A Trellis-Based Passive Beamforming Design for an Intelligent Reflecting Surface-Aided MISO System

In this letter, the downlink transmission of an intelligent reflecting surface (IRS)-assisted multiple-input single-output (MISO) system is investigated where the IRS elements are selected from a predefined discrete set of phase shifts. We minimize the mean square error (MSE) of the received symbols in the system via optimizing the phase shifts at the IRS jointly with beamforming vectors at the base station (BS) and equalizers at the user terminals. In order to find the optimal IRS phase shifts, a trellis-based structure is used that smartly selects the discrete phases. Moreover, for the sake of comparison, a semi-definite programming (SDP)-based discrete phase optimization is also presented. The BS beamformer and the optimal equalizers are determined via closed-form solutions. Numerical results demonstrate that the trellis-based scheme has better performance compared to other discrete IRS phase shift designs, such as SDP and quantized majorization-minimization technique, while maintaining a very low computational complexity.