The performance of free-space optical (FSO) communication is significantly affected by atmospheric turbulence, along with other factors such as misalignment, weather conditions, and transmission distance. Turbulence-induced signal fluctuations degrade the high-capacity advantage of FSO systems, necessitating robust compensation techniques. To address this challenge, we propose an entropy-power loading method for mitigating atmospheric turbulence effects in FSO systems. This approach combines channel estimation, probabilistic shaping (PS)-based entropy allocation, and water-filling power distribution to enhance generalized mutual information (GMI) and system robustness. Furthermore, to optimize bit transmission efficiency, we introduce a normalized GMI (NGMI) threshold into entropy-power loading, formulating a joint-parameter entropy-power loading strategy. We aim to demonstrate that this method can effectively compensate for turbulence-induced degradation and improve spectral efficiency and link reliability in FSO communication.

This study proposes an atmospheric turbulence compensation method based on entropy-power loading. Initially, a Gaussian white noise channel model was established to numerically investigate the correlation between source entropy, signal-to-noise ratio (SNR), and GMI performance. We then developed an entropy-power loading algorithm, whose core innovation involved employing the golden section method to optimize the probabilistic shaping coefficient λ, thereby maximizing GMI for each subcarrier under its pre-estimated SNR conditions. For experimental verification, we constructed an atmospheric turbulence simulation platform using a spatial light modulator (SLM) with dynamically loaded random phase screens. The implementation process involves: (1) conducting preliminary communication to estimate the SNR of each OFDM subcarrier; (2) computing the corresponding symbol order, probabilistic shaping coefficient, and power allocation for each subcarrier via entropy-power loading; (3) modulating the bit stream into OFDM symbols; and (4) transmitting and receiving optical signals through a complete system comprising a laser, Mach?Zehnder modulators, signal generators, and so on. Additionally, the relationship between source entropy, SNR, and NGMI performance was studied via numerical simulation, and an NGMI threshold was incorporated into entropy-power loading to improve the system’s bit transmission efficiency. Finally, the improved method was implemented on the experimental platform for verification.

Using 256QAM as an example, we investigated the relationship between source entropy (H), SNR, and GMI via numerical simulation, with H stepped at 0.1 bit intervals and SNR at 0.5 dB intervals. The results were visualized in a 3D graph (Fig. 3(a)). For clarity, projections at SNRs of 10 dB, 15 dB, and 20 dB were presented, revealing that GMI is a unimodal function of H (Fig. 3(b)). We determined the maximum GMI and optimal λ for various SNRs and QAM orders, as shown in Fig. 4. Performance evaluations over 50 turbulence realizations indicate that entropy-power loading performs best under both strong and weak turbulence conditions. Specifically, entropy-power loading offers mean GMI gains of 43.5 bit and 58.0 bit over bit-power loading under strong and weak turbulence conditions, respectively, translating to gains of 0.35 bit/symbol and 0.47 bit/symbol across 123 subcarriers (Fig. 6).

Numerical simulations investigating the relationship between source entropy (H), SNR, and NGMI reveal that NGMI is a monotonically decreasing function of H at a given SNR (Fig. 7). Incorporating an NGMI threshold into the maximum GMI strategy enables simultaneous optimization of GMI and NGMI, outperforming conventional strategies. Figure 8 presents NGMI performance with and without the threshold via numerical simulation, demonstrating that joint-parameter entropy-power loading effectively meets NGMI requirements, especially at higher SNRs.

Figure 9 shows that the GMI performance of PS-256QAM with joint-parameter entropy-power loading slightly underperforms that of PS-256QAM with GMI maximization strategy between 3 dB and 22 dB but surpasses that of fixed-order 256QAM, reaching maximum GMI above 22 dB. Verification in a real OFDM-FSO system with an NGMI threshold of 0.92 shows that joint-parameter entropy-power loading averages 15.9 bit and 13.2 bit lower GMI than GMI maximization entropy-power loading under strong and weak turbulence, respectively, but still outperforms bit-power loading by 27.6 bit and 44.8 bit (Fig. 10). NGMI performance (Fig. 11) indicates that joint-parameter entropy-power loading performs best under both strong and weak turbulence.

The GMI-maximizing entropy-power loading strategy outperforms bit-power loading and fixed-order 64QAM modulation in GMI performance under both strong and weak turbulence. Additionally, based on the constraint relationship between GMI and NGMI, NGMI control is achieved by introducing an NGMI threshold. Experiments show that when the NGMI threshold is set to 0.92, the GMI performance of joint-parameter entropy-power loading is slightly lower than that of the GMI-maximizing strategy but still superior to bit-power loading and fixed-order 64QAM modulation. Moreover, the NGMI performance of joint-parameter entropy-power loading is optimal. In summary, joint-parameter-based entropy-power loading balances GMI and NGMI and outperforms bit-power loading and fixed-order QAM modulation in both metrics. The proposed method can effectively improve the channel capacity and robustness of optical communication systems under atmospheric turbulence.