Low-Complexity Iterative Precoding Design for Near-field Multiuser Systems With Spatial Non-Stationarity

Extremely large antenna arrays (ELAA) are regarded as a promising technology for supporting sixth-generation (6G) networks. However, the large number of antennas significantly increases the computational complexity in precoding design, even for linearly regularized zero-forcing (RZF) precoding. To address this issue, a series of low-complexity iterative precoding are investigated. The main idea of these methods is to avoid matrix inversion of RZF precoding. Specifically, RZF precoding is equivalent to a system of linear equations that can be solved by fast iterative algorithms, such as random Kaczmarz (RK) algorithm. Yet, the performance of RK-based precoding algorithm is limited by the energy distributions of multiple users, which restricts its application in ELAA-assisted systems. To accelerate the RK-based precoding, we introduce the greedy random Kaczmarz (GRK)-based precoding by using the greedy criterion-based selection strategy. To further reduce the complexity of the GRK-based precoding, we propose a visibility region (VR)-based orthogonal GRK (VR-OGRK) precoding that leverages near-field spatial non-stationarity, which is characterized by the concept of VR. Next, by utilizing the information from multiple hyperplanes in each iteration, we extend the GRK-based precoding to the aggregation hyperplane Kaczmarz (AHK)-based pecoding algorithm, which further enhances the convergence rate. Building upon the AHK algorithm, we propose a VR-based orthogonal AHK (VR-OAHK) precoding to further reduce the computational complexity. Furthermore, the proposed iterative precoding algorithms are proven to converge to RZF globally at an exponential rate. Simulation results show that the proposed algorithms achieve faster convergence and lower computational complexity than benchmark algorithms, and yield very similar performance to the RZF precoding.