Reduced-dimension cooperative precoding for MIMO two-way relay channels

Abstract—We investigate efficient communications over MIMO two-way relay channels (TWRCs) of nT < nR, where nT denotes the number of antennas at each user and nR denotes that at the relay. We propose a new reduced-dimension (RD) cooperative precoding scheme. In the proposed scheme, the two users cooperatively create nT aligned eigen-modes, supporting nT streams of physical-layer network coding. We investigate the design of the RD cooperative precoder and derive an asymptotically optimal solution. We analytically show that, in the worst case, the proposed scheme is within 1 2 bit per transmit antenna of the asymptotic sum-capacity of the MIMO TWRC. For fading MIMO TWRCs with i.i.d. Gaussian coefficients, we derive a closed-form expression of the average sum-rate of the proposed scheme using large system analysis. Our analytical result shows that, for a large system with nT nR = 1 2, the proposed scheme is less than 0.16 bit per transmit antenna away from the capacity. Furthermore, this gap reduces as nT nR increases, and vanishes as nT nR tends to 1. It is demonstrated that the proposed scheme can significantly outperform other existing schemes in the literature. Index Terms—MIMO, two-way relay channel, physical-layer network coding, precoding, capacity. I