A fast beam training method for a couple of user equipment, UE, and base station, BS, belonging to a mobile communication network such as a 5G network. A pair of iterative loops involves the UE and the BS, and iteratively refine the respective orientation and beamwidth of the transmit beam at the BS side and receive beam at UE side, based on an iteratively refined estimate of the UE position and Angle of Arrival at the UE. The iterative loops can be performed in series or in parallel. The beam training method converges when predetermined constraints on the standard deviations of the estimated UE position and estimated angle of arrival of the downlink signal at the UE are both met. The refined position of the UE can be used for a subsequent localization-assisted communication.