................................................................................... 83 8 REFERENCES ......................................................................................... 84 Books .......................................................................................................................................... 84 Papers and tutorials .................................................................................................................. 84 Websites ..................................................................................................................................... 85 9 ACRONYMS ............................................................................................ 86
Figures Index Figure 1. 1 FDM symbols general scheme ......................................................... 3 Figure 1. 2 FDM modulation concept ................................................................. 4 Figure1. 3 IQ modulator ..................................................................................... 4 Figure1. 4 Analogue receiver ............................................................................. 5 Figure1. 5 IQ demodulator.................................................................................. 5 Figure1. 6 FDM spectra ...................................................................................... 6 Figure1. 7 Time domain subcarriers within an OFDM symbol ............................ 6 Figure1. 8 OFDM spectra ................................................................................... 7 Figure1. 9 Spectrum efficiency: FDM signals and OFDM signals ...................... 7 Figure1. 10 Ideal filtre at the DAC ...................................................................... 9 Figure1. 11 OFDM transmitter in digital domainusingan IFFT block ................... 9 Figure1. 12 OFDM receiver in digital domainusingan FFT block ...................... 10 Figure1. 13 IFFT block and the frequency domain OFDM symbol at its output, [P2] ............................................................................................................ 10 Figure1. 14 VPI pulse shaping used ................................................................. 11 Figure1. 15 OFDM raised cosine filter: System transfer function and System impulse response with different roll-off factor ............................................ 11 Figure1. 16 VPI impulse response for the raised cosine forα= 0 and α= 0.5 .... 12 Figure1. 17 Oversampling used to shift aliases away, [P2] .............................. 13 Figure1. 18 Cyclic prefix in an OFDM symbol (time domain sequence), [P2] ... 13 Figure1. 19 ISI because an insufficiently large CP [P2] .................................... 14 Figure1. 20 Synchronizationwith CP, [P2] ........................................................ 14 Figure1. 21 OFDM signalgenerationschematic ................................................ 15 Figure1. 22 OFDM signalreceptionschematic................................................... 15 Figure2. 1 Schematic and characteristic curve of a laser diode ....................... 20 Figure2. 2 Schematic of an Intensity Modulation and Direct Detection ............ 20 Figure2. 3 Spectrum of anintensity modulated optical signal ........................... 21 Figure2. 4 Mach-Zehnder modulator ................................................................ 22 Figure2. 5 Transfer functions of the opticali ntensity and optical field .............. 23 Figure2. 6 Optical OFDM modulation using a standard MZM........................... 24 Figure2. 7 Conventional IM/DD transmission Systems with an ideal fibre ........ 25 Figure2. 8 Transmission systems for a dispersive fibre ................................... 25 Figure2. 9 CO-OFDM receiver ......................................................................... 26 Figure2. 10 Phasedistortions on the received constellation ............................. 26 Figure2. 11 Received constellation without equalization .................................. 27 Figure2. 12 Received constellation with equalization ....................................... 27 Figure2. 13 Optical spectrumatthefibre input .................................................... 28 Figure2. 14 Mathematical expressions in fibre input and output....................... 28 Figure2. 15 X(f) and H(f) spectrums centred and symmetric ............................ 30 Figure2. 16 VPI hierarchy ................................................................................. 30 Figure2. 17 Temporal samples vector .............................................................. 32 Figure2. 18 Frequency samples vector ............................................................ 32 Figure2. 19 CosimInterfacemodule [VPI] .......................................................... 33 Figure2. 20 Main code function indicated in the RunCommandparameter ....... 34 Figure2. 21 CosimInterface interconnection for Optical signa lprocessing ....... 34
Figure3. 1 Optical OFDM transmission systems .............................................. 37 Figure3. 2 Electrical upconversion of the complex OFDM baseband signal [B1] .................................................................................................................. 39 Figure3. 3 RF upconversion based on Intensity Modulation schematic [P2] .... 40 Figure3. 4 Optical IQ modulation schematic [P2] ............................................. 41 Figure3. 5 OFDM transmitter using hermitian symmetry .................................. 42 Figure3. 6 Optical-Electric Conversion ............................................................. 42 Figure3. 7Long-haulopticalcommunicationsystem ............................................ 43 Figure3. 8 Received optical spectrum .............................................................. 44 Figure3. 9 Useful components in the electrical spectra .................................... 44 Figure3. 10 Unwanted out of band noise .......................................................... 45 Figure3. 11 Direct detection at the receiver ...................................................... 45 Figure4. 1 Schematic of the OFDM transmittermodule [VPI] ............................ 47 Figure4. 2 Universe parameters ....................................................................... 48 Figure4. 3 Modulation galaxy ........................................................................... 48 Figure4. 4 OFDM Transmitter Parameters ....................................................... 50 Figure4. 5 Demodulation galaxy ....................................................................... 51 Figure4. 6 OFDM Receiver Parameters ........................................................... 52 Figure4. 7 Matlab representation of the demo equalization curve .................... 53 Figure4. 8 Optical modulation stage ................................................................. 53 Figure4. 9 Fibre link .......................................................................................... 54 Figure4. 10 Photodiode at the receiver ............................................................ 54 Figure5. 1 General scheme .............................................................................. 57 Figure5. 2 Universe parameters ....................................................................... 60 Figure5. 3 Transmitter galaxy ........................................................................... 60 Figure5. 4 Receiver galaxy ............................................................................... 61 Figure5. 5Detail of coder output real part in customized demo ........................ 62 Figure5. 6Coder output real part in customized demo ...................................... 62 Figure5. 7 Detail coder output real part in Long-Haul Transmission demo ....... 62 Figure5. 8 Coder output real part in Long-Haul Transmission demo ................ 62 Figure5. 9 Ideal equalization versus Long-Haul equalization ........................... 65 Figure5. 10 Received constellation with equalizations of figure 5.9 and normal cyclic prefix extraction ............................................................................... 66 Figure5. 11Received constellation with training sequence equalization and normal cyclic prefix extraction with received EVM = 0,225272195083735 67 Figure5. 12 Improvement extracting CP ........................................................... 69 Figure5. 13 Cyclic prefix extraction second possibility and ideal equalization with ............................................................................................................ 69 Figure5. 14 Cyclic prefix extraction second possibility and training sequence equalization with EVM = 0,160851282209057 ......................................... 69 Figure5. 15 Received constellation in Long Haul demo withe qualization and cyclic prefix. ............................................................................................... 70 Figure6. 1 General scheme .............................................................................. 74 Figure6. 2 Transmitter galaxy ........................................................................... 75 Figure6. 3 Imaginary pulse shaping output ...................................................... 75 Figure6. 4 Real pulse shaping output ............................................................... 75
Figure6. 5 Correct order of the sequence in Matlab code ................................ 76 Figure6. 6 Receiver galaxy ............................................................................... 77 Figure6. 7 Received constellation in Hermitian Symmetry demo ..................... 78 Figure6. 8 Simulation parameters in Hrmitian Symmetry demo ....................... 78
6 Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing pass filter rejection. However that reduces the spectral efficiency to sometimes unacceptable values. Figure1. 6 FDM spectra In OFDM systems an appropriate selection of the integration interval is needed and the subcarrier spacing has to fulfil the condition: f T OFDM ∆ =1 (I.3) This means that in an OFDM symbol period each subcarrier contains an integer number of periods (figure 1.7). Figure1. 7 Time domain subcarriers within an OFDM symbol Figure 1.7 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 (As it can be seen in the expression I.1). With the choice in I.3 for the subcarriers, the orthogonality condition in I.2 is still fulfilled in spite of the fact that the subcarriers spectrally overlap, see figure 1.8. The respective symbols may be recovered by the receiver in figure1.4with the appropriate sampling interval.
