Probabilistically shaped polar-coded MIMO-FSO communication systems with spatially correlated fading

In this paper, the probabilistically shaped polar-coded multiple-input multiple-output free-space optical (MIMO-FSO) communication system with or without spatially correlated (SC) fading is investigated to improve transmission performance. The designed shaping-polar encoder can flexibly generate three typical shapes of distribution via shaping bits and be decoded in the conventional method. The achievable information rate (AIR) of MIMO-FSO systems with or without SC fading is evaluated to determine the number of shaping bits for the shaping-polar encoder. The non-pairwise distributions are demonstrated to be more suitable for turbulence channels than other distributions. The results show that the AIR of the shaped 4 × 4 systems even exceeds that of the uniform 4 × 5 systems in the low signal-to-noise ratio regions over strong turbulence channels. In terms of bit error rate performance, more than 15 dB shaping gains can be achieved by the shaped 4 × 4 systems compared to the uniform single-input single-output polar-coded systems. In addition, the shaped 4 × 4 systems outperform the uniform ones ranging from 1 dB to 1.9 dB over different atmospheric turbulence channels with or without SC fading, comparable to the uniform MIMO systems with one more physical receiver.