Sphere Manifold Optimization Empowered Joint Antenna Selection and Precoding for XL-MIMO Systems

Abstract

This letter investigates the joint optimization of antenna selection and precoding design in extremely large-scale MIMO systems. Unlike previous works, we transform the joint antenna selection and precoding optimization problem into a single-variable optimization problem over the sphere manifold to significantly facilitate solution designs, while a manifold optimization-based algorithm is proposed to enhance solution accuracy, thereby improving overall system performance. Specifically, the joint antenna selection and precoding optimization problem is transformed into an $\ell _{2,0}$ -norm constrained problem over the sphere manifold. To address this nonconvex constraint, an alternating direction method of multipliers-based manifold optimization (ADMM-MO) algorithm is proposed to decompose the primary problem into two subproblems. The manifold subproblem is solved through the Riemannian conjugate gradient descent method, while the $\ell _{2,0}$ -norm constraint is handled via a hard thresholding operator. Furthermore, the proposed ADMM-MO algorithm is theoretically demonstrated to achieve global convergence. Simulation results show that our algorithm significantly outperforms the benchmark.