Joint signal‐labeling optimization under peak power constraint

SUMMARY In this paper, we introduce a variation of simulated annealing algorithm for optimizing two‐dimensional constellations with finite number of signals by maximizing the symmetric and pragmatic capacity. Our method also allows the joint optimization of constellation and binary labeling when the objective function is the pragmatic capacity. The algorithm can be applied with constraints on both the peak power and the average and peak power of the constellation. The proposed algorithm does not impose any a priori geometrical structure on the constellation and labeling. Here, we provide results only for the peak power constraints and constellations with up to 32 signals. For the symmetric capacity, optimal constellations depend on the signal to noise ratio and match in several cases the amplitude phase shift keying (APSK). On the other hand, for the pragmatic capacity several novel labeling constellation schemes are introduced, showing interesting differences between the two approaches. For modulation schemes with 32 signals, our optimized constellations perform up to 0.6 dB better than the optimized 4+12+16‐APSK used as the digital video broadcasting (DVB‐S2) standard.