A Linear Time Algorithm for the Optimal Discrete IRS Beamforming

Abstract

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.Index Terms-Intelligent reflective surface (IRS), reconfigurable intelligent surface (RIS), discrete beamforming for IRS/RIS.

A Linear Time Algorithm for the Optimal Discrete IRS Beamforming

“…. , θ * n ) to problem (8), each θ * n must satisfy θ * n = arg min θn∈ΦK |(θ n + α n − µ) mod 2π| (11) where µ stands for the phase of µ in (10) 1 .…”

“…In this table, we look at the simple case of K = 2, N = 2. According to Lemma 1 in [1], the condition in (11) should satisfy (8) for this simple case. We draw values of h n according to the first paragraph of Sec.…”

“…We draw values of h n according to the first paragraph of Sec. IV in [1]. We list these values in rows 2-4 of Table 1.…”

“…At this point, we would like to emphasize that [1] uses a particular convention for the phases of complex numbers. They are defined to be in [0, 2π), see the text that follows (2) in [1].…”

“…At this point, we would like to emphasize that [1] uses a particular convention for the phases of complex numbers. They are defined to be in [0, 2π), see the text that follows (2) in [1]. We use the same convention in generating Table 1, see its column 5, as well as in generating Table 2.…”