CHAPTER I. OFDM SYSTEMS____________________________________________________________________7 Figure1. 8 OFDM spectra The orthogonality condition in OFDM may be understood from the spectral domain viewpoint by considering that through the downconversion stage the targeted subcarrieris set at the zero frequency position and then by low-pass filtering the value at zero frequency is obtained. So, it can be said that OFDM is better than FDM due to the spectral efficiency but in exchange it is very sensitive to frequency shifts which lead to Intercarrier Interference (ICI). Figure1. 9 Spectrum efficiency: FDM signals and OFDM signals It is important to take into account that in a general case many analogue components are needed in case a large number of subcarriers are required. This gives rise to a tradeoff between the desire to use as many subcarriers as possible to make the OFDM signal stronger against transmission impairments,
8 Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing and the system complexity associated to the use of analogue components, especially when many of them are needed. 1.2 Digital OFDM systems Following the conclusions obtained in the previous section, in order to create an OFDM signal with a large number of subcarriers an extremely complex architecture involving many oscillators and filters at both the transmit and receive ends is required. Currently in OFDM transmissions, this complexity is reduced by transferring it from the analogue to the digital domain. Mathematically, if the temporal expression of an OFDM signal is taken, expression I.3: (I.3) Where 1 1 ( · ) OFDM S f T N T ∆ = = . and considering it is sampled every T s it leads to: (I.4) The expression I.4 represents the Inverse Fast Fourier Transform (IFFT) of an OFDM symbol. In a digital OFDM system then, the IFFT is performed in the transmitter module after the QAM mapping process. Therefore, the modulation stage involves the IFFT application [P1]. For the parallel demodulation of all subcarriers at the receiver side, the procedure involves the subcarrier detection in the digital domain using theFast Fourier Transform (FFT) [P2]. The most important advantage in digital systemsis that they are able to avoid the hardware complexity and to allow cost-effective implementations. The drawback is that digital to analogue converters and analogue to digital converters are needed. Note that the analogue filtering to separate the subcarriers is not required in the digital system [P1]. ∑ ∑∑ ∑ = − == ⋅ ⋅ ⋅ − = ⋅=⋅=Χ OFDMOFDM N i N Knj N k ik N i Tsn TsN kj N k ik eaeCnTs 0 2 1 00 1 2 1 0 )( π π )()( 2 1 00 OFDM ftkj N k ik N i iTtpeatX OFDM −⋅⋅= ∆ − == ∑∑ π
CHAPTER I. OFDM SYSTEMS____________________________________________________________________9 Ideally, D/A conversion should convolve each temporal sample by a sinc function. This ideal pulse shaping is translated into a perfectly rectangular filter that removes the alias in the frequency domain, as shown in figure 1.10: Figure1. 10 Ideal filtre at the DAC In the figure 1.10 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 following scheme (figure 1.11) represents the OFDM transmitter in the digital domain where a IFFT block is used in order to modulate the OFDM signal. Figure1. 11 OFDM transmitter in digital domain using an IFFT block Figure 1.12 represents in a similar way, how the subcarriers that form 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.
10 Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing Figure1. 12 OFDM receiver in digital domain using an FFT block The frequencies of an OFDM signal are represented in each branch of an IFFT operation as it can be seen in the following figure 1.13, where ... are the input sequence symbols from subcarrier 1 to the total number of subcarriers N, and ... 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. Figure1. 13 IFFT block and the frequency domain OFDM symbol at its output, [P2] The first output channel ( ) 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. This is an important fact to be taken into account in the VPI simulations, for example when the ideal equalization is performed (Chapter IV). Thus, the so called “Nyquist channel” is located at y Nc/2+1 , which corresponds to the highest frequency that the subsequent digital-to-analogue converter can modulate: the Nyquist frequency (f N ), or half the sampling frequency according to the sampling theorem
CHAPTER I. OFDM SYSTEMS____________________________________________________________________11 Aliasing is the effect that causes continuous signals become indistinguishable when they are digitally sampled. When this happens, the original signal cannot be reconstructed uniquely from the digital signal. This is the effect when the analogue band-limited signal is sampled below its Nyquist frequency. In the analogue to digital conversion stage, the ADC filter has to be designed according to an antialiasing procedure. The frequencies which do not fulfill the Nyquist criterion have to be filtered out, limiting the bandwidth of the signal. 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, and then assign the real and imaginary parts of the OFDM signal respectively to the in-phase and quadrature components of an RF frequency as in the RF upconversion optical OFDM system which is the object of chapters IV and V . An alternative would be to apply the Hermitian symmetry to the subcarriers so that the imaginary part of the OFDM signal will be cancelled. That would save one DAC/ADC pair at the expense of transmitting half the information. That is the subject of chapter VI. 1.2.1 Pulse shaping In order to take into account the non-idealities of the DAC/ADC in VPI simulations, the DAC and ADC pulse shaping are modelled using a raised cosine function The approach used in our studies is the raised-cosine filter. Figure1. 14 VPI pulse shaping used The raised-cosine filter with a determined roll-off factor can be used to model the pulse shaping process in both transmitter and receiver modules of the transmission system. The following figure 1.15 shows the transfer function and the impulse response of the raised-cosine filter. Figure1. 15 OFDM raised cosine filter: System transfer function and System impulse response with different roll-off factor
12 Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing ( ) [ ] ( ) [ ] 2 41 2cos )2(sin2)( tWoW tWoW tWocWoth −− − ⋅⋅= π Mathematically the transfer function of the raised cosine filter can be expressed as: (I.5) (I.6) Where W is the absolute Bandwidth. W o = 1/2T represents the minimum Bandwidth for the rectangular spectrum and the -6dB Bandwidth. The roll-off factor is defined as: (I.7) In the following figures the impulse response of the raised cosine filter forα= 0 and α= 0.5 is shown. Figure1. 16 VPI impulse response for the raised cosine forα= 0 and α= 0.5 In our simulations a typical roll-off factor value will be 0.2. 1.2.2 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. Due to imperfect sampling, after the DAC some residual alias appear and make impossible for any practical filter to separate the alias form the desired signal. The solution is to use zero padding in the correct positions of the IFFT input sequence in order to shift the aliases away from the OFDM signal, as shown in figure 1.17. Wf WafWWo WWof fH WW WWf > <<− −< = − −+ 2 2 )( 0 cos 1 )( 0 02 4 2 π Wo WoW r − =
