Optimized capacity bounds for the half-duplex Gaussian MIMO relay channel

In this paper, the optimization of the cut-set bound (CSB) and the achievable decode-and-forward (DF) rate for the half-duplex Gaussian multiple-input multiple-output (MIMO) relay channel is considered. In particular, it is shown that evaluating the cut-set bound and the maximal achievable DF rate is equivalent to solving convex optimization problems if perfect channel state information (CSI) is available at all nodes. Our work therefore extends results for the full-duplex relay channel, which we also revisit here, and it demonstrates that it is possible to efficiently determine (generally loose) bounds on the capacity of the half-duplex MIMO relay channel.