Diversity of MIMO Multihop Relay Channels

TL;DR

This paper analyzes the diversity-multiplexing tradeoff in multihop MIMO relay channels, proposing optimal and near-optimal relaying schemes that maximize diversity and multiplexing gains in various relay configurations.

Contribution

It introduces the flip-and-forward scheme that achieves both maximum diversity and multiplexing gains in multihop relay channels, along with universal coding strategies.

Findings

Decode-and-forward scheme attains the cut-set bound in clustered relays.

Parallel amplify-and-forward improves diversity over naive AF.

Flip-and-forward scheme achieves optimal diversity and multiplexing gains.

Abstract

We consider slow fading relay channels with a single multi-antenna source-destination terminal pair. The source signal arrives at the destination via N hops through N-1 layers of relays. We analyze the diversity of such channels with fixed network size at high SNR. In the clustered case where the relays within the same layer can have full cooperation, the cooperative decode-and-forward (DF) scheme is shown to be optimal in terms of the diversity-multiplexing tradeoff (DMT). The upper bound on the DMT, the cut-set bound, is attained. In the non-clustered case, we show that the naive amplify-and-forward (AF) scheme has the maximum multiplexing gain of the channel but is suboptimal in diversity, as compared to the cut-set bound. To improve the diversity, space-time relay processing is introduced through the parallel partition of the multihop channel. The idea is to let the source signal go through K different "AF paths" in the multihop channel. This parallel AF scheme creates a parallel channel in the time domain and has the maximum diversity if the partition is properly designed. Since this scheme does not achieve the maximum multiplexing gain in general, we propose a flip-and-forward (FF) scheme that is built from the parallel AF scheme. It is shown that the FF scheme achieves both the maximum diversity and multiplexing gains in a distributed multihop channel of arbitrary size. In order to realize the DMT promised by the relaying strategies, approximately universal coding schemes are also proposed.