On the diversity-multiplexing tradeoff of multiuser amplify & forward multihop networks

We consider an amplify & forward multihop network with n single-antenna nodes in the source and destination stage each, as well as n
_R

^(l)
, l ¿ {1, ..., L}, single-antenna relay nodes in the l-th relay stage. The relay gain allocation scheme proposed in decouples this network into parallel single-input single-output (SISO) links between n source-destination pairs under certain conditions on the network topology. Hence, all degrees of freedom are achieved in a distributed fashion. We extend this as follows: for i.i.d. CN(0, 1) fading coefficients and SISO coding/decoding at source and destination nodes, we derive an upper-bound on the diversity-multiplexing tradeoff curve of the network. Moreover, we devise a scheme that we conjecture to achieve the bound, if the network can be decoupled and L ¿ 2.