Probabilistic Shaping in MIMO: Going Beyond 1.53dB AWGN Gain With the Non-Linear Demapper

Constellation shaping is a well-established method to improve upon a regular quadrature amplitude modulation (QAM). It is known that the gain achieved by any shaping method for an additive white Gaussian noise (AWGN) channel is upper-bounded by 1.53dB. However, the situation becomes less clear in the multiple-input and multiple-output (MIMO) setting.In this paper, we study the application of probabilistic shaping for MIMO channels. We utilize an efficient near-optimal demapper based on sphere decoding (SD) and demonstrate that it is possible to achieve more than 2dB gains, breaking the AWGN limit. It becomes possible because both signal and interference are shaped and the non-linear methods can capture this property and leverage on it to improve the demodulation performance.