# Optimized Accelerated Over-Relaxation Method for Robust Signal Detection: A Metaheuristic Approach
## 5 Simulation Results and Discussion
It shows that the proposed method achieves optimal performance while other methods struggle, and their error rates are higher than OAOR. In the higher modulation of 64-QAM, Figure 11 shows that with one higher iteration count, the proposed model still performs optimally. The total error rate in 16-QAM is lower than that in 64-QAM because of the amplified Euclidean distance among constellation points. However, the proposed method still maintains a substantial performance gap over AOR and IGS, especially at high SNR levels. Overall, in both modulation schemes, the proposed method exhibits faster decay in SER at higher SNR values, which indicates faster convergence at a small \(N/K\) antenna ratio. Figure 11: Performance comparison of various detectors for \(N\times K=512\times 128\) in 64-QAM modulation. Figure 10: Performance comparison of various detectors for \(N\times K=512\times 128\) in 16-QAM modulation. Figure 9: Performance comparison of different detectors for \(N\times K=160\times 32\) antenna systems with 64-QAM modulation. Now, we simulate a more complex antenna scenario employing 600 BS antennas and 200 users. In Figure 12, we evaluate the performance of different detectors for 16-QAM modulation and Figure 13 utilizes 64-QAM. Both results show that the proposed method consistently gives good results under very challenging conditions and achieves near-MMSE performance earlier than the IGS and AOR. If we closely observe the performance of the final iteration in Figure 12, to achieve the SER level of \(10^{-4}\), we can see that our proposed method achieves such a low error rate with the difference of 0.1 dB SNR with MMSE. Meanwhile, the error rate of the AOR detector at the same level of SNR is very high. A similar trend can be observed in the higher modulation scheme of 64-QAM as shown in Figure 13. In this case, the proposed method required one extra iteration to achieve near-MMSE results. In contrast, all other methods require a greater number of iterations to achieve the same performance at this higher order of modulation. Figures 14 and 15 show the performance comparison between the proposed algorithm and E-SOR in 32-QAM signaling. We can see that E-SOR has a trend similar to that of AOR and IGS, but it performs slightly better than IGS because it handles iterations efficiently while having a fixed relaxation parameter value. However, its performance is still lower compared to the proposed method because of its fixed parametric values. By increasing the number of user antennas from 18 to 21, we observe that E-SOR, at a higher iteration count (i.e., \(i=4\)), surpasses IGS by 0.21 dB at an SER level of \(10^{-4}\). Nonetheless, it shows a greater difference from MMSE compared to the proposed method, which clearly demonstrates that our proposed method has the advantage of being implemented in diverse signaling and antenna configurations. Overall, this shows that the proposed method is easily scalable for a large number of antennas for both transmitter and receiver antennas in very dense and loaded system configurations, which is more suitable for practical implementation. In summary, the OAOR method consistently delivers near-MMSE performance across various system configurations, outperforming other detectors. Specifically, it converges quickly and achieves the desired performance with fewer iterations. Moreover, the complexity analysis, as discussed in Section 4, already reveals the superior performance of the proposed algorithm. Thus, we can conclude that the proposed method's ability to converge quickly and attain near-MMSE performance with fewer iterations, as well as its ability to efficiently handle large antenna systems makes it a promising candidate for signal detection in massive MIMO systems. Additionally, this method can also be applied to other signal processing problems, to achieve low complexity, such as channel estimation in massive MIMO systems.