MIMO Two-Way Compress-and-Forward Relaying with Approximate Joint Eigen-Decomposition

While compress-and-forward (CF) is one of the basic relay protocols in cooperative transmission, little is known about the optimal design of CF in multiple-input multiple-output (MIMO) two-way relay channels (TWRC). An intuitive method is to compress each element of the superimposed signal vector during the multiple-access (MAC) phase independently and with identical compression noise variance. In this paper, we introduce an improved compression method. The key idea is to apply approximate joint diagonalization (AJD) to realize simultaneous eigen-decomposition of the two channel matrices in the MAC phase of two-way relaying in an approximate manner. After that, a novel covariance matrix design of the compression noise vector is derived for sum-rate maximization. Numerical results show that the proposed CF design can improve the spectral efficiency, especially when the relay node is close to any of the two source nodes instead of in the midpoint.