CHAPTER I. OFDM SYSTEMS____________________________________________________________________13 Figure1. 17 Oversampling used to shift aliases away, [P2] In order to ensure the main OFDM signal is preserved, the zero data values are mapped onto the highest positive frequencies and lowest negative frequencies (those around ), while the nonzero data values are mapped onto the subcarriers around 0 Hz, so the zero-padded frequencies have to be around the Nyquist channel. Due to the subcarrier numbering in the IFFT/FFT process, these subcarriers are located in the middle of the N subcarrier sequence. 1.2.3 Cyclic Prefix As said before, dividing the data stream into N subcarriers makes the symbol period N times longer, and it also reduces the delay spread or chromatic dispersion relative to the symbol time. To avoid interferences between OFDM symbols (meaning null ISI) and also to eliminate ICI, a guard time is introduced for each OFDM symbol after the IFFT, where the OFDM symbol is cyclically extended, as shown in figure 1.18. This cyclical extension is called the cyclic prefix (CP). Figure1. 18 Cyclic prefix in an OFDM symbol (time domain sequence), [P2] As long as the cyclic prefix duration is equal or longer than the maximum delay caused by the channel, the effect of one symbol over its neighbours will be limited to this cyclic prefix guard time without damaging the information part. The effect of a cyclic prefix length shorter than the drift caused by chromatic dispersion in optical OFDM is shown in figure 1.19, where an OFDM signal is represented with different colours for each subcarrier:
14 Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing Figure1. 19 ISI because an insufficiently large CP [P2] 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 [B3]. The addition of enough CP not only eliminates ISI but provides some flexibility in the starting time of the FFT sequence thus easing synchronization as shown in Figure 1.20 and in [P2] Figure1. 20 Synchronization with CP, [P2] 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 values for a cyclic prefix in an OFDM system range from 10 to 20%. Figure 1.21 represents the OFDM signal generation process specifying how the cyclic prefix and zero padding are added.
CHAPTER I. OFDM SYSTEMS____________________________________________________________________15 Figure1. 21 OFDM signal generation schematic 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 1.22: Figure1. 22 OFDM signal reception schematic All that is explained in this section is from the electrical OFDM signal point of view. In the following chapter the optical channel will be analysed in order to see how to modulate and detect the signal in the optical domain.
22______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing Figure2. 4 Mach-Zehnder modulator The operating principle of the Mach-Zehnder is based on the electro optical effect that occurs in some crystals such as the lithium niobate (LiNbO3). This effect makes the optical signal sensible to a refraction index whose value depends on the electrical field E applied. The three electrodes depicted in figure 2.4 induce the electrical field which depends on the RF signal applied over the electrooptical crystal. Due to the electrooptical properties the phase of the optical wave propagating inside it receives a phase modulation proportional to the applied electrical field. The optical signal will be amplitude-modulated after the two optical arms recombine at the device output owing to the phase difference between the signals into each arm. In the configuration of figure 2.4 based on a coplanar line, the field applied into each of the optical arms follows opposite directions which leads to a phase change equal in magnitude and opposed in sign, therefore the relative phase change is twice that experienced by the wave in one of the arms. If the optical power C at the output of the MZM is expressed as a function of this phase difference ∆[ which is proportional to the drive voltage, we get: C(G)=C(G)∙(G)=C(G)8\F']∆[(G)^ , (II.15) Where d(t) is the MZM power transfer function. Figure 2.5, represents the transfer functions of the optical intensity and optical field..
CHAPTER II. Optical Channel_____________________________________________________________________23 Figure2. 5 Transfer functions of the opticali ntensity and optical field An appropriate bias must be applied in order to work into each one of the interest working points: • Quadrature Point: IM systems, used in conjunction with DD mainly. • Null-point: AM systems with suppressed carrier, used mainly in combination with coherent detectors. 2.2.2.1 Chromatic Dispersion amplitude fading 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” (DSB), as the OFDM signal is present symmetrically at both sides of the optical carrier. Since each of the sidebands will experience different phase shifts due to Chromatic Dispersion, when they are detected into the same electrical frequency their interference will result in amplitude fading or even total cancellation. The optical modulation can be thought as a mixing upconverting process which generates two frequencies. In reception, an image rejection filter is required in order to avoid destructive interference when the two frequencies are downconverted to the same original frequency. This is shown in figure 2.6, where A* is the complex conjugate of the main OFDM signal A.
24______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing Figure2. 6 Optical OFDM modulation using a standard MZM It will be seen that this is a relevant fact to take into account in the different optical OFDM systems implementation. 2.3 Optical demodulation techniques Basically there are two techniques in which an optical signal can be detected at the receiver: direct detection (DD) and coherent detection (CO-D). 2.3.1 Direct Detection The direct detection is the simplest and more cost-effective optical detection method. Only a single photodiode is required to detect the transmitted optical signal. Mathematically the detected photocurrent is obtained by applying the square modulus operation over the low-pass equivalent of the incoming optical field. 2 )()( txtI ∝ (II.16) 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 detector’s 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 contributions between harmonics to cancel, as shown in figure 2.7:
CHAPTER II. Optical Channel_____________________________________________________________________25 Figure2. 7 Conventional IM/DD transmission Systems 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 a 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 2.8: Figure2. 8 Transmission systems for a dispersive fibre Intuitively, 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 anymore. 2.3.2 Coherent Detection Coherent detection-based systems have a better sensitivity at the receiver side and their spectral efficiency is higher. In addition, they allow to compensate for linear channel impairments such as chromatic dispersion because the detected photocurrent is proportional to the optical field amplitude. However, the main drawback is the high requirements in the receiver design because they use a local oscillator and also require polarization control.
