# Energy-Efficient Coordinated Multi-Cell Multigroup Multicast Beamforming with Antenna Selection

## TL;DR

This paper proposes an energy-efficient beamforming method for multi-cell multigroup multicast systems that incorporates antenna selection, leading to improved energy efficiency and convergence performance.

## Contribution

It introduces a novel antenna selection formulation and a successive convex approximation approach for energy-efficient beamforming in multi-cell multicast networks.

## Key findings

- Significant energy efficiency gains demonstrated.
- Proposed algorithm shows superior convergence.
- Near-binary solutions from continuous relaxation.

## Abstract

This paper studies energy-efficient coordinated beamforming in multi-cell multi-user multigroup multicast multiple-input single-output systems. We aim at maximizing the network energy efficiency by taking into account the fact that some of the radio frequency chains can be switched off in order to save power. We consider the antenna specific maximum power constraints to avoid non-linear distortion in power amplifiers and user-specific quality of service (QoS) constraints to guarantee a certain QoS levels. We first introduce binary antenna selection variables and use the perspective formulation to model the relation between them and the beamformers. Subsequently, we propose a new formulation which reduces the feasible set of the continuous relaxation, resulting in better performance compared to the original perspective formulation based problem. However, the resulting optimization problem is a mixed-Boolean non-convex fractional program, which is difficult to solve. We follow the standard continuous relaxation of the binary antenna selection variables, and then reformulate the problem such that it is amendable to successive convex approximation. Thereby, solving the continuous relaxation mostly results in near-binary solution. To recover the binary variables from the continuous relaxation, we switch off all the antennas for which the continuous values are smaller than a small threshold. Numerical results illustrate the superior convergence result and significant achievable gains in terms of energy efficiency with the proposed algorithm.