# Optimized Accelerated Over-Relaxation Method for Robust Signal Detection: A Metaheuristic Approach
## 1 Introduction
### Related Work  
In order to overcome the challenge of complexity in direct inversion techniques, several approximate matrix inversion and iterative methods have been developed. In massive MIMO, a good performance and complexity trade-off can be achieved by utilizing these methods because of higher BS antennas than users [21]. In [22; 23], Neumann series (NS) detection has been developed to approximate large matrix inversion. NS achieves low complexity effectively if the BS to users antenna ratio is large (e.g., \(\geq 16\)). The complexity is reduced from \(O(K^{3})\)to \(O(K^{2})\) when \(i<3\). But as \(i\geq 3\), the complexity is higher even than the direct MMSE solver. Here, \(K\) represents the number of users. Another method to approximate the matrix inverse such as Newton iteration (NI) and its improved version, diagonal band NI, has been developed, which has faster convergence as compared to NS [24]. NI was further improved in [25], which requires fewer iterations to achieve matrix inversion with the required accuracy. However, as the number of uses increases to obtain satisfactory results, its computational complexity also increases. This has led further to the development of more sophisticated algorithms, i.e., iterative algorithms. The concept behind iterative techniques is the estimation of the transmitted symbol without calculating the inverse of the large matrix. Typically, these methods have significantly lower complexity compared to approximate matrix inversion methods [26]. So, several iterative signal detectors have been investigated recently. Richardson iteration (RI) [27; 28; 29] is employed to achieve near-MMSE performance. It requires more iterations to achieve optimal results [30] and it is greatly affected by the relaxation parameter [31]. The work in [32] introduced the joint steepest descent algorithm to achieve optimal performance. However, its slow convergence leads to high computational complexity, making it inefficient for large-scale systems. To achieve better performance in challenging conditions, successive over-relaxation (SOR) [33; 34] and Gauss-Seidel (GS) [35; 36; 37; 38] methods have been proposed. These techniques have drawn significant attention due to their ability to attain nearly optimal performance while reducing complexity. However, their sequential iteration process makes parallel implementation difficult. Another promising approach in iterative detection is the AOR method [39], where the authors presented a comprehensive analysis of the AOR method for massive MIMO systems, highlighting its potential for improved convergence rates compared to traditional methods. However, the performance of the AOR method is highly reliant on selecting its relaxation and acceleration parameters, which presents a challenge for varying system conditions. AOR is further improved in [40], which utilizes the AOR method and Neumann series to reduce computational complexity. But this method is again highly dependent on the values of acceleration and relaxation parameters. Most of these methods adopt fixed values, which make these methods less accurate in terms of detection accuracy and performance under high antenna configurations and continuously varying channel conditions. Concurrently, there has been a growing utilization of nature-inspired optimization algorithms in many areas of wireless communication [41; 42; 43]. Particle Swarm Optimization (PSO), in particular, has shown remarkable versatility in solving complex optimization problems. The work in [44] demonstrated the effectiveness of PSO in system identification, while [45] proposed an improved PSO variant with enhanced convergence characteristics. These observations of optimization are essential in optimizing different parameters of over-relaxation methods in signal detection. In summary, most of the detection algorithms possess huge computational complexity, and it increases as the number of antennas is increased. Therefore, achieving the trade-off between accuracy and cost complexity is difficult.