On the beamforming design for efficient interference alignment

An efficient interference alignment (IA) scheme is developed for k-user single-input single-output frequency selective fading interference channels. The main idea is to steer the transmit beamforming matrices such that at each receiver the subspace dimensions occupied by interference-free desired streams are asymptotically the same as those occupied by all interferences. Our proposed scheme achieves a higher multiplexing gain at any given number of channel realizations in comparison with the original IA scheme, which is known to achieve the optimal multiplexing gain asymptotically.