26______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing Figure2. 9 CO-OFDM receiver Since they are not a nuclear part of the works developed within this Master Thesis, the studies related to coherent receiver carried out have been placed in annex D. 2.4 Equalization and Reference frequency 2.4.1 Equalization concept In order to obtain an OFDM signal without errors at the receiver, the use of cyclic prefix (explained in chapter I) 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 different phase changes depending in which subcarrier they have been assignedas shown in the following figure 2.10: Figure2. 10 Phasedistortions on the received constellation Consequently, an equalizing stage has to be introduced right after the FFT operation at the receiver in order to correct the phase and amplitude levels. The design parameters for this stage should be obtained through a channel estimation, which is usually performed with training sequences. In the chapter V it will be explained how to implement a training sequence based equalizationin order to compensate the required phase for each OFDM subcarrier
CHAPTER II. Optical Channel_____________________________________________________________________27 An ideal equalization can be calculated based on the chromatic dispersion model in section 2.1 according to which each subcarrier is affected by a phase shift: _= ' ' ' B (II.16) Where L is the fibre length, is the subcarrier frequency, and ' is the second term order of the signal phase delay, expression II.7. From the D value in the fiber, which is related to ' according to expression II.8 an ideal equaliser can be designed based on the values of the fibre length, the D parameter and the positions of the subcarriers. With the basic aim of testing our understanding of the details of the optical OFDM transmission process it is our plan to design such an equalizer. The results obtained are found in chapter V. Training sequence based and ideal equalization are then the two types of equalization developed in these work. The following figures represent the received constellation in the VPI built-in demo scheme without equalization and with it. It is important to say at this point that the equalizer coefficients in the demo are given by the software and are only valid for the specific frequencies and fibre length used in it, without the slightest clue on their relation to the parameters choice or on how to obtain them if a different choice of parameters is made. Figure2. 11 Received constellation without equalization Figure2. 12 Received constellation with equalization 2.4.2 Reference frequency A mathematical analysis is needed in order to decide which the best fibre reference frequency selection is in the simulator. This analysis follows mainly from the chromatic dispersion based fibre transfer function described in section 2.1 as applied to an RF-UPconversion type optical OFDM system. This kind of systems are analysed in more detail in section 3.1.1 and constitute a nuclear part of the works carried out in the context of this Master Thesis. For the purposes of this section let us just consider that these systems modulate the OFDM signal at an RF frequency RF ω prior to their modulation at the optical frequency O ω .
28______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing In the following figure 2.13 the optical spectrum at the input of the fibre in the Long-Haul transmission demo is shown. The optical carrier and the OFDM sideband are clearly seen and also the single side band filter effect is apparent in the removal of the lower sideband. Figure2. 13 Optical spectrumatthefibre input As said, the choice of a fibre reference frequency in the simulator is to the time reference and therefore it is a somehow arbitrary choice which nevertheless has an effect on the proper OFDM signal detection. That is understood by considering that since proper time synchronization is required in practice for a proper detection of the OFDM signal, then also a proper fibre frequency reference is required for a proper OFDM signal detection at the simulator. This is why the analysis of this topic deserves some careful attention. Figure2. 14 Mathematical expressions in fibre input and output The spectrum of the input signal is expressed as follows: ))(()()( RFOOIN ZX ωωωωωδω +−+−= (II.17) Where the Dirac delta represents the carrier and z(t) is the OFDM signal. The expression of the fibre transfer function is: 2 Re )( )( f j eH ωωχ ω − = (II.18)
CHAPTER II. Optical Channel_____________________________________________________________________29 Where, linking that to expression II. 9, A= & ' B The expression of the output signal is: 2 Re 2 Re )()( ))·(()·()()·()( ffo j RFO j OINOUT eZeXHX ωωχωωχ ωωωωωδωωω −− +−+−== (II.19) With these expressions developed it is necessary to analyse the expression (II.19) with the two reference frequency positions possibilities: • of ωω = Re (II.20) 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. • RFof ωωω += Re (II.21) The constellation suffers a phase shift which also grows proportionally to the fibre length and L` , though no delay in the temporal received sequence is observed. In any case, while a constant phase shift can be compensated at the receiver, it is not that easy to try to compensate for a time delay. Thus, it has been concluded that in this matter it is best to follow the example set by the Long Haul transmission demo and to set RFof ωωω += Re in the performed simulations. In practice this will mean to synchronize the receiver so that the clock starts at the time in which the reference frequency arrives to the receiver end. A mathematical derivation has also been carried out in order to clearly establish the synchronization requirement to set the reference frequency exactly in the middle of the OFDM optical sideband. This mathematical derivation is based on
30______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing the symmetry condition of the Fourier transform (see Figure 2.15) and its details can be found in annex E. Figure2. 15 X(f) and H(f) spectrums centred and symmetric 2.5 VPI basic concepts Virtual Photonics Integrated (VPI) is a powerful simulation toolthat 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 of this project have been done with the VPI Transmission Maker application. And the results of the simulations are shown in the VPI Photonics Analyzer tool. 2.5.1 Hierarchical organization VPI is hierarchically organized. This allows the user an easy management of the modules. Each level of the hierarchycanbe treated independently or as a group when necessary. There are three hierarchy levels and they can be classified as: 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 as it can be seen in the following figure 2.16. Figure2. 16 VPI hierarchy
CHAPTER II. Optical Channel_____________________________________________________________________31 The following are the most important facts to bear in mind when working with the different hierarchy levels defined in VPI: • A star represents a unique module with a specific function which can’t be subdivided into other modules. • 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. • The universe is the only module that can be executed by the user. It represents the whole simulation scenario, and it may consist of a combination of interconnected stars and galaxies. 2.5.2 Simulation parameters 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. Each module has a Parameter editor window that allows the user to change values, to add or to delete parameters. There are two types of parameters: global parameters, which affect all the modules within a simulation, and specific parameters, belonging to a single module. 2.4.2.1 VPI global parameters VPI provides a set of defined global parameters, which are very important for the correct and efficient operation of the simulator. The most relevant are: • 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. It is linked to the bit rate since an integer number of bits needs to be simulated. Otherwise an error message is displayed. • LogicalInformation: 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 modules such as BER Estimators, Clock Recovery modules and the Channel Analyzer. • 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. • GH • BitRateDefault: it defines the transmission bit rate by setting the BitRate parameter of emitters, bit generators, etc. to BitRateDefault.
38______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing is needed. This automatically excludes IM systems where only the intensity of the optical signal is modulated. In the case of IM systems it is then assumed that the subcarriers comply with the Hermitian symmetry property (explained in detail in section 3.1.3) so that the resulting OFDM signal is real, but this means that only half of the input sequence symbols are used for bearing information. Following the scheme in figure 3.1: • Optical Intensity modulation can be achieved by using either a direct modulation laser, a MZM in quadrature point or an electro absorption modulator • For field modulation either a MZM in the null point may be used or else combination of IM with spectral guard bands. In order to understand how an IM modulation with spectral guard bands becomes effectively an optical field modulation, consider expression III.1: O (G)=1+ R ' F(G)− R& S F ' (G)+ RT U F V (G)+⋯ (III.1) If the spectra of s(t) and its harmonics do not overlap optically, they are detected at the receiver side at different electrical frequency bands and the intermodulation products can easily be filtered out. This entails to allocate a guardband between the optical carrier and the data sideband that is at least as wide as the signal’s band. The guardbands can be allocated in two different ways: • To use an RF upconversion stage with f RF =1.5BW. • To zero pad the first N/4 subcarriers at the input of the IFFT processor in Hermitian symmetry systems. Given the correspondence of the subcarrier numbering at the input of the FFT processor and the spectral location of subcarriers, see figure 1.3, the zeros will be located between the carrier and the data signal. In spite of requiring the extra RF hardware, the advantage of the first option is that a 4 times smaller IFFT processor can be used. In this Master thesis two of the combinations in figure 3.1 are analysed in more detail using the VPI software: • Field modulation with IM + Guard Bands + SSB Filtering and with electrical IQ. It will be called RF Up-conversion based on Intensity modulation.
