## 6 Result and Discussion
Since the actor network of MADDPG uses the multi-layer perceptron structure, the computational complexity of the MADDPG generating precoding matrix and combining per execution for one agent is given by [42]:  
\[\mathcal{O}\Bigg{(}N_{s}N_{eval}N_{step}\Bigg{(}dim_{state}n_{1}+ \sum_{l}^{L-1}n_{l}n_{l+1}+n_{L}dim_{action}\Bigg{)}\Bigg{)} \tag{35}\] \[=\mathcal{O}\Big{(}N_{s}N_{eval}N_{step}\gamma\Big{(}\frac{dim_{ state}}{dim_{action}}+(L-1)\gamma+1\Big{)}(dim_{action})^{2}\Big{)}\] \[=\mathcal{O}\Big{(}N_{s}N_{eval}N_{step}\gamma^{2}(L-1)(dim_{ action})^{2}\Big{)}\] \[=\mathcal{O}\Big{(}N_{s}N_{eval}N_{step}\gamma^{2}(L-1)\Big{(}N_ {t}^{2}+N_{r}^{2}\Big{)}\Big{)},\]  
where \(N_{eval}\) is the number of evaluation episodes; \(dim_{action}>dim_{state}\), \(N_{step}\) is the step number; \(L\) is the number of hidden layers; and \(n_{l}\) is the nodes number of \(l\)-th hidden layer. \(n_{l}=\gamma dim_{action}\) for \(1\leqslant l\leqslant L\). Note that \(\gamma\) is a scaling factor, which depends on the dimension of states, for the hidden-layer nodes. Figure 6 shows the BER of the proposed MMSE scheme under three different turbulence fading conditions, where \(\alpha=2/3,1.5,2.1\) and \(\beta=2/3,1.5,2.4\). It is observed that the proposed MMSE scheme could achieve a low BER as \(E_{b}\) increases, under each of the  
Figure 5: Performance comparison with traditional Gaussian schemes for \(N_{t}=8\) and \(N_{r}=2\) in strong turbulence. turbulence fading conditions. However, under stronger turbulence, a higher \(E_{b}\) is required to maintain the same BER target. Figure 7 shows the BER performance of the proposed scheme with different DC bias. As shown in Figure 7, when the DC bias is 1, the BER cannot decrease. This is because the bias is too small to allow the LED to operate in a linear range. Compare the other three curves; it is obvious that a smaller DC bias tends to provide a better performance. This is because when the total power is given, the less the power is applied to biasing, the more power can be saved for transmitting useful signals. Figure 6: Performance comparison under different turbulence channel. Figure 7: Performance comparison under different DC biases in strong turbulence. In FSO communication systems, CSI plays a critical role in designing and optimizing transmission schemes. However, CSI estimation errors can occur due to various factors, such as outdated or inaccurate feedback from the users. To investigate the BER performance of the proposed MIMO precoding scheme in the presence of imperfect CSI, the channel irradiance is modeled as \(\hat{g}_{i,j}=\delta g_{i,j}\), where the estimation error \(\delta\) is independently and uniformly randomly distributed within the interval \([-\delta,\delta]\), and \(\delta\) is the maximum error percentage. The CSI at the transmitter is modeled as a mapping \(\mathbf{G}\rightarrow\mathcal{G}\), where \(\mathcal{G}\) is an arbitrary subset of \(\mathbb{R}^{N_{r}\times N_{t}}\). To evaluate the robustness of the proposed MIMO precoding scheme, Figure 8 shows the BER performance in the presence of different levels of CSI imperfection in a strong gamma-gamma fading channel, where \(N_{r}=2\) and \(N_{t}=8\). In Figure 8, the value of \(\delta=1\) indicates perfect CSI, and it is observed that the proposed scheme is resilient to imperfect CSI. More specifically, it is clear that our scheme achieves a BER of \(10^{-3}\) or lower at \(E_{b}=-155\) dBJ even when the estimation error percentage is as high as \(\delta=0.6\). These results indicate the robustness of the proposed precoding scheme in practical communication systems. The background light intensity is a key factor affecting the performance of the FSO system. Figure 9 shows the system BER performance under different background light intensities (i.e., \(-188.18\) dBJ, \(-180\) dBJ, \(-175\) dBJ, and \(-170\) dBJ). It is clear that the proposed scheme can resist strong background light interference.