The diversity-multiplexing tradeoff for independent parallel MIMO channels

The diversity-multiplexing tradeoff has become a powerful tool to analyze MIMO fading channels. In this paper, we first derive the diversity-multiplexing tradeoff for the case that the transmitter and receiver are connected by multiple parallel and independent MIMO channels, each of which may be utilized for some limiting fraction of the total time. Our main result in this respect is an elegant geometric characterization of the tradeoff curve in terms of the Zheng-Tse tradeoff for a single MIMO channel. We then apply this result to compute bounds on the DMT for a three phase bi-directional cooperation (or two-way relay) protocol. These bounds are shown to be tight in the case of single antenna nodes and the optimal relative time duration of each phase that maximizes the diversity of the end-users is determined. The DMT derived here may also be of importance to problems where a node can be seen to receive information over channels that can be decomposed into parallel independent components, which is often the case in protocols for half-duplex cooperative networks.