There is disclosed a method performed by a wireless communication device 100 to enable the reception of a beam sweep transmission. The method comprises obtaining S1 information enabling said wireless communication device 100 to determine whether it is stationary, or essentially stationary. The method also comprises acquiring S2 configuration information comprising information about the starting time for the beam sweep transmission. The method also comprises determining S3 a time when to initiate a reception of the beam sweep transmission based at least partially on the obtained information and the acquired configuration information, thereby allowing said wireless communication device to enter, or remain in, a first activity state until the determined time. The method also comprises entering S4, at the determined time, a second activity state whereby said wireless communication device is capable to receive the beam sweep. There is also disclosed a complementary method performed by a radio network node as well as corresponding devices and computer programs.