Optimal Transmit Strategies in Multi-Antenna Bidirectional Relaying

We study the transmit strategies in a MIMO bidirectional relaying scenario with individual power constraints. In two phases a half-duplex relay node decodes-and-forwards the signals of two nodes. Each node has multiple antennas. We deduce the transmit strategy in the first phase from the general Gaussian MIMO-MAC. Since each node knows a priori the interference of its own message in the second phase interference-free reception is achieved. Therefore, the optimal relay transmit strategy is given by two point-to-point water-filling solutions which are coupled by the relay power distribution. In the large SNR, the sum of any bidirectional rate tuple on the boundary of the rate region is asymptotically proportional with the minimum spatial degree of both MIMO channels.