Low-Complexity Beam Domain Precoding for XL-MIMO Downlink with User Grouping and Beam Extraction

This paper proposes a low-complexity beam domain precoder design for the three-dimensional (3D) extra-large-scale multi-input multi-output (XL-MIMO) downlink with multi-antenna user equipments (UEs). To reduce the complexity while maintaining the performance of the eigen zero forcing (EZF) precoder, we divide the UEs into different groups. Each group designs its precoding matrix using selected beam vectors, respectively. We call this precoder the beam domain group precoding (BDGP). We formulate a combinatorial optimization problem and derive a heuristic algorithm to solve the grouping problem based on statistical channel state information (CSI). Moreover, we introduce a novel beam extraction algorithm to maximize the inter-group signal to interference plus noise ratio (SINR). To further reduce the complexity of BDGP, we leverage the sparsity of the beam domain channel and inter-group interference and replace the matrix inversion with the approach that solves linear equations twice through Cholesky decomposition. Simulation results show that BDGP significantly reduces the complexity while achieving comparable sum-rate performance.