Bounds on the capacity regions of half-duplex Gaussian MIMO relay channels

This article considers uni- and bidirectional communication in the half-duplex Gaussian multiple- input multiple-output (MIMO) relay channel. Assuming perfect channel state information at all nodes and the use of time division duplex communications protocol to separate transmissions and recep- tions at all nodes, we propose a dual decomposition approach to efficiently determine upper and lower bounds on the capacity and the capacity region of the half-duplex relay channel and the restricted half- duplex two-way relay channel, respectively. Our approach allows to quantify the fundamental limits of the considered relay networks, and the obtained results may serve as benchmarks when studying different and/or suboptimal relay strategies or the impact of channel estimation errors. Furthermore, we discuss how our dual decomposition approach may be used for designing optimal resource alloca- tion protocols.