Optimal Linear Precoding in Multi-User MIMO Systems: A Large System Analysis

TL;DR

This paper analyzes the design of optimal linear precoding in large multi-user MIMO systems, showing that regularized zero-forcing can be optimal under certain conditions and proposing modifications based on statistical information.

Contribution

It provides a large system analysis of optimal precoding, revealing conditions where RZF is optimal and proposing heuristic designs using asymptotic insights.

Findings

RZF precoder is asymptotically optimal when SINR-to-channel ratio is uniform.

Modified RZF achieves near-optimal performance with statistical UE position info.

Numerical results demonstrate the performance gap in finite systems.

Abstract

We consider the downlink of a single-cell multi-user MIMO system in which the base station makes use of $N$ antennas to communicate with $K$ single-antenna user equipments (UEs) randomly positioned in the coverage area. In particular, we focus on the problem of designing the optimal linear precoding for minimizing the total power consumption while satisfying a set of target signal-to-interference-plus-noise ratios (SINRs). To gain insights into the structure of the optimal solution and reduce the computational complexity for its evaluation, we analyze the asymptotic regime where $N$ and $K$ grow large with a given ratio and make use of recent results from large system analysis to compute the asymptotic solution. Then, we concentrate on the asymptotically design of heuristic linear precoding techniques. Interestingly, it turns out that the regularized zero-forcing (RZF) precoder is equivalent to the optimal one when the ratio between the SINR requirement and the average channel attenuation is the same for all UEs. If this condition does not hold true but only the same SINR constraint is imposed for all UEs, then the RZF can be modified to still achieve optimality if statistical information of the UE positions is available at the BS. Numerical results are used to evaluate the performance gap in the finite system regime and to make comparisons among the precoding techniques.