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In this paper, we investigate a robust joint precoder-decoder design scheme for a multiple-input multiple-output physical layer network coding (PNC)-based two-way relay system. An orthogonal training sequence is used to estimate the channels. The estimate is imperfect, and a robust design is proposed to find precoders at the source nodes and decoder at the relay node to facilitate PNC operations during multiple-access stage. Both channel estimation error and antenna correlations are used to formulate the optimization problem to minimize the weighted mean square error (WMSE) under a total power constraint. The problem becomes non-convex, and we propose an algorithm to solve it optimally. During the broadcast stage, an algorithm is proposed to find a precoder at the relay node and decoders at source nodes. The system performance is evaluated with estimation error and antenna correlation parameters. The effect of weighting parameters, relay location, and number of antennas at nodes are also considered in the numerical analysis. Numerical results confirm that our joint precoder-decoder algorithms provide the optimal solution to the minimization of WMSE with the total available power.

Robust precoder-decoder design for physical layer network coding-based MIMO two-way relaying system