DMT of multi-hop cooperative networks

Abstract

Some basic results that help in determining the Diversity-Multiplexing Tradeoff (DMT) of cooperative multihop networks are first identified. As examples, the maximum achiev able diversity gain is shown to equal the min-cut between source and sink, whereas the maximal multiplexing gain is shown to equal the minimum rank of the matrix characterizing the MIMO channel appearing across a cut in the network.Two multi-hop generalizations of the two-hop network are then considered, namely layered networks as well as a class of networks introduced here and termed as K -parallel-path (KPP) networks. The DMT of KPP networks is characterized for K > 3.It is shown that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for fully-connected, layered networks. Explicit coding schemes achieving the DMT that make use of cyclic-division-algebra-based distributed space-time codes underlie the above results.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, amplify and-forward protocols are often sufficient to attain the optimal DMT. I. IN TRODUCTIONWe present an overview of the results contained in [1], [2]. The setting for these results is a single-source, single-sink (ss ss) wireless network where each link experiences Rayleigh fading and where the additive noise on each link is CN(O, 1).The focus is on performance as measured by the diversity multiplexing tradeoff (DMT).The results are of two kinds: basic results that apply to such networks in general as well as results that provide information about the DMT of specific classes of networks. A. Prior Work While two-hop cooperative relay networks have been stud ied in considerable detail in the literature, (see for example, [4]-[8], [17]-[19], [27]-[31]), in terms of the DMT, few results are available for more general networks. Yang and Belfiore in [33]consider Amplify-and-Forward (AF) protocols for a family of MIMO multi-hop networks (which are termed as multi-antenna layered networks in the current paper). They derive the optimal DMT for the Rayleigh-product channel which they prove is equal to the DMT of the AF protocol applied to this channel. They also propose AF protocols to achieve the optimal diversity of these multi-antenna layered networks.Oggier and Hassibi [23] have proposed distributed space time codes for multi-antenna layered networks that achieve diversity gain equal to the minimum number of relay nodes among the hops. Vaze and Heath [24] construct distributed space time codes based on orthogonal designs that achieve the optimal diversity of the multi-antenna layered network. In [25], the same authors study the question of the circumstances under which coding is required to achieve full diversity in a layered network.Borade, Zheng and Gallager in [26] consider AF schemes on a class of multi-hop layered networks where each layer has the same number of relays (termed as regular networks in the curr...

A Low-Complexity Protocol for K-Parallel-Path Multihop Networks

“…Existing works 1) Edge coloring strategy: In [1], [2], authors defined and studied the KPP channel from a theoretical point of view. In particular, the optimal DMT of such a channel is proven to be…”

“…Multihop protocols have also been proposed to reach these theoretic performance. Diversity is usually brought by space-time coding [1]- [5]. However, this strategy induces a high decoding complexity.…”

Diversity multiplexing tradeoff of asynchronous cooperative relay networks

“…The resulting noise term Gv +w is not white in general. But it has been shown in [11] that for the class of AF protocols in general the resulting noise at the destination is white in the scale of interest. Hence from now on we will work with the model…”

“…One possible way to lower bound the DMT is to drop some symbols from the received vector such that the channel matrix between the remaining subset of input and output symbols is lower triangular. For if the matrix is lower triangular, we can use results from [11] to lower bound the DMT. For the channel in equation (5), it is clear that after dropping {y 2 , y 4 , y 6 } the resulting channel model will be ⎡…”

“…In order to derive a lower bound on the DMT of the proposed protocol we make use of the following important result from [11].…”