Low-High SNR Transition in Multiuser MIMO

TL;DR

This paper introduces the concept of the bend point to characterize the transition between low and high SNR regimes in multiuser MIMO systems, providing analytical insights and practical approximations for medium SNR performance.

Contribution

It proposes the bend point as a new analytical tool to understand the low-high SNR transition in MU-MIMO and derives its expression for zero-forcing precoding.

Findings

Bend point quantifies the transition between low and high SNR regimes.

Derived the bend point for MU-MIMO with zero-forcing precoding.

Provided a new approximation of sum-rate at the bend point.

Abstract

Multiuser MIMO (MU-MIMO) plays a key role in the widely adopted 3GPP LTE standard for wireless cellular networks. While exact and asymptotic sum-rate results are well known, the problem of obtaining intuitive analytical results for medium signal-to-noise ratios (SNRs) is still not solved. In this paper, we propose the bend point, which quantifies the transition between low and high SNR; i.e., the beginning of the high SNR region. We derive the bend point for MU-MIMO with zero-forcing precoding and show that it is intimately related to the intercept of the high SNR asymptote with the zero sum-rate line. Using this result, we obtain a new approximation of the sum-rate at the bend point---providing a useful rule of thumb for the effect of increasing the number of antennas at medium SNR.