An integrated circuit includes a control module and a physical layer device. The control module (i) during each of multiple beacon intervals, operates a mobile device in a sleep mode or a listen mode, and (ii) for each of the beacon intervals, selects a length of the sleep mode or the listen mode such that resulting lengths of the sleep mode or the listen mode vary randomly. The control module partially or fully powers down the mobile device during the sleep mode. The physical layer device (i) wirelessly transmits, while the control module operates the mobile device in an active mode, a signal to discover one or more peers in a peer-to-peer network, and (ii) while the control module is operating the mobile device in the listen mode, receives responses to the signal. The control module determines which of the peers are discoverable based on the responses.