Blind polarization demultiplexing algorithms based on complex independent component analysis (ICA) by negentropy maximization for quadrature amplitude modulation (QAM) coherent optical systems are disclosed. The polarization demultiplexing is achieved by maximizing the signal's non-Gaussianity measured by the information theoretic quantity of negentropy. An adaptive gradient optimization algorithm and a Quasi-Newton algorithm with accelerated convergence are employed to maximize the negentropy. Certain approximate nonlinear functions can be substitutes for the negentropy which is strictly derived from the probability density function (PDF) of the received noisy QAM signal with phase noise, and this reduces the computational complexity. The numerical simulation and experimental results of polarization division multiplexing (PDM)-quadrature phase shift keying (QPSK) and PDM-16QAM reveal that the ICA demultiplexing algorithms are feasible and effective in coherent systems and the simplified ones can also achieve equivalent performance.
Method and apparatuses for algorithm on QAM coherent optical detection