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...

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Abstract-Wireless fading networks with multiple antennas are typically studied information-theoretically from two different perspectives -the outage characterization and the ergodic capacity characterization. A key parameter in the outage characterization of a network is the diversity, whereas a first-order indicator for the ergodic capacity is the degrees of freedom (DOF), which is the pre-log coefficient in the capacity expression. In this paper, we present max-flow min-cut type theorems for computing both the diversity and the degrees of freedom of arbitrary single-source single-sink multi-antenna networks. We also show that an amplify-and-forward protocol is sufficient to achieve this. The degrees of freedom characterization is obtained using a conversion to a deterministic wireless network for which the capacity was recently found. We show that the diversity result easily extends to multi-source multi-sink networks and evaluate the DOF for multi-casting in single-source multi-sink networks.

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The assumption of nodes in a cooperative communication relay network operating in synchronous fashion is often unrealistic. In the present paper we consider two different models of asynchronous operation in cooperativediversity networks experiencing slow fading and examine the corresponding diversity-multiplexing tradeoffs (DMT). For both models, we propose protocols and distributed space-time codes that asymptotically achieve the transmit diversity bound for all multiplexing gains and for number of relays N ≥ 2.