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UROS Report

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UROS Report

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UROS Report

  1. 1. Dispersion Tolerant Flexible Bandwidth Multi-subcarrier Modulation UROS Report | September 2014 | Author: Itrat Rahman | Supervisor: Dr Robert Killey | University College London Introduction: The motivation of the research is to investigate a new fibre-dispersion tolerant multi-subcarrier modulation scheme that consists of variable bandwidth subcarrier positioned at the peaks of dispersive fibre transfer function. The investigation is carried out using MATLAB simulation. First some related modulation schemes and fibre dispersion are briefly described, then the modulation scheme is overviewed and finally results of the simulation are discussed. Multicarrier modulation techniques: Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation scheme where the available bandwidth is divided into multiple narrowband sub-channels positioned at equidistant frequencies. It is based on overlapping sinc(f) methods, assuming that each subcarrier is made rectangular by pulse shaping. Orthogonally of the subcarrier is maintained as each subcarrier is positioned at the nulls of sinc functions of other subcarriers, and owing to this mutual orthogonally, each subcarrier signal can recovered by simple mathematical correlation technique. To combat ISI a guard interval known as cyclic prefix is added which is a copy of last part of symbol prepended to the transmitted symbol. As long as the cyclic extension is sufficiently larger than multipath delay spread of the channel, ISI is completely removed. However due to cyclic prefix, OFDM is a spectrally inefficient modulation scheme, and also the high sidelobes of OFDM symbols lead to significant power leakage to adjacent bands. In contrast, Filtered Multitone (FMT) modulation scheme, based on filter bank technique achieves high spectral containment. Here spectral partitioning is done by non- overlapping sinc(f) methods. The uniform synthesis bank consists of M branch filters, which are frequency shifted versions of lowpass prototype filter and each carry out signal processing on separate symbol. Cyclic prefix is not required to maintain subcarrier orthogonally, this increases the throughput. However, the time domain responses of the filter may overlap several symbol periods so per subchannel equalisation is necessary to remove the remaining ISI. [1] & [2] describe the efficient realisation of FMT using M polyphase components of filter and FFT, so that filtering is performed at a rate of 1/T instead of M/T, where T is the symbol period. Dispersive-fibre transfer function: Fibre dispersion adds nonlinearity in fibre transfer function. [4] & [5] gives analysis of dispersive fibre transfer function, the latter in microwave optical system. For this research linear propagation is assumed and adiabatic chirp is neglected, these assumptions reduce the fibre transfer function to a simple cosine function: x(f)=cos(β2ω2 z) | β2=-λ2 D/2πc, where ω is frequency in radian, z is the distance of the link, D is the dispersion parameter, and c is the speed of light. Figure 1 Parameters used in the transfer function: D=16.2 ps/nm km; λ=1532nm; z=100km Figure 1 shows the dispersive fibre transfer function which contains a series of decreasing bandwidth windows. Signal suffers maximum attenuation and phase distortion at frequencies corresponding to troughs of the plot. Figure 2 Spectrum of sinusoid & spectrum of dispersed electrical signal The dispersion affect is simulated in MATLAB with a function. Initially the function is verified and tested with sinusoids. An example is given in fig 2; the first trough of the fig 1 is at 6.281GHz, so a sinusoid of 6.281GHz is added to an optical carrier and then made to suffer dispersion through the simulation function, then it underwent square law optical detection. The plot on the right shows the expected result; the sinusoid has been completely supressed, only the sidelobe is appearing. Modulation scheme: It is evident that standalone without any compensation techniques either OFDM or FMT modulated subcarriers would suffer dispersion if the bandwidth of a subchannel spans across one of the troughs; the probability of this increases further at higher frequency since size of window decreases with frequency, hence this also limits the bandwidth of subcarriers and number of subcarriers used in modulation. Complex compensation techniques are required to compensate for the dispersion which proves to be both compromising and expensive.
