Abstract
Probabilistic constellation shaping (PCS) is a promising solution to improve the transmission performance of quadrature amplitude modulation (QAM) optical signals in free-space optical (FSO) communication. The Maxwell–Boltzmann (MB) distribution is currently the predominant PCS scheme in FSO systems, however, it is regarded as the optimal distribution form in additive white Gaussian noise (AWGN) channels, and when in the face of the turbulence effect, it may no longer be the optimal PCS scheme. In this paper, the PCS scheme based on particle swarm optimization (PSO) algorithm in Gamma–Gamma atmospheric turbulence channel is proposed, which breaks through the constraint of MB distribution form. The block diagrams of transmitter and receiver under the probabilistic amplitude shaping (PAS) architecture are presented and illustrated. Moreover, the signal transmission model is theoretically established and the algorithm steps are designed. Furthermore, the bit error rate (BER) of probabilistic constellation shaped M 2 QAM (PCS- M 2 QAM) is mathematically derived in Gamma–Gamma atmospheric turbulence channels. Taking 64QAM as an example, through simulations, we find that when signal-to-noise ratio (SNR) and turbulence intensity are fixed, PCS-64QAM with PSO algorithm achieves superior generalized mutual information (GMI) and BER performance compared to MB distribution and uniform distribution. For example, when SNR = 30 dB, as σ R 2 varies from 0.1 to 3, the GMI gap between PSO algorithm and MB distribution varies from 0.06 to 0.16 bits/symbol, and that between PSO algorithm and uniform distribution varies from 0.54 to 0.42 bits/symbol; when SNR = 35 dB, as σ R 2 varies from 0.1 to 3, the BER performance gap between PSO algorithm and MB distribution varies from 0.4 dB to 0.9 dB, and that between PSO algorithm and uniform distribution varies from 4.2 dB to 3.2 dB. When forward error correction (FEC), such as quasi-cyclic low-density parity-check (QC-LDPC) coding, is employed, the BER performance of PCS-64QAM with PSO algorithm can obtain more improvement by QC-LDPC compared to MB distribution and uniform distribution. For example, when SNR = 40 dB, the BER performance with PSO algorithm, MB distribution, and uniform distribution can increase 18.2 dB, 17.8 dB, and 11 dB respectively when σ R 2 = 0.1; 11.3 dB, 10.5 dB, and 7.2 dB respectively when σ R 2 = 0.5; 6.2 dB, 5.2 dB, and 3.9 dB respectively when σ R 2 = 3. In addition, PCS-64QAM with PSO algorithm can achieve a longer transmission distance compared to MB distribution and uniform distribution in Gamma–Gamma atmospheric turbulence channels.