A low-complexity relay transmit strategy for two-way relaying with MIMO amplify and forward relays

In this paper we consider two-way relaying with a MIMO amplify and forward (AF) relay. In the literature, the relay amplification matrix which maximizes the sum rate in two-way relaying is not known for the general MIMO case. However, the maximization of the channels´ Frobenius norms is easily achieved via the Algebraic Norm-Maximizing (ANOMAX) transmit strategy. While this scheme provides a significant improvement in the received signals´ strengths, it does not reach the full multiplexing gain for high SNRs due to its low rank nature. Therefore, we propose a simple strategy to restore the rank while preserving the same subspaces via an optimization over the profile of the singular values. The resulting scheme is called rank-restored ANOMAX (RR-ANOMAX). The main benefit of this approach is that the computational complexity is very low. Moreover, its performance is very close to the one-way upper-bound which is obtained by considering the two transmission directions as independent one-way relaying channels.