Distributed (Space-Time) Codes for the MIMO Multihop Channel via Partitions of the Channel

Abstract

Summary form only given. In this paper, we consider multiantenna multihop relay channels in which the source signal arrives at the destination through N independent relaying hops in series. The main concern of this work is to design relaying strategies that efficiently utilize the relays in such a way that the diversity is maximized. First, we focus on the amplify-and-forward (AF) strategy with which the relays simply scale the received signal and retransmit it. More specifically, we characterize the diversity-multiplexing tradeoff (DMT) of the AF scheme in a general multihop channel with arbitrary number of antennas and arbitrary number of hops. The DMT is derived in closed-form expression as a function of the number of antennas at each node: as a first step, we provide some basic results on the DMT of the general Rayleigh product channels. It turns out that these results have very simple and intuitive interpretation. Then, the results are applied to the AF multihop channels which is shown to be equivalent to the Rayleigh product channel, in the DMT sense. Then, we mitigate the diversity suboptimality of the AF scheme via two kinds of partitions of the multihop channel : serial and parallel partitions. The serial partition corresponds to the intermediate decoding scheme. By supposing the relaying nodes could have full antenna cooperation, we study the fundamental problem that is when and where to decode to avoid diversity degradation. This scheme has minimum coding delay. The parallel partition corresponds to the distributed space-time processing. We establish conditions for the parallel partition to achieve the maximum diversity of the multihop channels. The parallel partition being rate-deficient in general, we propose a flip-and-forward (FF) scheme that achieves both the maximum diversity gain and multiplexing gain. The FF scheme is based on the parallel partition and works in a completely distributed manner. Coding schemes for both relaying strategies are proposed as well.