  2. 2. The novel modulation technique under investigation is implemented by putting variable bandwidth subcarriers that fit the different sized windows of the dispersive fibre transfer function and do not span across a trough. The operations in MATLAB simulation are carried out in the following chronological order: 1) four QPSK channels of different bandwidth are created separately and shaped by Bessel filter of 8GHz and then filtered out by brick wall filter 2) the channels are frequency-shifted by appropriate amounts and added together with an optical carrier such that they are positioned at the peaks of the dispersive fibre transfer function and fit the different sized windows, this forms the symbol 3) the subcarriers from a DSB spectrum suffer dispersion and then undergo square-law optical detection 4) the subchannels are separately filtered out using brick wall filters and are frequency downshifted to the zero of the spectrum 5) the constellation of QPSK subchannels are plotted and investigated. Results of simulation: Results of two useful simulations are shown. The parameters for 1st simulation: λ=1532nm, z=100km, D=4.5 ps/nm km, symbol period Ts=15.626ps, symbol-rate of subcarrier 1 & 2 & 3 & 4 = 16 & 32 & 64 & 128 respectively (symbol-rate has an inverse relationship with bandwidth, so bandwidth of a subcarrier is half to that of the previous one), optical carrier amplitude=10. Figure 3 gives a sense about how the subcarriers are positioned. Figure 3 Different bandwidth subcarriers fitting the different sized windows Figure 4 Constellation plots of four subchannels The constellation plots of the four subchannels clearly correspond to that of a QPSK signal with four distinct phases with very little dispersion. Dispersion is lesser in the 1st subchannel but it remains same with the other three channels, this is because bandwidth of the first subchannel is relatively much smaller than the 3dB bandwidth of its window. Figure 5 Effects of dispersion after putting the subcarriers at the troughs of dispersive fibre transfer function Figure 5 gives the constellation plots of the subchannels when they are positioned at the troughs of the dispersive fibre transfer function instead of the peaks of the windows. The plots clearly show the signal suffered so much phase distortion that QPSK modulation format of each subchannel is completely unrecognisable. Parameters for 2nd simulation: same parameters as in simulation 1, except D=16.2 ps/nm km (typical dispersion parameter of fibre), symbol-rate of subcarrier 1 & 2 & 3 & 4 = 32 & 64 & 128 & 128 respectively (last two rates are same since the difference between the windows is very small). Results are very similar to that of 1st simulation with very little dispersion, except that the constellation plots show a slight increasing trend of dispersion with index number of subchannel. Simulations carried out on the same parameter settings, varying only the optical carrier amplitude show that dispersion decreases with increase in amplitude, and there is minimum threshold amplitude which can support QPSK modulation before phase distortion completely impairs it. Conclusion: The results of the MATLAB simulation are promising. This modulation technique could provide a good multi-subcarrier scheme for fibre network without having to use complex expensive compensation techniques. The next stage of the research would be to design the optical transmitter and receiver of the modulation and run simulation in hardware description language like Verilog. The transmitter and receiver designs are almost close to completion using the HDL coder of MATLAB. References: [1] Santosh V Jadhav (2005), Filtered Multitone Modulation and Equalization Techniques, Ph.D., Indian Institute of Technology, Bombay, India [2] IBM Zurich Research Laboratory (2000), Filtered Multitone Modulation, IBM Europe [3] OFDM: Concepts for Future Communication Systems (Signals and Communication Technology). 2011 Edition. Springer. [4] Wedding, B., "Analysis of fibre transfer function and determination of receiver frequency response for dispersion supported transmission," Electronics Letters, vol.30, no.1, pp.58, 59, 6 Jan 1994 [5] Ramos, F.; Marti, J., "Frequency transfer function of dispersive and nonlinear single-mode optical fibres in microwave optical systems," Photonics Technology Letters, IEEE, vol.12, no.5, pp.549, 551, May 2000

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