Joint Precoding and Antenna Selection for Sum Spectral Efficiency Maximization

Antenna selection is an effective technique for reducing system complexity and power consumption in large-scale communication systems by efficiently utilizing antennas. In this paper, we propose an algorithm that jointly optimizes an active antenna subset and a beamforming precoding matrix to maximize sum spectral efficiency (SE) in a multi-user multiple-input multipleoutput (MU-MIMO) downlink system under a constraint of the maximum number of active antennas. The joint problem presents several challenges: non-smoothness due to the antenna selection constraint and non-convexity of the maximization problem. To address these problems, we first incorporate the antenna selection constraint into the sum SE maximization problem through an indicator function and resolve the non-smoothness of the indicator function through approximation. Subsequently, we identify the first-order optimality condition based on given Lagrange multiplier and cast it as a nonlinear eigenvalue problem. Then, we apply a power iteration method to find the superior stationary precoding matrix, which contains information about the superior precoding vectors and the optimized active antenna subset. After calculating the precoding matrix, we iteratively count the number of active antennas, check its feasibility, update the Lagrange multiplier and recalculate the precoding matrix until the number of active antennas satisfies the antenna constraint. Simulation results demonstrate the superiority of our antenna selection precoding algorithm over benchmarks.