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

This article considers uniand 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 receptions 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 allocation protocols.