Low-Complexity Joint Antenna Selection and Beamforming for an IRS Assisted System

Abstract

Intelligent reflecting surface (IRS), which uses passive reflective elements instead of active radio frequency (RF) chains, is a cost and energy-efficient solution to improve the wireless system performance. With a similar objective, transmit antenna selection (AS) reduces the number of RF chains at the base station while harnessing the benefits of multiple antennas. In our work, we focus on joint optimization of antenna subset and transmit beamforming at the base station, and passive beamforming at the IRS to maximize the receive signal power. For single AS, we first derive a closed-form optimal rule. We then propose a simpler AS rule, which significantly reduces the computational complexity and the number of pilot transmissions required. For a system with N t antennas at the base station and N IRS elements, the optimal AS rule requires $N_{t}+N_{t}N$ pilots. However, the proposed simpler rule requires only $2N_{t}+N$ pilots. For subset AS, we develop a manifold optimization based algorithm. To reduce its subset search complexity, which is exponential in the number of RF chains at the base station, we propose an alternating optimization based iterative algorithm. Our numerical results show that the proposed simpler AS rules are near optimal.