Singularity analysis and elimination of CMA in multistage PMD channel model

Polarization-division-multiplexed(PDM) optical coherent systems is considered a promising technique for next generation optical networks. With coherent detection, various impairments in the optical transmission system can be compensated by using digital signal processing (DSP) in the electrical domain. Constant modulus algorithm (CMA), due to its simplicity and immunity to phase noise, has been widely used to demultiplex polarizations and compensate received signals. On the other hand, CMA suffers from the singularity problem which results from Polarization- Dependent-Loss (PDL) and the less sensitivity in phase of CMA. Although many people have researched the singularity problem of CMA both in theory and experiments (modify CMA to avoid singularity problem), their theoretical channel model only contains fiber birefringence and does not consider the situation of multistage channel model which is used in long distance transmission system. Then we analyse the performance of CMA in the channel with multistage channel model through simulation. We change the initial tap of the traditional CMA which can achieve correct polarization demultiplexing without singularity in one stage channel model. But it is not very suitable in multistage channel model. We analysed singularity ratio in long distance transmission system. The simulation results play an active role in following research on singularity problem and the performance of CMA.