Joint Signal-Labeling Optimization for Pragmatic Capacity under Peak-Power Constraint

In this paper we introduce a variation of simulated annealing algorithm for optimizing two-dimensional constellations with finite number of signals when the objective function is the symmetric 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. For the usual symmetric capacity, optimal constellations depend on the signal to noise ratio and match in several cases the constellations already found in literature (APSK). On the other hand, for the pragmatic capacity several novel labeling-constellation schemes are introduced, showing interesting differences between the two approaches.