Cooperative Transmission for a Vector Gaussian Parallel Relay Network

TL;DR

This paper analyzes cooperative transmission schemes in a multi-antenna parallel relay network, demonstrating the conditions under which decode-and-forward, amplify-and-forward, and compress-and-forward schemes are optimal or asymptotically optimal.

Contribution

It introduces and compares three cooperative transmission schemes, showing their optimality conditions and asymptotic behaviors in a vector Gaussian relay network.

Findings

DF scheme achieves capacity under certain conditions.

CF scheme is asymptotically optimal at high relay power.

AF scheme is asymptotically optimal only with full-rank relay-to-destination channels.

Abstract

In this paper, we consider a parallel relay network where two relays cooperatively help a source transmit to a destination. We assume the source and the destination nodes are equipped with multiple antennas. Three basic schemes and their achievable rates are studied: Decode-and-Forward (DF), Amplify-and-Forward (AF), and Compress-and-Forward (CF). For the DF scheme, the source transmits two private signals, one for each relay, where dirty paper coding (DPC) is used between the two private streams, and a common signal for both relays. The relays make efficient use of the common information to introduce a proper amount of correlation in the transmission to the destination. We show that the DF scheme achieves the capacity under certain conditions. We also show that the CF scheme is asymptotically optimal in the high relay power limit, regardless of channel ranks. It turns out that the AF scheme also achieves the asymptotic optimality but only when the relays-to-destination channel is full rank. The relative advantages of the three schemes are discussed with numerical results.