Diversity-multiplexing tradeoff of the dynamic decode and forward protocol on a MIMO half-duplex relay channel

We compute the diversity-multiplexing tradeoff (DMT) curve for a three node multi-input-multi-output (MIMO) half-duplex (HD) relay network, operating in the dynamic decode-and-forward (DDF) [1] mode. We consider the case where the source and the destination have n antennas each and the single relay node has m antennas. Denoting such a channel as a (n, m)-relay channel, we provide an analytical characterization of the DMT curve for certain simple configurations such as (n, 1), (1, m) and (2, 2). We employ a numerical method to compute the DMT for more general channel configurations. Interestingly, for low multiplexing gains the achievable diversity orders of the HD-DDF protocol coincides with the diversity orders achieved by the full-duplex decode-and-forward (FDDF) protocol analyzed in [2]. In fact, the HD-DDF and FDDF protocols achieve the same diversity orders for all integer multiplexing gains. Thus, the half duplex constraint does not significantly affect the achievable DMT for the DF protocol when the source and the destination have the same number of antennas.