On Symbol Error Performance of Probabilistic Shaping in Noise-Limited and Fading Channels

In this work, we present symbol error performance analysis of probabilistic shaping (PS) for wireless communications in noise-limited and fading channels. Two fading models considered are the Rayleigh and log-normal fading channels. The results are corroborated with simulation and compared with the conventional uniformly distributed input symbols. In all channel conditions, PS results in significant reductions in the SNR required to achieve a specific error probability compared to the conventional uniformly shaped symbols. For example, in a noise-limited channel, PS based quadrature amplitude modulation (QAM) signal results in SNR gains of 1.16 dB, 1.41 dB, and 1.52 dB compared to the uniformly distributed QAM symbols at equal entropy rates of 4, 6, and 8 bit/symbol and a symbol error ratio (SER) of
$1\times 10^{-3}$
.