A detector includes a frequency multiplier and a transceiving node. The frequency multiplier includes a first terminal, a second terminal and an output terminal. The first terminal is used to receive a first injection signal having a first frequency. The output terminal is used to output an output signal. The second terminal is used to receive a second injection signal having a second frequency. The frequency multiplier is used to output the output signal at a frequency substantially equal to a multiple of the first frequency by injection locking and pull the output signal to the second frequency by injection pulling. The transceiving node is coupled to the output terminal and the second terminal of the frequency multiplier. The transceiving node is used to transmit the output signal, and receive a received signal having a third frequency. The received signal is used to update the second injection signal.