Joint pre-coder and decoder design for physical layer network coding based MIMO two-way relay system

We investigate a joint precoder decoder design scheme for multiple-input multiple-output (MIMO) channel physical layer network coding (PNC) based two-way relay system. Precoders at source nodes and decoder at relay node are designed to facilitate PNC operations at the relay node. We consider minimizing the weighted mean square error (MSE) at relay node to enhance the accuracy of the PNC. Formulated optimization problem is non-convex and we propose an algorithm to solve it optimally. Numerical results confirm that the joint precoder decoder algorithm provides the optimal solution to minimizing weighted MSE with the total available power. Effect of weighting parameters, relay location and number of antennas at nodes are considered in the system analysis.