Optimal Antenna Selection and Beamforming for an IRS Assisted System

Abstract

An intelligent reflecting surface (IRS) is a cost and energy-efficient solution to improve wireless system performance. Transmit antenna selection (AS) harnesses the benefits of multiple antennas with a smaller number of radio frequency (RF) chains. We focus on joint optimization of antenna subset and transmit beamforming at the transmitter (Tx) and passive beamforming at the IRS to maximize the receive signal power. We derive a closed-form optimal AS rule for a Tx and receiver (Rx) equipped with single RF chain each and ideal IRS. We analyze its performance with a correlated channel model and then extend it to non-ideal IRS. We also propose a simpler rule that significantly reduces the number of computations and pilots. For an Rx that performs maximal ratio combining, we propose a manifold optimization algorithm and a low-complexity selection rule. For a Tx with multiple RF chains, we propose a subset selection algorithm that yields a locally optimal solution and an alternating optimization algorithm that reduces complexity. Our simulations study the impact of estimation errors, discrete phase shifts, and channel correlation on the proposed selection rules, which perform better than the existing AS rules. They also show that the proposed low-complexity rules are near-optimal.