An integrated circuit configured to operate in a mobile device includes a discovery generator module. The discovery generator module is configured to generate a corresponding random value for each beacon interval. A discovery control module is configured to determine a duration of time of a given beacon interval in which the mobile device is to operate in at least one of an active mode and a sleep mode. The duration of time is based on the corresponding random value generated for the given beacon interval. A physical layer (PHY) device is configured to wirelessly transmit a discovery request signal during the time the mobile device is operating in the active mode. The mobile device is partially powered down or fully powered down during the time the mobile device is operating in the sleep mode.