I. Introduction
MmWave communications employs a large number of antennas at the base station (BS) and user equipment (UE) to enable beamforming (BF) that can combat the high pathloss in mmWave bands. The resulting beams are narrow and there is a significant challenge to find the best directions in which to point the beams. This task is called beam alignment (BA). The mmWave channel typically exhibits a small number of scatterers [1], and hence has a sparse channel matrix in the angle domain. Compressive sensing (CS) based BA methods have been developed for this problem [2]–[12].