A packet-based radio receiver (10) comprises an automatic gain control system (17) and a signal-level detector (18, 19, 20) for monitoring an analog signal derived from radio signals received by the radio receiver. The signal-level detector (18, 19, 20) comprises a binary memory cell (22, 24) and a monitoring system. The monitoring system comprises a comparator (21, 23) arranged to receive a reference voltage at a first input and the analog signal at a second input. The monitoring system is arranged to (i) continuously monitor the voltage of the analog signal, (ii) detect when the monitored signal exceeds the reference voltage, and (iii) store a predetermined binary value in the memory cell (22, 24) in response to such a detection. The automatic gain control system (17) is arranged to control the gain of a variable-gain component (12, 13, 14) of the radio receiver in dependence on the contents of the binary memory cell (22, 24).