Space-division approach for multi-pair MIMO two way relaying: A principal-angle perspective

This work investigates the maximum sum-rate of multi-pair MIMO two-way relay channels (TWRCs), in which a relay is responsible for forwarding information between multiple pairs of users. In this system, each pair of users forms a TWRC, and a user exchanges information only with its counterpart in the same TWRC. We focus on the multi-access channel (MAC) phase of the two-pair TWRCs. We first put forth a new interpretation of the space-division (SD) method based on the classical concept of principal angles in linear algebra. We argue that the signal spaces of the two users in a TWRC can be divided into the physical-layer network coding (PNC) signal subspace and the complete decoding (CD) signal subspace according to the principal angles between the two signal spaces of different user pairs. Based on the principal-angle framework, we then propose an extended SD method to mitigate the interference among the PNC signals and CD signals. We further derive the optimal decoding strategy and optimal precoder design principles that maximize the sum-rate of the MAC phase. The associated optimization problem, however, is non-convex. We therefore propose a suboptimal solution for precoder design and analyze the asymptotic rate gap benchmarked against the cut-set bound. Significant performance improvements have been observed for the proposed hybrid PNC-CD system compared with pure complete decoding and pure PNC decoding.