Optimizing receipt of call/broadcast paging messages by self-powered wireless communications devices

A wireless communications network (120) responds to each incoming call placed to a wireless communications device (134) by transmitting a call-paging message (418) within a corresponding partition of a digital radio frame of prescribed format. Responsive to each occurrence of a broadcast event (404), the network transmits (414) a repeating broadcast-paging message announcing the availability of broadcast content from the network. The broadcast-paging message is transmitted multiple times within each digital radio frame. Another sequence (500) describes WCD operation in this network. Responsive to wakcup (502) from sleep, the WCD detects (509) received signal quality. The WCD also receives (510) scheduled network transmission of a call-paging message and a number of instances (at least one) of a repeating network transmitted broadcast-paging message that occurs multiple times for each scheduled transmission of the call-paging message. This number varies inversely with the detected signal quality.