Chapter III. Optical OFDM systems_________________________________________________________________39 • Intensity modulation with a MZM in quadrature point,this scheme will be called Hermitian since it uses Hermitian symmetry. 3.1.1 RF upconversion based on intensity modulation As said, when performing optical modulation of a baseband OFDM signal with a standard MZM, in order to avoid chromatic dispersion amplitude fading, one of the two resulting sidebands must be suppressed. An optical filter at the MZM output can be used for that purpose. Also, in order to avoid overlap of the different harmonic optical sidebands resulting from the IM modulation a guardband of at least the size of the OFDM signal band must be allocated between the optical carrier and the signal’s band (see the spectrum in figure 3.2) . This guardband is also good for avoiding electrical frequency overlap when using direct detection. To that effect, the baseband OFDM electrical signal can be first upconverted to a proper RF frequency, as depicted in figure 3.2. Figure3. 2 Electrical upconversion of the complex OFDM baseband signal [B1] So, 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, hence the name Field Modulation. This is the technique used in the RF upconversion based on Intensity Modulation kind of optical OFDM; the following figure 3.3 shows its schematic.
40______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing Figure3. 3 RF upconversion based on Intensity Modulation schematic [P2] In this configuration, the whole input sequence of the IFFT is carrying data, though the zero padding oversampling method described in Chapter I can be applied 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 in QP configuration. 3.1.2 Optical IQ modulation By using an IQ MZM 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 3.4, where the real and imaginary components of the OFDM signal are directly fed to the IQ modulator consisting in the parallel association of two MZMs with a biascontrolled phase shift in one of the two parallel arms. In the optical IQ OFDM scheme the two MZMs are biased at the null point and the phase shift is adjusted to π/2. For simplicity, oversampling is neglected.
Chapter III. Optical OFDM systems_________________________________________________________________41 Figure3. 4 Optical IQ modulation schematic [P2] This scheme provides the possibility of a full-data IFFT input sequence 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. This configuration will not be considered in the simulations of the following chapters and is left to future works. 3.1.3 Hermitiansymmetry In general, the output of an IFFT is complex rather than real. In systems where a single real output is required, the input vector to the IFFT, I, is constrained to have Hermitian symmetry so that the imaginary component of the IFFT output is zero. The following figure 3.5 shows the input vector 12/0 ... − = N XXX being mapped to the IFFT inputs 10 ... − = N III * 1 *12/2/12/010 ...,,...... XXXXXII NNNN −−− = (III.2) where * 1 X denotes the complex conjugate of K X and N is the size of the IFFT. The inputs O X and 12/ −N X which correspond to the dc and Nyquist frequencies are set to zero, as are the inputscorresponding to guard band frequencies. The number of independentcomplex values transmitted perOFDMsymbol depends on the width of the guard band. If the guardband between the optical signal and the OFDM signal (W g ) is equal to the bandwidth used for the OFDMsignal(W U ) (as it can be seen in figure 3.5), then only N/2 independent complex values can be transmittedperOFDMsymbol. The transmitter is simple to set up.
42______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing Figure3. 5 OFDM transmitter using hermitian symmetry The hermitian symmetry mathematical expression starting from the OFDM basic mathematical expression I.3 can be seen in annex G. 3.2 Optical OFDM demodulation techniques As said before in chapter II, there are two basic kinds of techniques allowing the demodulation of an optical signal into the originally transmitted electrical signal: those are the direct detection (DD) and the coherent detection (CO-D). Figure3. 6 Optical-Electric Conversion About detection the usual would be to use DD with IM systems, and CO-D with field modulation. In the case of the IM+guardbands type of Field Modulation the same non-overlaping sidebands principle used to justify effective AM modulation through IM modulators (section 3.1) may be applied to justify that direct detection plus electrical downconversion is effectively a form of linear (non square-law) detection. Because of the simulated transmission scenarios within this work use direct detection, in the following some important concepts of this kind of OFDM receivers are explained. Coherent OFDM receivers are described in annex D. 3.2.1 OFDM Direct Detection The simulations shown in Chapter IV will use the RF upconversion based on IM technique with DD at the receiver. For this configuration, the optical OFDM signal F ) (t) can be described as: F)(G)='a; + +b'a(; + c∆;) ∙F(G) (III.3)
Chapter III. Optical OFDM systems_________________________________________________________________43 Where: • is the main optical carrier frequency. • ∆ is the guard band between the main optical carrier and the OFDM band • bis a scaling coefficient that describes the OFDM band strength related to the main carrier. • The term F(G) represents the baseband OFDM signal Thus, the real valued electrical OFDM signal is available after upconversion and drives directly the e/o modulator. The following figure 3.7 shows the schematic designed byLowery and Armstrong in [P1] for one of the first direct detection optical OFDM published simulations using VPI software. Figure3. 7Long-haulopticalcommunicationsystem After the signal passes through the fibre link with chromatic dispersion, the OFDM signal can be approximated as: d(G)= ('a;+cef(∆;)cg()) +b ('a(;+c∆;)cg()) ∙ h 8 i ('a;jcef(;j)) k &l imk &lc [ n =783 i' / ' (III.4) Where: • [ n ( i ) is the phase delay due to chromatic dispersion for the p * subcarrier • 3 is the accumulated chromatic dispersion in unit of picoseconds per picometer (ps/pm) • is the centre frequency of O-OFDM spectrum • c is the speed of light.
44______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing At the receiver, only one photodetector is used, which can be modelled as the square law detector so the resultant photocurrent is: H(G)∝|d(G)|'=1+2bMs'a∆;∑8i('a; j ce f (; j )e f (∆;)) k & l im k & l c u+ |b'|∑ ∑ 8i & ∗8i k ('a(; jkw@j&) ce f x; jk ye f x; j& y) k & l i & m k & l c k & l i k m k & l c (III.5) • 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. The following figure 3.8 shows the received optical spectrum: Figure3. 8 Received optical spectrum The OFDM subcarriers have a bandwidth z { and there is a gap,z /|) , between the carrier and the subcarriers, which can be obtained by RF upconversion of the electrical OFDM signal or by zero padding at the input IFFT sequence. 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 3.9 shows the optical spectra of the contributions to this mixing and the resulting electrical spectra after downconversion. Figure3. 9 Useful components in the electrical spectra
Chapter III. Optical OFDM systems_________________________________________________________________45 When a frequency guard band is used (z /|) }z { ) 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: Figure3. 10 Unwanted out of band noise The single tap equalizer function in the OFDM receiver is needed in order to correct the amplitude distortions caused by frequency roll-off of the components and the phase distortions. Figure 3.11 represents a typical DD receiver used in optical OFDM, where the optical and electrical spectra before and after the photodetector are also represented. Figure3. 11 Direct detection at the receiver It can be seen that the second-order intermodulation products are 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 electrical filtering. 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 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.
