An access point communicates with a wireless station based on a point-to-point channel, to determine time instances of future communication to be received from the wireless station. In intervals between such future communications, the access point powers down at least some portions of a circuit contained within the access point for at least a partial duration between such future communications. In an embodiment, the powered-down portions include the receiver portions of the access point. The access point may be battery-powered, and the powering-down of the receiver portions enables reduction of power consumption in the access point.