Constellation shaping for rate maximization in AWGN channels with non-linear distortion

It is well known that distortion in wireless transmit signals occurs due to the non-linearity of power amplifiers. The typical cost of wireless hardware and the relatively large distances between devices allowed for such distortion to be thus far widely neglected in the wireless literature. However, recent paradigm shifting trends point to high-density networks of extreme low-cost devices. In this article we therefore target the problem of non-linear distortion in the transmit wireless signals, which is known to be adequately modelled by non-linear noise with power proportional to the energy of transmit symbols. Specifically, we propose a probabilistic constellation shaping technique in which the discrete Maxwell-Boltzmann (MB) distribution is employed to build the optimization problem for the maximization of the mutual information between transmit and receive signals, which is efficiently achieved via a golden section method. The approach is validated via simulated comparisons against systems employing conventional constellations.