Optimized beamforming for the two stream MIMO interference channel at high SNR

We investigate the high SNR behavior of the two-user multiple-input/multiple-output (MIMO) interference channel with two antennas at each terminal, where the receivers treat the interference as noise. It is known that themaximum multiplexing gain of such a system is two, and that it can be achieved with zero-forcing. We introduce the high SNR rate offset as a performance measure to further differentiate between solutions achieving the full multiplexing gain and, by maximizing the high SNR rate offset, formulate a system of multivariate polynomial equations necessary for the globally optimal high SNR transmit strategy in terms of sum rate. We furthermore define a two-player game in which the two users are constrained to transmit exactly one data stream, but compete for the beamformer design; the Nash equilibria of this game can be explicitly calculated. The so-found sum rate optimal and semi-competitive solutions are also shown in simulations to outperform the conventional competitive approach to the MIMO interference channel even at finite SNR.