Linear Precoder Design for an AF Two-Way MIMO Relay Node with No Source Node Precoding

In this paper, an amplify-and-forward two-way relay (TWR) precoding is designed with no source node (SN) processing in order tomaximize sum rate and concurrently reduce the network latency and signaling overhead. For the arbitrary pre-/postprocessing at the SNs that have N antennas, it is rigorously shown that an N-by-N optimal TWR precoder matrix is symmetric when the noise power of the TWR node is relatively small compared with that of the SNs and/or each of the channel matrices is spatially orthogonal. Using the symmetric structure of the TWR precoding matrix, a constrained nonlinear-multivariable optimization problem is formulated that can be solved with polynomial time complexity. Furthermore, a closed-form optimal TWRprecoding matrix is designed for aTWR system with N = 2. When compared with an optimal joint SN andRNprecoding method, it is verified that the proposed precoding method provides a good tradeoff between the system complexity and sum rate performance.