## 6 Result and Discussion  
In this section, we present the simulation results to estimate the BER performance of the proposed RL-based MMSE precoding scheme in the UV NLOS MIMO communication systems. For the simulation setup, the PD efficiency is set to \(\eta=0.06\), and the wavelength of the UV light is set to \(266\) nm [38]. We use the gamma-gamma channel model as the channel fading model. We set background radiation fixed at \(-188.18\) dBJ and increase \({}_{E}b\) from \(-160\) dBJ to \(-155\) dBJ. A single user is considered with two data streams. MIMO configurations with \(2\times 8,2\times 6,2\times 4\) are set for simulation. Each data point in Figures 4-9 is the average of five independent tests, and different random seeds are used for the tests. Figure 3 shows the average reward in the \(95\%\) confidence interval for five runs to show statistical significance. As shown in Figure 3, the average reward converges with the number of training increases. This reward includes the optimization objective's MSE and the penalty of constraint conditions. In the later stage of training, the penalty term is \(0\), and the entire reward represents MSE, which shows the effectiveness of our proposed scheme. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Episode M & 600 \\ Time step N & 1000 \\ Gaussian random process \(\mathcal{N}\) & \(\mathcal{N}\) (0, 0.5) \\ Minibatch size & 100 \\ Discouting factor \(Y\) & 0.9 \\ Soft replacement factor \(\tau\) & 0.001 \\ Learning rate of behavior critic & 0.0001 \\ Learning rate of behavior actor & 0.00001 \\ Replay buffer \(\mathcal{D}\) size & 100,000 \\ Layers and Hidden Units \(8\times 2\) & (4, 200) \\ Layers and Hidden Units \(6\times 2\), \(4\times 2\) & (3, 128) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Hyperparameters of MADDPG. The impact of the number of LEDs is analyzed in Figure 4, where the background radiation is \(n_{b}=-188.18\) dBJ. The increase in the number of LED arrays (\(N_{t}\)) helps to reduce the BER. In particular, for a \(2\times 8\) MIMO configuration, the proposed scheme achieves an average BER of \(10^{-5}\) at an energy per bit of \(E_{b}=-155\) dBJ, providing a performance gain of about 2 dB over the \(2\times 4\) system. This indicates that the proposed scheme can efficiently utilize the spatial diversity. The result suggests that the proposed scheme can provide reliable and efficient data transmission even under low receive energy conditions. Figure 5 presents the performance comparison between our scheme and traditional AWGN-based precoding schemes in a severe fading channel with \(N_{t}=8\) and \(N_{r}=2\). For  
Figure 4: Performance comparison under different \(N_{t}\) with \(N_{r}=2\) in strong turbulence. Figure 3: Average reward of the proposed scheme. traditional schemes, we considered different schemes at the receiver side and transmitted side [39; 40; 41]: MMSE-MMSE, ZF-MMSE, and SVD-MMSE. The background radiation is \(n_{b}=-188.18\) dBJ. It is clear that the AWGN-based MMSE precoding schemes perform poorly in the Poisson shot-noise photon-counting systems. The MMSE precoding scheme in the Gaussian system can only achieve a BER of \(10^{-3}\) when \(E_{b}=-155\) dBJ, while our proposed scheme can reach \(10^{-5}\). For the computational complexity analysis, we exploit the number of float number operations with Big-O notation. According to the formula, we can know that the computational complexity of the MMSE-MMSE, ZF-MMSE, and SVD-MMSE scheme is \(\mathcal{O}\big{(}N_{r}^{3}+N_{t}N_{r}^{2}\big{)}\).