Maximum sum rate of non-regenerative two-way relaying in systems with different complexities

This paper considers the two-hop relaying case with bi-directional communication of two multiple-antenna nodes S1 and S2 via an intermediate multiple-antenna node, namely the relay station (RS). A general framework for the sum rate maximization in linear, non-regenerative two-way relaying with multiple-antenna nodes is proposed assuming all nodes have perfect channel state information (CSI) in order to perform linear beamforming (BF). There may be application cases in which the system cannot provide perfect CSI to all nodes or the nodes cannot be such complex. Hence, three different cases of system complexity are investigated which are shown to be special cases of the introduced framework. Firstly, all nodes can perform BF, secondly only S1 and S2 can perform BF, and thirdly only the RS can perform BF. The optimum performances of all three cases are compared to each other by means of numeric optimizations, and approaches to solve the resulting optimization problems are proposed. It is shown that applying BF exclusively at the RS provides the same performance as applying BF at all nodes.