Performance analysis of polar-coded FSO systems using turbulence-oriented rotational probabilistic shaping.

Free-space optical (FSO) communications can provide high speed and large capacity, yet atmospheric turbulence poses a challenge. We propose a novel turbulence-oriented rotated probabilistic shaping (TRPS) scheme to achieve joint gains in coding, shaping, and signal space diversity for FSO systems. Our approach significantly enhances achievable rates in high signal-to-noise ratio (SNR) regions as turbulence intensity increases by optimizing probabilities and rotation angles. For instance, the achievable rate can be increased by 0.08 to 0.23 b/s from weak to strong turbulence compared to non-rotated uniform 16-ary quadrature amplitude modulation (16QAM) with a rate of 3.0 bits per symbol (b/s). Accordingly, the non-equivalent pairwise error probability as an upper bound on the average symbol error rate (ASER) is derived and verified, theoretically validating the superiority of TRPS in FSO systems. Furthermore, simulation results on ASER, and post-forward error correction bit error rate (BER) using polar codes demonstrate the potential of the proposed scheme. Compared to the uniform transmission without rotation, TRPS achieves joint gains of over 11.5 dB and 3 dB in ASER and BER for both 16QAM and 32QAM with a shaping depth of 0.05 in strong turbulence conditions.