# Optimized Accelerated Over-Relaxation Method for Robust Signal Detection: A Metaheuristic Approach
## 5 Simulation Results and Discussion  
This section presents the numerical results and performance analysis of the proposed OAOR method. The performance of the OAOR method is first compared with the conventional AOR [39] and IGS [38]. We then extend our comparison to include another method, E-SOR [34], in terms of SER for various system configurations, with MMSE used as the benchmark. The SER is an important performance evaluation metric in communication systems to evaluate the performance of signal detection[53; 54]. The simulations are performed under 16, 32, and 64 quadrature amplitude modulation (QAM) schemes, assuming perfect Channel State Information (CSI) at the receiver. The results are derived by averaging the SER across a suitable number of Monte Carlo trials, i.e., \(6\times 10^{4}\) to \(7\times 10^{4}\). To evaluate the performance of the proposed method, the simulation results of SER as a function of iteration number are presented in Figure 5. An antenna configuration of \(N\times K\) = 384 \(\times\) 64 is considered to compare the results across different SNR levels in 64-QAM. The results demonstrate that the performance of our proposed method becomes stable right after a few iterations, and it shows that our method achieves faster convergence. It is also evident that at lower SNR values, fewer iterations are required. For example, for the SNR levels of 8 and 10, only 2 iterations are required for stability. It also gives the insight that our proposed method has robust performance under varying conditions and low-SNR situations, which is more suitable for practical applicability. Now we evaluate the performance comparison of the proposed method with other detectors in different antenna configurations. First, we take a less dense antenna scenario with \(N=512\) BS antennas and \(K=64\) users in 16- and 64-QAM modulation schemes. Figure 6 presents the comparison in 16-QAM, while Figure 7 presents that with 64-QAM modulation. In both figures, the performance of all methods improves with the increase in iteration count, but the performance of the proposed method is better than all other  
Figure 4: Comparison of computational complexity for different signal detectors. Figure 5: SER performance vs. iteration number for \(N\times K\) = 384 \(\times\) 64 in 64-QAM at different SNR values. methods at iteration \(i=3\) in 16-QAM and \(i=4\) in 64-QAM, closely achieving the near-optimal performance of MMSE. It can be observed that the AOR converges very slowly for such a small ratio between the users and BS antennas, resulting in a large estimation error. This validates the effectiveness of the OAOR method in achieving near-MMSE performance with high detection accuracy. Figure 8 illustrates the SER performance versus SNR for different signal detectors in 16-QAM modulation for the antenna configuration of \(N\times K=160\times 32\). Here, the proposed method demonstrates superior performance compared to the AOR and IGS detectors and achieves near-optimal performance of the MMSE detector with only four iterations. It highlights its ability to provide excellent detection accuracy of the received signal. If we employ a higher modulation of 64-QAM in Figure 9 for the same antenna configuration, we can observe that the AOR error rate is higher as compared to our proposed detector. IGS has slightly better performance than AOR, but the detection accuracy of our method is better than IGS at iteration \(i=4\). In these results, although AOR and IGS have better performance at the initial 2 iterations, at the final iteration, our proposed method surpasses the other detectors by achieving near-MMSE performance with the lowest error rate. Now we evaluate the performance of various detectors in challenging conditions by increasing the number of BS antennas \(N\) and users \(K\). First, we test our proposed method for \(N=512\) and \(K=128\) employing 16-QAM in Figure 10 and compare its performance with other methods.