A wireless receiver is activated periodically to measure the level of received signals. It measures the average received level over a plurality of the activation periods, and enables the supply of power to receiver circuitry dependent on the measured average value. In one embodiment the power is enabled if an increase in the average value is detected which is greater than a predetermined margin. The average value may be measured in a sliding or stepped window. In another embodiment the power is enabled if the level in an activation period exceeds the average value by a predetermined margin.