# Globally Optimal Beamforming Design for Downlink CoMP transmission with Limited Backhaul Capacity

## TL;DR

This paper introduces a globally optimal algorithm for beamforming in multicell downlink systems with limited backhaul, improving over existing suboptimal methods and serving as a benchmark.

## Contribution

It develops the first globally optimal solution for joint beamforming and link selection under backhaul and power constraints in CoMP systems.

## Key findings

- The optimal algorithm converges in finite iterations.
- Suboptimal methods achieve only 70-90% of optimal performance.
- The proposed method provides a benchmark for future solutions.

## Abstract

This paper considers a multicell downlink channel in which multiple base stations (BSs) cooperatively serve users by jointly precoding shared data transported from a central processor over limited-capacity backhaul links. We jointly design the beamformers and BS-user link selection so as to maximize the sum rate subject to user-specific signal-to-interference-noise (SINR) requirements, per-BS backhaul capacity and per-BS power constraints. As existing solutions for the considered problem are suboptimal and their optimality remains unknown due to the lack of globally optimal solutions, we characterized this gap by proposing a globally optimal algorithm for the problem of interest. Specifically, the proposed method is customized from a generic framework of a branch and bound algorithm applied to discrete monotonic optimization. We show that the proposed algorithm converges after a finite number of iterations, and can serve as a benchmark for existing suboptimal solutions and those that will be developed for similar contexts in the future. In this regard, we numerically compare the proposed optimal solution to a current state-of-the-art, which show that this suboptimal method only attains 70% to 90% of the optimal performance.