Constellation Design for Channels Affected by Phase Noise
  In this paper we optimize constellation sets to be used for channels affected by phase noise. The main objective is to maximize the achievable mutual information of the constellation under a given power constraint. The mutual information and pragmatic mutual information of a given constellation is calculated approximately assuming that both the channel and phase noise are white. Then a simulated annealing algorithm is used to jointly optimize the constellation and the binary labeling. The performance of optimized constellations is compared with conventional constellations showing considerable gains in all system scenarios. 
Farbod Kayhan and Guido Montorsi
cs.IT math.IT