The diversity-multiplexing tradeoff of the symmetric MIMO half-duplex relay channel

The diversity-multiplexing tradeoff (DMT) is obtained for the symmetric MIMO half-duplex (HD) relay channel where the source and the destination have n antennas each and the relay node has m antennas (hereafter, such a channel is referred to as an (n, m)-relay channel). The characterization of the DMT requires the joint eigenvalue distribution of three specially correlated central Wishart random matrices, which is derived using a related result in. The explicit characterization of the DMT, besides providing the theoretical benchmark for evaluating performance of practical cooperative protocols on this channel, reveals several interesting facts such as: a) the HD operation of the relay fundamentally limits relay channel performance in the sense that the DMT of the full-duplex (FD) relay channel can be strictly greater than that of the HD relay channel; b) an extra antenna at the relay node on a HD relay channel does not always improve the achievable diversity order, unlike that on an FD relay channel. While the fundamental DMTs of the two channels (FD and HD) coincide for a range of low multiplexing gains (MG), this range becomes smaller and the gap between the two (HD and FD) at higher MGs become larger with increasing number of antennas at the relay node, thus potentially justifying the extra cost of an FD relay. It is also proved that the DMTs of the HD and FD (n, 1)-relay channels are the same. Finally, it is shown that the DMT of the (1, m) relay channel can be achieved over different ranges of multiplexing gains by the dynamic decode-and-forward (DDF) and the quantize-and-forward (QF) protocols.