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

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.