DMT of Multi-hop Cooperative Networks - Part II: Half-Duplex Networks with Full-Duplex Performance

Abstract

We consider single-source single-sink (ss-ss) multihop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversitymultiplexing gain tradeoff (DMT), few results are available for more general networks. In a companion paper, we characterized end points of DMT of arbitrary networks, and established some basic results which laid the foundation for the results presented here. In the present paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP) networks and layered networks.KPP networks may be viewed as the union of K nodedisjoint parallel relaying paths. Generalizations of these networks include KPP(I) networks, which permit interference between paths and KPP(D) networks, which possess a direct link between source and sink. We characterize the DMT of these families of networks completely for K > 3 and show that they can achieve the cut-set bound, thus proving that the DMT performance of full-duplex networks can be obtained even in the presence of the half-duplex constraint. We then consider layered networks, which are comprised of layers of relays, and prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fullyconnected(fc) layered networks. This is shown to be equal to the cut-set bound on DMT if the number of relaying layers is less than 4, thus characterizing the DMT of this family of networks completely. For multiple-antenna KPP and layered networks, we provide lower bounds on DMT, that are significantly better than the best-known bounds.All protocols in this paper are explicit and use only amplifyand-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes. In addition, it is shown that codes achieving full diversity on a MIMO Rayleigh channel achieve full diversity on arbitrary fading channels as well.Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT.