Statistical beamformer design for the two-antenna interference channel

The focus of this work is on the two user interference channel with two antennas at each transmitter and a single antenna at both users. We assume that both the transmitters use a linear beamforming scheme for signaling and the users treat interference as noise. The links are assumed to be spatially correlated and the focus is on understanding the structure of the beamforming vectors that maximize the average sum-rate as a function of the statistics of all the channels and the SNR level at both the transmitters. Building on recent work that studies Pareto optimality in a similar context, we show that (from the class of linear beamforming schemes) a rank-1 beamformer is always optimal when both the transmitters are of low-SNR. In general, the rank of the optimal beamforming matrix is a complicated function of the SNRs and channel statistics. Nevertheless, it is shown that the high-SNR optimal rank-1 beamformer is the generalized eigenvector of the two links as seen from each transmitter.