Asymptotic Analysis of Amplify and Forward Relaying in a Parallel MIMO Relay Network

TL;DR

This paper introduces an Incremental Cooperative Beamforming scheme for parallel MIMO relay networks, demonstrating it achieves capacity asymptotically as the number of relays grows, with full multiplexing gain and minimal gap to capacity.

Contribution

The paper proposes a simple scheme that asymptotically achieves the network capacity in large relay networks, extending previous work with a new beamforming approach.

Findings

Achieves capacity asymptotically as relay count increases.

Ensures full multiplexing gain regardless of relay number.

Relays' power scales as (rac{\u2212^9(K)}{K}) for the results to hold.

Abstract

This paper considers the setup of a parallel MIMO relay network in which $K$ relays, each equipped with $N$ antennas, assist the transmitter and the receiver, each equipped with $M$ antennas, in the half-duplex mode, under the assumption that $N\geq{M}$. This setup has been studied in the literature like in \cite{nabar}, \cite{nabar2}, and \cite{qr}. In this paper, a simple scheme, the so-called Incremental Cooperative Beamforming, is introduced and shown to achieve the capacity of the network in the asymptotic case of $K\to{\infty}$ with a gap no more than $O(\frac{1}{\log(K)})$. This result is shown to hold, as long as the power of the relays scales as $\omega(\frac{\log^9(K)}{K})$. Finally, the asymptotic SNR behavior is studied and it is proved that the proposed scheme achieves the full multiplexing gain, regardless of the number of relays.