SINR Constrained Beamforming for a MIMO Multi-user Downlink System

TL;DR

This paper proves the convergence of key beamforming algorithms for MIMO multi-user downlink systems with QoS constraints, introducing a new MMSE-DUAL algorithm that unifies existing methods and demonstrates robust performance.

Contribution

The paper establishes convergence proofs for MMSE-SOCP and UDD algorithms, and introduces the MMSE-DUAL algorithm connecting these methods for QoS-constrained power minimization.

Findings

All algorithms reach similar objective values regardless of initialization.

MMSE-SOCP/MMSE-DUAL algorithms perform reliably.

UDD algorithm can fail with infeasible initialization.

Abstract

Consider a multi-input multi-output (MIMO) downlink multi-user channel. A well-studied problem in such system is the design of linear beamformers for power minimization with the quality of service (QoS) constraints. The most representative algorithms for solving this class of problems are the so-called MMSE-SOCP algorithm [11-12] and the UDD algorithm [9]. The former is based on alternating optimization of the transmit and receive beamformers, while the latter is based on the well-known uplink-dowlink duality theory. Despite their wide applicability, the convergence (to KKT solutions) of both algorithms is still open in the literature. In this paper, we rigorously establish the convergence of these algorithms for QoS-constrained power minimization (QCPM) problem with both single stream and multiple streams per user cases. Key to our analysis is the development and analysis of a new MMSE-DUAL algorithm, which connects the MMSE-SOCP and the UDD algorithm. Our numerical experiments show that 1) all these algorithms can almost always reach points with the same objective value irrespective of initialization, 2) the MMSE-SOCP/MMSE-DUAL algorithm works well while the UDD algorithm may fail with an infeasible initialization.