  In this paper we use a variation of simulated annealing algorithm for
optimizing two-dimensional constellations with 32 signals. The main objective
is to maximize the symmetric pragmatic capacity under the peak-power
constraint. The method allows the joint optimization of constellation and
binary labeling. We also investigate the performance of the optimized
constellation over nonlinear satellite channel under additive white Gaussian
noise. We consider the performance over systems with and without
pre-distorters. In both cases the optimized constellations perform considerably
better than the conventional Amplitude Phase Shift Keying (APSK) modulations,
used in the current digital video broadcasting standard (DVB-S2) on satellite
channels. Based on our optimized constellations, we also propose a new labeling
for the 4+12+16-APSK constellation of the DVB-S2 standard which is Gray over
all rings.
