Optimal Constellations for the Pragmatic Receiver in the DVB-S2 Standard

In this paper we use a variation of simulated annealing algorithm for optimizing two-dimensional constellations with up to 32 signals. We focus on optimizing the \emph{pragmatic} average mutual information, which is shown to be the relevant measure for pragmatic schemes usually adopted in the receiver. The method allows the joint optimization of constellation and binary labeling. We investigate the performance of the optimized constellation over both AWGN channel and nonlinear satellite channel. The optimized constellations perform considerably better than the conventional Amplitude Phase Shift Keying (APSK) modulations over the AWGN, used in the current digital video broadcasting standard (DVB-S2). As for the nonlinear channel, we consider the so called Soft Limiter model for the high power amplifier. We provide simulation results in realistic scenarios using the DVB-S2 standard LDPC to show the gains obtained by the proposed constellations.