DMT of Multi-hop Cooperative Networks - Part I: Basic Results

TL;DR

This paper analyzes the diversity-multiplexing tradeoff in multi-hop cooperative networks with full-duplex relays, establishing fundamental limits and explicit protocols based on amplify-and-forward relaying, with a focus on the min-cut and min-cut rank.

Contribution

It introduces new theoretical results linking DMT to network min-cut and min-cut rank, and provides explicit AF-based protocols for full-duplex multi-hop networks.

Findings

Maximum diversity equals the network min-cut.

Maximum multiplexing gain equals the min-cut rank.

Linear diversity-multiplexing tradeoff is achievable with AF protocols.

Abstract

In this two-part paper, the DMT of cooperative multi-hop networks is examined. The focus is on single-source single-sink (ss-ss) multi-hop relay networks having slow-fading links and relays that potentially possess multiple antennas. The present paper examines the two end-points of the DMT of full-duplex networks. In particular, the maximum achievable diversity of arbitrary multi-terminal wireless networks is shown to be equal to the min-cut. The maximum multiplexing gain of arbitrary full-duplex ss-ss networks is shown to be equal to the min-cut rank, using a new connection to a deterministic network. We also prove some basic results including a proof that the colored noise encountered in AF protocols for cooperative networks can be treated as white noise for DMT computations. The DMT of a parallel channel with independent MIMO links is also computed here. As an application of these basic results, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable for full-duplex networks with single antenna nodes. All protocols in this paper are explicit and rely only upon amplify-and-forward (AF) relaying. Half duplex networks are studied, and explicit codes for all protocols proposed in both parts, are provided in the companion paper.