In this paper, a constant modulus algorithm (CMA) with reduced probability of singularity is proposed. Before implementing the conventional CMA, the correlation matrix of the signals on different polarizations is evaluated. Through singular value decomposition (SVD), it is possible to find the polarization-dependent loss (PDL) and conduct the channel inversion operation by multiplying two matrices on the received signals, i.e., the unitary matrix obtained from SVD and the inverse of the PDL matrix. The proposed algorithm has been implemented in an optical link which is divided into multiple sections. Each section has a 60-km fiber and the PDL of 0.6 dB. It is found that the proposed method greatly improves the singularity avoidance performance in comparison with the standard CMA. The proposed method can be combined with the existing singularity avoidance techniques to further improve the performance. In the combined algorithm, the data are pre-processed by multiplying the PDL mitigation matrix and is then de-multiplexed by the tap-coefficient constrained CMA or the two-stage CMA. Promising performance is obtained with the combined algorithms so that the singularity problem is completely eliminated with the optical signal-to-noise ratio of 18 dB and the PDL of 15 dB. The proposed algorithm, in combination with the existing algorithms, is expected to significantly improve the performance of the polarization-division multiplexing systems.
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