On Achievable Rate Regions for Half-Duplex Gaussian MIMO Relay Channels: A Decomposition Approach

We consider uni- and bidirectional communication in the half-duplex multiple-input multiple-output (MIMO) relay channel. Assuming perfect channel state information at all nodes and the use of time division duplex communication protocols with a peak power constraint for every protocol phase, we propose a dual decomposition approach to efficiently determine the cut-set bound and the maximum achievable decode-and-forward rate for the Gaussian MIMO relay channel. A general outer bound on the rate regions that can be achieved in the restricted two-way MIMO relay channel is established, and we present an achievable rate region based on the decode-and-forward scheme which is a superset of several previously derived achievable rate regions. Finally, it is shown how the stated outer bound and achievable rate region can also be evaluated by means of the proposed dual decomposition approach, and we discuss how our work may be used for designing optimal protocols.