Precoding design for denoise-and-forward network coding in MIMO two-way relay systems

In this paper, a denoise-and-forward network coding (DNF-NC) scheme is proposed for multiple-input and multiple-output (MIMO) two-way relaying channels. Specifically the relay jointly detects the M-quadrature amplitude modulation (M-QAM) messages from two sources, and remaps the network coded detections into the same modulation mode. Furthermore, the precoding design for DNF-NC is studied to minimize the total mean square error (MSE). To ensure the relay denoising performance, two necessary conditions are presented first, and then the general optimal precoding matrices can be obtained by solving two convex problems independently. Moreover, a channel diagonalization scheme with power allocation is introduced, and the closed-form solution for high SNR region is also derived. Compared with the optimized amplify-and-forward network coding (AF-NC) scheme, DNF-NC has much lower computational complexity, and the simulation results show that it can achieve better BER performance than AF-NC in high SNR region.