Constellation Design for Memoryless Phase Noise Channels

In this paper, we optimize the constellation sets to be used in communication systems affected by phase noise. The main objective is to find the constellation which maximizes the channel mutual information under given power constraints. For any given constellation, the average mutual information (AMI) and the pragmatic average mutual information (PAMI) of the channel are calculated approximately, assuming that both the additive noise and phase noise are memoryless. Then, a simulated annealing algorithm is used to optimize the constellation. When the objective function is the PAMI, the proposed algorithm jointly optimizes the constellation and the binary labeling. We focus on constellations with 8, 16, 64 and 256 signals. The performances of the optimized constellations are compared with conventional constellations showing considerable gains in all system scenarios. In particular, it is shown that the optimized constellations are much more robust with respect to the changes in the phase noise characteristics than the phase shift keying (PSK) modulation and quadrature amplitude modulation (QAM).