Multi-hop MIMO relay networks: diversity-multiplexing trade-off analysis

A multi-hop relay network with multiple antenna terminals in a quasi-static slow fading environment is considered. The fundamental diversity-multiplexing gain tradeoff (DMT) is analyzed in the case of half-duplex relay terminals. While decode-and-forward (DF) relaying achieves the optimal DMT in the full-duplex relay scenario, it is shown that the dynamic decode-and-forward (DDF) protocol achieves the optimal DMT if the relay is constrained to half-duplex operation. For the latter case, static DF protocols are considered as well, and the corresponding DMT performance is shown to fall short of the optimal performance, which indicates that dynamic channel allocation is required for optimal DMT performance. The optimal DMT is expressed as the solution of a convex optimization problem and explicit DMT expressions are presented for some special cases. In the case of multiple relays, it is shown that the optimal diversity gain, which is achieved by exploiting the available "hop-diversity", is dominated by the neighboring two-hops with the minimum diversity gain.