DMT of multi-hop cooperative networks

Some basic results that help in determining the Diversity-Multiplexing Tradeoff (DMT) of cooperative multihop networks are first identified. As examples, the maximum achievable 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 d_max 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.