Majorization-Minimization Algorithms for Analog Beamforming with Large-Scale Antenna Arrays

Beamforming with large-scale antenna arrays (LSAA) is one of the predominant operations in designing wireless communication systems. However, the implementation of a fully digital system significantly increases the number of required radio-frequency (RF) chains, which may be prohibitive. Thus, analog beamforming based on a phase-shifting network driven by a variable gain amplifier (VGA) is a potential alternative technology. In this paper, we cast the beamforming vector design problem as a beampattern matching problem, with an unknown power gain. This is formulated as a unit-modulus least squares (ULS) problem where the optimal gain of the VGA is also designed in addition to the beamforming vector. We also consider a scenario where the receivers have the additional processing capability to adjust the phases of the incoming signals to mitigate specular multipath components. We propose efficient majorization-minimization (MM) based algorithms with convergence guarantees to a stationary point for solving both variants of the proposed ULS problem. Numerical results verify the effectiveness of the proposed solution in comparison with the existing state-of-the-art techniques.