On the Diversity-Multiplexing Tradeoff in Multiple-Relay Network

TL;DR

This paper introduces a new amplify-and-forward based scheme called random sequential (RS) for multiple-relay networks, achieving maximum diversity gain and optimal diversity-multiplexing tradeoff in various configurations, especially for single-antenna two-hop networks.

Contribution

It proposes the RS scheme for multiple-relay networks and derives its DMT, demonstrating optimality in certain network setups and highlighting limitations in others.

Findings

RS scheme achieves maximum diversity gain in general multiple-antenna networks.

RS scheme attains the optimal DMT in single-antenna two-hop multiple-access relay networks.

In single relay multiple access scenarios, RS reduces to naive amplify-and-forward and is not DMT-optimal.

Abstract

This paper studies the setup of a multiple-relay network in which $K$ half-duplex multiple-antenna relays assist in the transmission between a/several multiple-antenna transmitter(s) and a multiple-antenna receiver. Each two nodes are assumed to be either connected through a quasi-static Rayleigh fading channel, or disconnected. We propose a new scheme, which we call \textit{random sequential} (RS), based on the amplify-and-forward relaying. We prove that for general multiple-antenna multiple-relay networks, the proposed scheme achieves the maximum diversity gain. Furthermore, we derive diversity-multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple-access multiple-relay ($K>1$) networks (without direct link between the transmitter(s) and the receiver), the proposed RS scheme achieves the optimum DMT. However, for the case of multiple access single relay setup, we show that the RS scheme reduces to the naive amplify-and-forward relaying and is not optimum in terms of DMT, while the dynamic decode-and-forward scheme is shown to be optimum for this scenario.