Alternating rate profile optimization in single stream MIMO interference channels

We consider a set of transmitter-receiver pairs operating concurrently in the same spectral band. The transmitters and receivers are equipped with multiple antennas and are restricted to apply single stream beamforming. This setting corresponds to the single stream multiple-input multiple-output (MIMO) interference channel. We assume perfect channel state information at the transmitters and the single-user decoding receivers. Efficient operating points in this setting correspond to points on the Pareto boundary of the achievable rate region. Characterizing all Pareto optimal points in the MIMO interference channel is still an unsolved problem. An approach to attain different Pareto optimal points in the MIMO interference channel is rate profile optimization. Given the nonconvexity of the problem, we propose an alternating approach based on successive optimization of the transmit and receive beamforming vectors. For fixed receive beamforming vectors, a solution for the rate profile optimization exists and is solved by a set of convex feasibility problems. For fixed transmit beamforming vectors, we show that the rate profile optimization can be solved by a set of feasibility problems each corresponding to an inverse field of values problem. The convergence of the alternating algorithm is guaranteed to a stationary point of the original problem.