A communication system includes a demodulator configured to demodulate an amplified modulated signal responsive to a first carrier signal. The demodulator includes a filter and a gain adjusting circuit. The filter is configured to generate a filtered first signal based on a first signal. The first signal is based on the first carrier signal and the amplified modulated signal. The filter has a gain adjusted based on a set of control signals. The gain adjusting circuit is coupled to the filter, and configured to generate the set of control signals based on at least a voltage of the filtered first signal or a voltage of a second signal. The gain adjusting circuit includes a first peak detector configured to output a peak value of the voltage of the second signal. The voltage of the second signal includes a voltage of the first signal or a voltage of a reference signal.