Mirror-Prox SCA Algorithm for Multicast Beamforming and Antenna Selection

TL;DR

This paper introduces a low-complexity Successive Convex Approximation algorithm utilizing Saddle Point Mirror-Prox for joint multicast beamforming and antenna selection, outperforming traditional SDR methods in quality and efficiency.

Contribution

It proposes a novel SCA algorithm combined with SP-MP for efficient joint multicast beamforming and antenna selection, reducing computational complexity and improving solution quality.

Findings

SP-MP SCA outperforms SDR in solution quality.

The proposed method has lower computational complexity.

Simulation results confirm the effectiveness of the approach.

Abstract

This paper considers the (NP-)hard problem of joint multicast beamforming and antenna selection. Prior work has focused on using Semi-Definite relaxation (SDR) techniques in an attempt to obtain a high quality sub-optimal solution. However, SDR suffers from the drawback of having high computational complexity, as SDR lifts the problem to higher dimensional space, effectively squaring the number of variables. This paper proposes a high performance, low complexity Successive Convex Approximation (SCA) algorithm for max-min SNR "fair" joint multicast beamforming and antenna selection under a sum power constraint. The proposed approach relies on iteratively approximating the non-convex objective with a series of non-smooth convex subproblems, and then, a first order-based method called Saddle Point Mirror-Prox (SP-MP) is used to compute optimal solutions for each SCA subproblem. Simulations reveal that the SP-MP SCA algorithm provides a higher quality and lower complexity solution compared to the one obtained using SDR.