Optimizing the probability mass function of complex modulated signals through adaptive channel characterization

We propose a probability mass function (PMF) optimization scheme for quadrature amplitude modulation (QAM) signals by considering the parametric characteristic of the training sequence. The training sequence for optimization is mapped in standard Maxwell-Boltzmann (M-B) distribution, and the considered characterizing parameters incorporate either the noise variance or the error matrix of the received symbols. The proposed PMF optimization is based on independent reallocation within each constellation ring, generating new distribution with almost the same entropy and transmitted power as the original distribution. This reallocation mechanism is model-free and iterative-free with very low computational complexity. By characterizing the channel in terms of constellation performance asymmetry, PMF reallocation can be effectively implemented to supplement the existing equalization algorithm. The effectiveness of this approach is experimentally verified in a 40-km transmission system with 24 Gbaud 64-QAM signals under three different scenarios. Through PMF reallocation, we achieve generalized mutual information (GMI) improvement of ∼0.06 and throughput improvement of ∼1.5 Gbit/s before forward error correction in comparison with the standard M-B distribution. The proposed mechanism provides a solution to obtain the optimal PMF in practical communication channels, which suffer from various types of noises and distortions.