Passive Beamforming Optimization for 3D Beam Coverage in IRS-Aided Communications

Intelligent reflecting surface (IRS) has emerged as a promising technology to improve wireless communication performance. In this paper, we aim to maximize the minimum (i.e., max-min) received signal-to-noise ratio (SNR) over all locations in the target area, by optimizing the IRS passive beamforming. The formulated problem includes 1) a non-convex constant-modulus constraint and 2) a non-convex and semi-infinite beamforming gain constraint, which is difficult to solve. To solve this problem, we propose an efficient passive beamforming scheme by first decoupling the original problem to two similar max-min beamforming gain subproblems corresponding to the x- and z - dimension, respectively, and then propose an efficient solution to solve them efficiently. Specifically, both of them are reformulated to be finite and convex in the lifted matrix space with an additional rank-one constraint, and difference-of-convex (DC) and successive convex approximation (SCA) techniques are used to solve the reformulated problem. Our simulation results show that the proposed passive beamforming scheme achieves a three-dimensional (3D) passive coverage beam for the target area with nearly received SNR and outperforms the existing algorithms in terms of the minimum received SNR.