46______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing
Chapter IV. OFDM for Long-Haul Transmission demo___________________________________________________47 4 Chapter IV. OFDM for Long-Haul Transmission demo The objective of this section is to analyse in detail the OFDM for Long-Haul Transmission Demo provided by VPI. This demo consists in a transmission over 1000km optical fibre link following the upconversion amplitude modulation and direct detection downconversion technique described in chapter III. This chapter is structured as follows. First of all a general idea from the scenario is explained, analysing in detail the important global parameters. Secondly an inside view is done into the modulation and demodulation galaxies, so the RF upconversion and downconversion are shown. Finally the optical channel and its relevant parameters are analysed. 4.1 General idea Figure4. 1 Schematic of the OFDM transmittermodule [VPI] Analysing the universe of this demo it can be seen that the OFDM coder module is placed inside an OFDM transmitter galaxy, where a frequency upconversionis applied to the signal after being generated, as it will be seen later by looking inside the galaxy. In addition the RF frequency value can be selected so that a gap between the OFDM signal spectrum and the optical carrier exists so the unwanted mixing products appearing due to the intensity modulation (IM) and direct detection (DD) method used fall outside the OFDM bandwidth. This demo shows to the user three kinds of output results: the received constellation, the spectrum at the receiver input and the error vector magnitude (EVM) at the receiver output. The EVM can be considered as an indicator of how far the received constellation points are from their ideal location(see mathematical explanation in annex B).
54______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing the OFDM coder and the DriverAmplitude value will have an effect on the sideband to carrier ratio which is an important parameter in the simulations. In the built-in demo the DriverAmplitude value is set to 0.17. In the MZM module the bias parameter is fixed at 0.5 because the MZM must work in quadrature point (QP). The laser operating at CW provides the optical carrier to be modulated, and its most relevant parameters are: o Emission frequency: 193.12 THz. o Average power: 5 mW o Linewidth: 1 MHz The optical filter it is connected to the MZM output. It is used to suppress the lower sideband resulting from the optical modulation. The values of the attenuation and chromatic dispersion coefficient are typical for a transmission in 3rd window (α=0.2 dB/Km and D=17ps/nmKm ). The rest of values are set to default. 4.4.2 Fibre link In order to better resemble the real fiber link conditions in the simulation scenario the fiber link is arranged as a recirculating loop where in every loop losses are compensated by optical amplification, and optical filtering is used to remove ASE (Amplified Spontaneous Emission) noise resulting from the amplification. The simulation example comprises 10 loops of 100 Km. Figure4. 9 Fibre link 4.4.3 Photodiode in direct detection configuration Figure4. 10 Photodiode at the receiver
Chapter IV. OFDM for Long-Haul Transmission demo___________________________________________________55 The signal at the receiver is detected by a photodiode in DD configuration. After DD and decoding, chromatic dispersion is compensated by correcting the phase of each sub-carrier separately with the equalization.
56______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing
Chapter V. Customized demo____________________________________________________________________57 5 Chapter V. Customized demo The main objective of this chapter is to generate a customized simulation performed in VPI, this demo will be called Customized demo. These simulations were built to perform the same functions as the Long Haul transmission demo, but presenting more flexibility in coder and decoder parameters and functions, and also introducing new advantages and functionalities to the simulation scenarios. The coder and decoder will be implemented with a Matlab coding offering the user the possibility to modify the functions to adapt them to his/her specific needs. When building the new simulation scenario some additional features have been added with the main goal of making the work with the demo more user friendly and flexible. These are: - BER calculation - Zero Padding mask - Improved cyclic prefix extraction taking into account the fibre reference frequency choice - Two types of equalization: ideal and training sequence-based - Definition of coder and decoder global parameters 5.1 General scenario Figure 5.1 shows the general scenario of the Customized demo. As it can be seen it is very similar to the general scheme of Long Haul transmission demo. The coder and decoder can be distinguished because of the images of ‘UPC’ and ‘EPSC’. Figure5. 1 General scheme
58______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing Except for the coder and decoder modules the rest of the modules have been configured as in the Long Haul Transmission demo built-in VPI demo. In order to see the differences and the introduced improvements, it is necessary to look inside the transmitter and receiver galaxies. It is important to show the different graphical outputs of this scheme and to compare them with the outputs in the Long-Haul Transmission demo. The following table represents the output graph in each point in the figure 5.1 for the two demos. 5.1.1 Long-Haul Transmission demo versus Customized demo Customized demo Long-Haul Transmission demo 1 a Electrical coder output 1 b Waveform coder output 2 Optical carrier spectrum 3 Optical spectrum at MZM output
Chapter V. Customized demo____________________________________________________________________59 4 Optical spectrum at the filter output 5 Received optical spectrum 6 Detected spectrum Table 5.1 Long Haul Transmission demo vs Customized demo in different stages As it can be seen in the table 5.1, all the outputs are the same in the two demos. Following is a study of the coder and decoder in order to see how the coder and decoder in Customized demo are implemented using Matlab and also which improvements have been done. 5.1.2 Global parameters Some parameters have been defined as global because the value will generally be the same in the transmitter and received galaxies and in all the modules of the scheme. This is an added feature which is found very convenient from a simulation user point of view. For specific simulations all parameters can also be changed in the particular module where they are used.
