Aspects of Favorable Propagation in Massive MIMO

TL;DR

This paper investigates the concept of favorable propagation in Massive MIMO, proposing new measures to evaluate it, and analyzing its behavior in different channel scenarios including Rayleigh fading and UR-LoS.

Contribution

It introduces a 'distance from favorable propagation' metric and analyzes favorable propagation in Rayleigh and UR-LoS environments, including a novel urns-and-balls model.

Findings

Favorable propagation maximizes sum-capacity in Massive MIMO.

Channel condition number is a useful proxy for favorable propagation.

UR-LoS channels can also offer nearly favorable propagation.

Abstract

Favorable propagation, defined as mutual orthogonality among the vector-valued channels to the terminals, is one of the key properties of the radio channel that is exploited in Massive MIMO. However, there has been little work that studies this topic in detail. In this paper, we first show that favorable propagation offers the most desirable scenario in terms of maximizing the sum-capacity. One useful proxy for whether propagation is favorable or not is the channel condition number. However, this proxy is not good for the case where the norms of the channel vectors may not be equal. For this case, to evaluate how favorable the propagation offered by the channel is, we propose a ``distance from favorable propagation'' measure, which is the gap between the sum-capacity and the maximum capacity obtained under favorable propagation. Secondly, we examine how favorable the channels can be for two extreme scenarios: i.i.d. Rayleigh fading and uniform random line-of-sight (UR-LoS). Both environments offer (nearly) favorable propagation. Furthermore, to analyze the UR-LoS model, we propose an urns-and-balls model. This model is simple and explains the singular value spread characteristic of the UR-LoS model well.