Comments on "A Linear Time Algorithm for the Optimal Discrete IRS Beamforming"

TL;DR

This paper refines the conditions and algorithms for optimizing discrete phases in reconfigurable intelligent surfaces, achieving faster convergence and optimal power with fewer steps than previous methods.

Contribution

Provides updated necessary and sufficient conditions, improved algorithms with proven convergence in N steps, and demonstrates superior performance over prior algorithms.

Findings

Achieves optimal received power with fewer steps than existing methods.

Proves convergence of the new algorithms in N or fewer steps.

Demonstrates improved simulation performance over previous algorithms.

Abstract

The problem of optimizing discrete phases in a reconfigurable intelligent surface (RIS) to maximize the received power at a user equipment is addressed. Comments on [1] are provided. Updated necessary and sufficient conditions for its Lemma 1 are given. Consequently, an updated Algorithm 1 is provided with full specification. Simulation results with improved performance over the implementation of Algorithm 1 are provided. New versions of the algorithm are given that are proven to achieve convergence in N or fewer steps, where N is the number of the elements in the reconfigurable intelligent surface. This is in contrast with KN or 2N number of steps on the average specified for Algorithm 1 in [1], where K is the number of discrete phases. As a result, for a discrete-phase RIS, the techniques presented here achieve the optimum received power in the smallest number of steps published in the literature.