Asymptotic Capacity and Optimal Precoding in MIMO Multi-Hop Relay Networks

TL;DR

This paper derives a closed-form expression for the asymptotic mutual information in multi-hop MIMO relay networks with correlated fading, and identifies optimal precoding strategies based solely on channel statistics.

Contribution

It provides a novel asymptotic analysis of mutual information in multi-hop MIMO systems and determines optimal precoding directions using channel statistics.

Findings

Closed-form asymptotic mutual information expression

Optimal precoding vectors aligned with channel eigenvectors

Precoding strategies depend only on channel statistics

Abstract

A multi-hop relaying system is analyzed where data sent by a multi-antenna source is relayed by successive multi-antenna relays until it reaches a multi-antenna destination. Assuming correlated fading at each hop, each relay receives a faded version of the signal from the previous level, performs linear precoding and retransmits it to the next level. Using free probability theory and assuming that the noise power at relaying levels-- but not at destination-- is negligible, the closed-form expression of the asymptotic instantaneous end-to-end mutual information is derived as the number of antennas at all levels grows large. The so-obtained deterministic expression is independent from the channel realizations while depending only on channel statistics. Moreover, it also serves as the asymptotic value of the average end-to-end mutual information. The optimal singular vectors of the precoding matrices that maximize the average mutual information with finite number of antennas at all levels are also provided. It turns out that the optimal precoding singular vectors are aligned to the eigenvectors of the channel correlation matrices. Thus they can be determined using only the known channel statistics. As the optimal precoding singular vectors are independent from the system size, they are also optimal in the asymptotic regime.