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 to maximize 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 TWR precoding matrix is designed for a TWR system with N = 2. When compared with an optimal joint SN and RN precoding method, it is verified that the proposed precoding method provides a good tradeoff between the system complexity and sum rate performance.