60______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing Figure5. 2 Universe parameters As it can be seen in the figure 5.2 the simulation uses a 4-QAM, a cyclic prefix of 0.2 and 64 subcarriers. From this point of view until now the values are equal to the Long Haul transmission demo. 5.2 Transmitterand receiver galaxies 5.2.1 Transmitter galaxy As it can be seen in the figure 5.3 the modulation galaxy has three stages as well as the Long-Haul transmission demo. These stages are OFDM coding, pulse shaping and RF up-conversion. Figure5. 3 Transmitter galaxy
Chapter V. Customized demo____________________________________________________________________61 Just the OFDM coding stage is different from the one in the Long-Haul Transmission demo. Since the coder is performed with a Matlab code, a cosimulator interface module has been added in the OFDM coding stage. As it can be seen in the figure 5.3 some modules havebeen used in order to adapt the cosimulator interface module to the VPI. 5.2.2 Receiver galaxy Figure5. 4 Receiver galaxy In the same way that in the transmitter galaxy, it can be seen that the OFDM decoding stage in this demo is different from that in the Long-Haul Transmission demo. Apart from the implementation modules needed to adapt the Matlab coding to the VPI interface, a new block is added to the decoder in order to calculate the BER estimation at the output. In fact this is one of the improvements of this demo. So at the output not only the EVM value and the received constellation are obtained as in the Long-Haul Transmission demo, but also the BER estimation. 5.3 OFDM basics results This section is devoted to the general ideal of generating from the OFDM theory study the code for the coder and the decoder and to check that the output signals at every signal stage were the same as in the Long-Haul transmission demo. 5.3.1 Normalization By looking at the VPI coder output it can be concluded that a normalization of the output signal was performed:
62______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing Figure5. 5Detail of coder output real part in customized demo Figure5. 6Coder output real part in customized demo Figure5. 7 Detail coder output real part in Long-Haul Transmission demo Figure5. 8 Coder output real part in Long-Haul Transmission demo Note that, in the figures only the real part is represented. By testing over the Long Haul demo (sending only ones and only zeros sequences) it can be deduced that the Long Haul transmission demo performs a normalization which takes the maximum modulus value of the complete temporal (contained in a Time Window) sequence obtained and then it divides its real and imaginary parts by this value before sending the complete TW sequence to the coder output. Thus the coder output signal is always normalized to have a maximum unity modulus in its largest temporal sample. The normalization constant is therefore dependent on the specific set of samples found at the coder input and on the parameters of the modulation and it is only defined after the whole temporal signal for a specific simulation is obtained. In the decoder the normalization is the same that is, it normalizes the decoder input sequence so that its largest sample has unity modulus. The piece of code developed in order to perform the normalization is shown below.
Chapter V. Customized demo____________________________________________________________________63 % Normalization at the output of the OFDM coder mod = sqrt(real(y).^2+imag(y).^2); maxmod = max(mod); y_real_mod = real(y)./maxmod; y_imag_mod = imag(y)./maxmod; % Paquete de información eléctrico que enviamos al MZM y = y_real_mod + y_imag_mod*1i; % Normalization at the input of the OFDM decoder mod = sqrt(y_real.^2+y_imag.^2); maxmod = max(mod); y_real_mod = y_real./maxmod; y_imag_mod = y_imag./maxmod; y = (y_real_mod + y_imag_mod*1i); In this case the BER estimation value will be not affected because the BER calculation module approximates the wrong points to the correct point. If the modulation is higher than 4-QAM the BER calculation will be wrong because the BER calculation module will perform a bad approach for example in 16-QAM the normalization will be 3 instead of 1 that is the maximum value in the constellation. Thus, the conclusion obtained from this point is that always the maximum value has to be found and all the sequence has to be normalized to this value. The following table 5.2 shows the resulting graphs in the Customized demo versus Long-Haul Transmission demos, with 4-QAM: Customized demo coder and decoder outputs Long-Haul Transmission demo coder and decoder outputs Coder electrical output (real part)
70______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing With the figures 5.13 and 5.14 it can be seen that with both equalizations the results are the approximately the same, but the improvement respect to LongHaul Transmission demo in figure 5.15 is evident. Figure5. 15 Received constellation in Long Haul demo withe qualization and cyclic prefix. EVM = 0,176069716600399 The Matlab code used for this possibility is the following: %% Cyclic prefix new extraction yy1_SP=reshape(yy1_adc,OFDM_LENGTH,NTS_OFDM); yy1_CP = zeros(OFDM_LENGTH,NTS_OFDM); yy1_CP(1:CP_LENGTH/2,:) = yy1_SP(OFDM_LENGTHCP_LENGTH/2+1:OFDM_LENGTH,:); yy1_CP(CP_LENGTH/2+1:OFDM_LENGTH,:) = yy1_SP(1:OFDM_LENGTHCP_LENGTH/2,:); yy1_CP_OUT = yy1_CP(CP_LENGTH+1:OFDM_LENGTH,:); 5.4.4 Zero padding implementation A zero padding mask is defined as a global parameter offering the user the possibility to insert zeros in the chosen subcarriers. It is a vector that indicates the positions of the subcarriers that have to be set to zero. As explained in section 1.2.2 this is another way to create a gap between the OFDM signal and the DC component which allows to avoid the problems carried by the use of analogue mixers and oscillators. The more zeros are added, the larger will be the created gap, though the bitrate efficiency will decrease. 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
Chapter V. Customized demo____________________________________________________________________71 products both in emission when using IM modulation and at the receiver when using DD. Apart from these, other zero padding schemes can be thought useful and that is why it has been chosen to provide this flexibility to the user and allow that he/she may introduce zeros in any subcarrier. A generalization of the zero padding concept would be the use of power-loading or bit loading schemes that could rely in the definition of bit-loading and power loading vectors which will follow the same basic idea of the zero padding mask. Since into the Matlab code the OFDM symbol sequence is arranged in a matrix of dimensions N_FFTxNTS_OFDM, where each row represents a subcarrier, the basic idea used into the Matlab code has been to create a vector (Nc_Mask) which contains the index of the zeroed rows. This is accomplished in the Matlab code by making use of the function find as seen in the code excerpt that follows. The ZP extraction follows a similar approach and it is also seen in the code excerpt. %% Zero padding is inserted to obtain a matrix of size (N_FFT x NTS_OFDM) A_ones = ones(1,N_FFT); % Vector of ones with length N_FFT A_ones(ZP_Mask) = 0; % Insert in the ones vector the zeros introduced by the user in ZP_Mask Nc_Mask = find(A_ones); % Generate a new vector Nc_Mask with the positions where it has to be information xx1_OFDM_ZP = zeros(N_FFT, NTS_OFDM); % Generate a zeros matrix of N_FTT x NTS_OFDM xx1_OFDM_ZP(Nc_Mask,:) = xx1_OFDM_INFO; % Fill in the zeros matrix with information in the positions indicated by Nc_Mask %% Zero padding extraction A_ones = ones(1,N_FFT); % Vector of ones with length N_FFT A_ones(ZP_Mask) = 0; % Insert in the ones vector the zeros introduced by the user in ZP_Mask [Nc_Mask] = find(A_ones); % Generate a new vector Nc_Mask with the positions where it has to be information yy1_QAM = yy1_FFT(Nc_Mask,:);
72______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing
Chapter VI. Hermitian symmetry demo______________________________________________________________73 6 Chapter VI. Hermitian symmetry demo This chapter is devoted to the pure baseband over optical system based in obtaining a real OFDM signal by imposing a Hermitian symmetry among the subcarriers, thereby wasting half the system’s capacity, the advantage being in the removed requirement of an RF upconversion stage. This real-valued OFDM signal is IM modulated over an optical carrier and sent through the fibre to be directly detected at the receiver side. Besides reducing by a factor of 2 the required capacity, this scheme is prone to both IM modulation sidebands overlap in the transmitter and intermodulations product corruption in the receiver. These two effects can be avoided by the allocation of spectral guardbands between the carrier and the data signal which in the RF upconversion scheme can be easily achieved by a proper selection of the RF frequency relative to the signals bandwidth. In the hermitian symmetry scheme the guardband can be allocated again by sacrificing half of the capacity still available (already a factor 4 reduction with respect to the RF upconversion scheme at the expense of avoiding the RF upconversion stage). Figure 3.5 shows this graphically. In this chapter the development of a second optical OFDM system demo scenario is described and studied. This scenario is based on the hermitian symmetry baseband over optical OFDM system with direct detection. This system is based on a pure and simple IM-DD optical transmission system and as such, in the longer distances and higher bandwidths scenario it will suffer from the chromatic dispersion nonlinear distortion explained in section 2.1. The goals here are first of all to develop the system so that further research can be carried on and also to establish which the limits of simple cost-effective systems are. And all of that in a user-friendly flexible simulation setup that can be easily and conveniently used by other people in the research.
