## 5 Numerical Results
Figure 3 shows the sum-rate performance of Algorithm 2 and the ZF precoding method as \(P_{\text{s}}\) increases, where \(K=2\) and \(N=16,32,64\). We can observe that an increase in the number of active LEDs in Algorithm 2 leads to an improvement in the system's (weighted) sum rate. In other words, to achieve the same (weighted) sum rate, increasing the number of LED arrays can save transmit peak power. This is because it leverages the properties of transmit diversity. However, in the ZF precoding scheme, as \(N\) increases, the elements become smaller when calculating the pseudo-inverse of the channel matrix, leading to a gradual deterioration in performance. Figure 2: Sum-rate performance of the proposed MU-PhC-MIMO VLC system with \(N=4\) and \(K=2\) using different algorithms. Figure 4 depicts the system's (weighted) sum rate based on Algorithm 2 under various DC bias power scenarios, where \(N=16,K=4\), and \(P_{\rm d}=-5,-6.2,-8,-11\) dBm. It is evident that an increase in the DC bias results in a reduction in the system's (weighted) sum rate. This indicates that the DC bias causes interference at the receivers. Therefore, in practical applications, selecting an appropriate value for the bias becomes crucial. It should comply with the non-negativity requirement of the transmitted signal while minimizing the impact on the receivers' rates. Figure 5 demonstrates the impact of increasing user numbers, resulting in multiple streams on the system's (weighted) sum rate for the proposed Algorithms 2 and 3, where \(N=16\) and \(K=2,3,4,5\). It can be observed that Algorithm 3 performs slightly lower than Algorithm 2 at low power levels. However, with the growth of the transmit peak power, the gap between them gradually diminishes, approaching convergence. At lower transmit peak power, \(\gamma_{k,1}\gamma_{k,2},\forall k\) cannot simultaneously fall within the convex intervals due to the limited considerations in Algorithm 3, resulting in gaps. Yet, with sufficient transmit peak  
Figure 4: Sum-rate performance of the proposed MU-PhC-MIMO VLC system with \(N=16\) and \(K=4\) under different DC bias power scenarios. Figure 3: Sum-rate performance of the proposed MU-PhC-MIMO VLC system with \(K=2\) under different numbers of LED arrays. power, the likelihood of being within the convex intervals increases. Algorithm 3 accounts for this possibility, thus converging with the performance of Algorithm 2. Additionally, we also notice that the performance diminishes at lower transmit-power levels as the number of users increases. However, increasing power demonstrates the advantages of multi-user scenarios. This is also a consequence of power limitations. Figure 6 plots the convergence behavior of Algorithm 1. Figure 6a depicts the iterative convergence of Algorithm 1 with five distinct \(\{\hat{\mathcal{U}}_{i},\hat{\mathcal{V}}_{i}\}\) scenarios selected in Algorithm 3 when \(P_{\mathrm{s}}=-16\) dBm. It can be observed that under the various \(\{\hat{\mathcal{U}}_{i},\hat{\mathcal{V}}_{i}\}\) scenarios, the system's (weighted) sum rate shows a step-like growth pattern. Figure 6b displays the iterative process of running Algorithm 1 corresponding to the optimal solutions obtained by Algorithm 3 under various transmit peak power levels, where \(P_{\mathrm{s}}=-24,-20,-18,-16\) dBm. The comparison reveals that at lower power conditions, fewer occurrences of \(\gamma_{k,1}\gamma_{k,2},\forall k\) fall within the convex intervals. However, as the power increases, the occurrences of \(\gamma_{k,1}\gamma_{k,2},\forall k\) within these intervals gradually rise, confirming our hypothesis in Proposition 3. Figure 6a,b collectively demonstrate that after a few iterations, Algorithm 1 converges to a solution, substantiating the effectiveness of the algorithm to a certain extent. Figure 7 shows the numerical results under scenarios where the transmitter possesses imperfect CSI because of the CSI estimation errors or delayed feedback from the receiver.