I'm studying the impact of nonlinearity on system performance in long haul transmission system.
So, I need to simulate the system completely with Matlab without any optical simulation tools like VPI or Optisystem.
My system includes 7 WDM channels, each channel carry 100Gb/s PM-QPSK.
The SMF length is 1000 km in 10 span and each span is followed by EDFA.
I will consider ASE noise of EDFA, Dispersion, Nonlinearity in SMF.
Dispersion will be compensated in the Rx side using DSP.
CW laser line width 0.1MHz.
How to start and how to include all of these parameters in my simulation?
I would start with a non-linear propagation module. I assume by PM-QPSK you mean two QPSK signals modulated on orthogonal polarisation states of each carrier, so you will need to model cross-polarisation modulation between co-propagating WDM channels, in addition to SPM, FWM and XPM.
A split step Fourier solver is straightforward to implement in Matlab. Propagation proceeds by alternate time-domain and frequency-domain steps. Linear attenuation, birefrengence and chromatic dispersion are applied in the frequency domain, and Kerr effect non-linearity in the time domain.
Agrawal's "Nonlinear fiber optics" describes the background. I don't have the latest edition (linked below) which appears to offer an improved treatment of polarisation effects.
Rather than attempting to model the instantaneous changes in polarisation state over a distance of one or a few metres, I would use the Manakov-PMD formulation of the nonlinear Schrodinger equation. This uses an effective 'polarisation-averaged' non-linear coefficient, while maintaining essential information such as the relative polarisations of the WDM channels. Menyuk and Marks 2006 paper describes the derivation, and discusses the rationale and the conditions for which it is valid.
I would suggest a split-step implementation of Menyuk & Marks equation 68, but initially set PMD to zero, as in equation 64, until you have verified that the linear and non-linear effects are correctly modelled in the absence of PMD.
It is important to use a sufficiently small distance step in the split step propagator. The dispersion-induced differential phase rotation between the most widely separated spectral components should be less than one radian - possibly much less, depending on the signal powers. Too large a step size leads to unrealistically high non-linear penalties. It is also possible to generate spurious FWM peaks if the optical window is too narrow, due to the cyclic boundary conditions implicit in the FFT algorithm.
EDFA line amplifiers can be simulated as a simple linear gain with the addition of broadband noise - either uniform or with a slow wavelength dependence.
Stimulated Raman Crosstalk is a potential concern with widely spaced WDM channels, but is probably not significant with only 7 channels at 50 or 100 GHz spacing. It could be incorporated into the split step propagator, but the impact will be small for a C-band sytem. It can probably be ignored or treated as a modest differential gain tilt applied at the end of each span.
WDM filtering at the receiver is a simple linear process.
I would handle CW laser line width in the transmiter and receiver local oscillator in a separate module. The split step simulation will require time steps around 1 ps, depending on the optical bandwidth. You will need time sequences of order one hundred microseconds or more to assess the impact of laser phase noise with 100 kHz line width. Simulationg waveform arrays with a 108 dual polarisation complex elements will be slow.
You can develop the receiver module using a clean transmitter waveform, then add linear noise, polarisation scrambling and laser phase noise. When this is working, build a test waveform by concatenating multiple split step propagated waveforms, adding carrier phase noise and additional ASE noise as required.
http://www.amazon.com/Nonlinear-Fiber-Optics-Edition-Photonics/dp/0123970237
http://photonics.umbc.edu/publications/PdfPapers/PAJ201.pdf
I have not insight into this field, although I have my background in physics. But I have some insight in use of software for simulation. It might be interesting for you to formulate the equations in Modelica rather than Matlab. Modelica support modularization based on "physical entities" and can therefore handle DAE-systems. There are manyl implementation of Modelica on the market. I have for several years used a free and open-source implementation called JModelica from Lund in Sweden, see http://www.jmodelica.org
If you have been able to develop the first principle model(s) of the system, you can write the code using mfile or develop its Simulink model and simulate. For the mfile, if the model(s) is/are differential equations, you may use a command like ode45
Alternatively, if the first principle model of the system is not available, you may develop its parametric models (ARX or ARMAX) using experimental data and simulate, also, using mfile or Simulink
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