In a communication system (100) where a remote unit is given a time offset for a base station (102) and hands off to the base station (102) if the remote unit (113) can acquire the base station within a time window surrounding the time offset, a remote unit (113) utilizes the time offset of each base station (supplied by a serving base station (101) via downlink communication signal (116)) and searches for neighboring base stations within the time window surrounding its PN offset. The time window surrounding an individual base station's PN offset is allowed to vary depending upon whether the communication system (100) is time synchronized. In particular, a base station (101) supplies the remote unit (113) with an indication that the communication system (100) is operating in a synchronized or an unsynchronized mode, and the remote unit (113) varies the time window (search window) accordingly.