A Low Complexity Linear Precoding Method for Extremely Large-Scale MIMO Systems

Massive multiple-input multiple-output (MIMO) systems are critical technologies for the next generation of networks. In this field of research, new forms of deployment are emerging, such as extremely large-scale MIMO (XL-MIMO), in which the antenna array at the base station (BS) is of extreme dimensions. As a result, spatial non-stationary features emerge as users view just a section of the antenna array, known as the visibility regions (VRs). The XL-MIMO systems can achieve higher spectral efficiency, improve cell coverage, and provide significantly higher data rates than standard MIMO systems. It is a promising technology for future sixth-generation (6G) networks. However, due to the large number of antennas, linear precoding algorithms such as Zero-Forcing (ZF) and regularized Zero-Forcing (RZF) methods suffer from unacceptable computational complexity, primarily due to the required matrix inversion. This work aims to develop low-complexity precoding techniques for the downlink XL-MIMO system. These low-complexity linear precoding methods are based on Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) techniques, which avoid calculating the complex matrix inversion and lead to stable linear precoding performance. To further enhance linear precoding performance, we incorporate the Chebyshev acceleration method with the SOR and GS methods, referred to as the Cheby-SOR and Cheby-GS methods. As these proposed methods require optimizing parameters, we create a deep unfolded network (DUN) to optimize the algorithm parameters. Our performance results demonstrate that the proposed method significantly reduces computational complexity from to O(K-2), where $K$ represents the number of users. Moreover, our approach outperforms the original algorithms, requiring only a few iterations to achieve the RZF bit error rate (BER) performance.