Precoding design for two-way MIMO relay networks based on CP-SC transmission

This paper proposes a new source and relay precoding design in a two-way MIMO relay network based on cyclic prefixed single carrier (CP-SC) transmission. The source precoding, relay precoding, and decision feedback equalization with noise-prediction (DFE-NP) receivers are jointly designed to minimize the sum-mean squared error (MSE) of the network. An iterative algorithm is proposed to optimize the source and relay precoding matrices. It has been proved that in a two-way MIMO relay network with frequency-selective channels, the optimal relay precoding is a frequency-domain beamforming with a diagonal power allocation matrix, which is the transmit power across multiple beamforming directions. In order to reduce the computational complexity, a projected gradient algorithm of the diagonal matrix form is also applied in determining the power allocation matrix.