# Distributed Multi-Stream Beamforming in MIMO Multi-Relay Interference Networks

## TL;DR

This paper proposes a distributed beamforming optimization method for multi-stream MIMO relay interference networks, achieving power minimization with convergence guarantees and improved efficiency over existing solutions.

## Contribution

It introduces a novel ADMM-based distributed algorithm for joint transmit and relay beamforming optimization in interference networks.

## Key findings

- ADMM algorithm converges to the optimal solution.
- Proposed method outperforms existing solutions in convergence rate and message exchange.
- Joint transmit and relay beamforming further reduces power consumption.

## Abstract

In this paper, multi-stream transmission in interference networks aided by multiple amplify-and-forward (AF) relays in the presence of direct links is considered. The objective is to minimize the sum power of transmitters and relays by beamforming optimization under the stream signal-to-interference-plus-noise-ratio (SINR) constraints. For transmit beamforming optimization, the problem is a well-known non-convex quadratically constrained quadratic program (QCQP) that is NP-hard to solve. After semi-definite relaxation (SDR), the problem can be optimally solved via alternating direction method of multipliers (ADMM) algorithm for distributed implementation. Analytical and extensive numerical analyses demonstrate that the proposed ADMM solution converges to the optimal centralized solution. The convergence rate, computational complexity, and message exchange load of the proposed algorithm outperforms the existing solutions. Furthermore, by SINR approximation at the relay side, distributed joint transmit and relay beamforming optimization is also proposed that further improves the total power saving at the cost of increased complexity.