A method of performing a beam alignment procedure in a mmW or upper centimeter wave system, usable for performing initial access (IA) for user equipment (UE) to establish a connection with a base station (BS) is disclosed. A UE receives a signal from a base station, divides a search space into a plurality of angular zones, locates a direction of peak received strength within each zone, and forms a beam along the direction of peak overall signal strength. The number of angular zones is chosen such that the probability that each zone contains one peak of signal strength exceeds some threshold. The method is applicable in mmW and upper cmW bands in both BS to UE and device-to-device (D2D) communications.