Parallel Methods for Optimizing High Order Constellations on GPUs

The increasing demand for fast mobile data has driven transmission systems to use high order signal constellations. Conventional modulation schemes such as QAM and APSK are sub-optimal, large gains may be obtained by properly optimizing the constellation signals set under given channel constraints. The constellation optimization problem is computationally intensive and the known methods become rapidly unfeasible as the constellation order increases. Very few attempts to optimize constellations in excess of 64 signals have been reported. In this paper, we apply a simulated annealing (SA) algorithm to maximize the Mutual Information (MI) and Pragmatic Mutual Information (PMI), given the channel constraints. We first propose a GPU accelerated method for calculating MI and PMI of a constellation. For AWGN channels the method grants one order of magnitude speedup over a CPU realization. We also propose a parallelization of the Gaussian-Hermite Quadrature to compute the Average Mutual Information (AMI) and the Pragmatic Average Mutual Information (PAMI) on GPUs. Considering the more complex problem of constellation optimization over phase noise channels, we obtain two orders of magnitude speedup over CPUs. In order to reach such performance, novel parallel algorithms have been devised. Using our method, constellations with thousands of signals can be optimized.