74______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing 6.1 General scheme Figure6. 1 General scheme The general scheme is very similar to the customized demo but as it can be seen in the figure 6.1 a different number of FFT is used. Due to the Hermitian symmetry nature only half of subcarriers are useful. So in the no-guardband approach the number of carriers has to be two times bigger than in the Customized demo in order to send the same data quantity. In the hermitian symmetry guardband approach, because of the zero padding insertion, the number of FFT is four times bigger than in the customized demo. The transmitter and receiver galaxies will be studied in detail in order to see the differences with the customized demo. 6.2 Transmitter galaxy In the following figure 6.2 it can be seen that in the transmitter galaxy the RF up-conversion stage has been eliminated.
Chapter VI. Hermitian symmetry demo______________________________________________________________75 Figure6. 2 Transmitter galaxy Only one output will be necessary in the transmitter, because only the real part is transmitted but in this scheme both outputs are implemented, in order to check what is happening in the imaginary part. In order to see that the hermitian symmetry is performed the two pulse shaping outputs are shown in the following figures 6.3 and 6.4. Figure6. 3 Imaginary pulse shaping output Figure6. 4 Real pulse shaping output With figures 6.3 and 6.4 it becomes evident that at the transmitter output only the real part is present so the hermitian symmetry is correctly performed. In the Matlab code the flipud function is used in order to allocate the complexconjucate symbols in the correct way i.e the last complex conjugate in the Nc/2+1 position, Nc is the number of subcarriers which carry information. A brief excerpt of the code showing that follows.
76______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing %% Zero padding of the Hermitic DMT mode hermitic_OFDM = zeros(N_FFT,NTS_OFDM); % Global zeros matrix hermitic_OFDM(2:(N_FFT/2),:) = xx1_OFDM_ZP; % The especial matrix is inserted in the first half of the global matrix but the first row is zero. hermitic_OFDM((N_FFT/2)+2:N_FFT,:) = flipud(conj(xx1_OFDM_ZP)); % The conjugate of the special matrix is flipped and inserted to the second half of the global matrix but with the first row is zero In order to generate the hermitian symmetry sequence, first of all two zeros are added and one of them is just in the first position of the matrix and the other in N/2 which is exactly the middle of the sequence. The information is allocated from No+1 until N/2-1 and from N/+1 to N the complex conjugate of the information is inserted. The following figure 6.5 shows the correct order of the sequence in the same form that are implemented at the Matlab code: Figure6. 5 Correct order of the sequence in Matlab code 6.2.1 Zero padding insertion As it is explained in the first section of this chapter zero padding can be used to allocate a guardband between the optical carrier and the OFDM sideband. In this setup the concept of the zero padding mask is applied on top of the required hermitian symmetry. That is, when the user selects the hermitian symmetry he/she must know that already half of the FFT subcarrier have been determined by the symmetry and therefore the ZP mask vector can only contains as a maximum positions N/2. The insertion of the ZP is then done exactly as in the previous case but restricted to the positive subcarriers. This is taken into account in the Hermitian Symmetry code as shown. %% Zero padding is inserted to obtain a matrix of size (N_FFT x NTS_OFDM) %This zero padding is used as a guard band A_ones = ones(1,(N_FFT-2)/2); A_ones(ZP_Mask) = 0;
Chapter VI. Hermitian symmetry demo______________________________________________________________77 Nc_Mask = find(A_ones); xx1_OFDM_ZP = zeros((N_FFT-2)/2,NTS_OFDM); xx1_OFDM_ZP(Nc_Mask,:) = xx1_OFDM_INFO; 6.3 Receiver galaxy Figure6. 6 Receiver galaxy In the receiver galaxy only one pulse shaping is used because only the real part of the signal is received. Although only the real part is received two inputs are needed in the cosimulator module, just for the received real signal and the other is the logical channel that contains the input sequence used to BER calculations, training sequence... 6.3.1 Zero padding extraction The zero padding is extracted at the receiver in the same way that is inserted at the transmitter. In the following Matlab code it can be seen the extraction: %% Zero padding extraction A_ones = ones(1,Nc+length(ZP_Mask)); % Vector of ones with length N_FFT A_ones(ZP_Mask) = 0; % Insert in the ones vector the zeros introduced by the user in ZP_Mask [Nc_Mask] = find(A_ones); % Generate a new vector Nc_Mask with the positions where it has to be information yy1_QAM = hermitic_OFDM(Nc_Mask,:);
78______________Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing 6.4 Final results In order to compare the results of this demo with the results in the Long-Haul demo and Customized demo, the received constellation and the EVM value is obtained. Figure6. 7 Received constellation in Hermitian Symmetry demo The used simulation parameters in order to obtain the constellation are the following: Figure6. 8 Simulation parameters in Hrmitian Symmetry demo
Chapter VI. Hermitian symmetry demo______________________________________________________________79 It can be observed that the Nc (number of information carriers) is different to the other simulation scenarios. In this case the number of useful carriers is N-2 because the positions 0 and Nc/2 have to be zero for the hermitian symmetry. In order to compare this scenario with Long Haul demo and Customized demo the same fibre length is being used, L=1000Km. The EVM in this demo is 0,25 so the conclusion is that this kind of scerarios can be compared with RF upconversion scenarios, altought the EVM value in this case is higher than the other EVM values studied in this work. The drawback is that in this scenario the quantity of information data sent is smaller compared with the RF upconversion scenarios using the same number of FFT. For this reason in hermitian symmery demo the N_FFT value is 256 instead on 64 used in Long Haul transmission demo and in Customized demos with this configuration the information data per OFDM symbol is the same. To achieve the same bandwidth information in RF upconversion demos, the bit rate in Hermitian symmetry demo is four times bigger (in this case BR=40 Gbps).
86 Cost-effective Optical Transmission Systems based on Orthogonal Frequency Division Multiplexing 9 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 • DDDirect 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 • TWTime Window • QAM – Quadrature amplitude modulation • VPI - Virtual Photonics Inc. • ZP-Zero Padding
ACRONYMS_________________________________________________________________________________87