On the Diversity–Multiplexing Tradeoff in Multiple-Relay Network

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper studies the setup of a multiple-relay network in which <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$K$</tex> </formula></emphasis> half-duplex multiple-antenna relays assist in the transmission between either one or 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 <emphasis emphasistype="italic">random sequential</emphasis> (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 <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">$(K &gt; 1)$</tex></formula></emphasis> 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 (AF) relaying and is not optimum in terms of DMT, while the dynamic decode-and-forward (DF) scheme is shown to be optimum for this scenario. </para>