Fig. 1. PDF of ideal channel gain and non-ideal channel gain. (a) Non-ideal channel, ρ=0.95; (b) non-ideal channel, ρ=0.85; (c) ideal channel

Fig. 2. Diagram of trust region algorithm for function f

Fig. 3. 16QAM constellation map optimisation trajectory

Fig. 5. GMI values of ideal channel GS and uniformly distribution

Fig. 6. GMI values versus SNR for non-ideal channels. (a) GMI values of GS and uniform distribution under different turbulence intensities; (b) effect of correlation coefficient on uniformly distributed GMI values

Fig. 7. GMI values of non-ideal channel GS and uniform distribution (correlation coefficient is varying and turbulence intensity is weak turbulence)

Fig. 8. GS GMI values of non-ideal and ideal channels

Fig. 9. NGMI values of ideal channel GS and uniform distribution

Fig. 10. NGMI values of non-ideal channel GS and uniform distribution

Fig. 11. NGMI values of non-ideal channel GS

Fig. 12. GS optimized constellations. (a) σI2=0.4, SNR is 5 dB; (b) σI2=0.4, SNR is 15 dB; (c) σI2=0.4, SNR is 20 dB; (d) σI2=1.0, SNR is 5 dB; (e) σI2=1.0, SNR is 15 dB; (f) σI2=1.0, SNR is 20 dB; (g) σI2=0.4, SNR is 5 dB, ρ=0.7 (non-ideal); (h) σI2=0.4, SNR is 5 dB, ρ=0.8 (non-ideal); (i) σI2=0.4, SNR is 5 dB, ρ=0.9 (non-ideal)