A terminal for use in a wireless network includes a radio frequency (RF) receiver, which is configured to receive and downconvert a RF signal. The RF signal includes a sequence of downlink frames, each downlink frame including at least a map zone followed by a data zone. The map zone contains an indication of a time allocation in the data zone during which downlink data will be transmitted to the terminal. An analog/digital (A/D) converter converts the output signal from the RF receiver into a stream of digital samples. A digital processing circuit processes the digital samples so as to identify the time allocation and to recover the downlink data transmitted during the identified time allocation, while shutting down the RF receiver during at least one interval during the downlink frame that is outside the identified time allocation.