A detector (200, 500, 600, 700, 800, 900) characterized by: an oscillation source (210, 710, 1010) configured to generate a first injection signal having a first frequency (fi); a frequency multiplier comprising: a first injection terminal configured to receive a first injection signal having a first frequency; an output terminal configured to output an output signal (Vo); and a second injection terminal configured to receive a second injection signal having a second frequency; wherein the frequency multiplier outputs the output signal (Vo) having an initial frequency equal to a multiple of the first frequency by injection locking, a frequency of the output signal (Vo) is updated by injection pulling to be a sum of a previous frequency of the output signal (Vo) and a difference frequency (fd), and the difference frequency (fd) is equal to a difference between the previous frequency of the output signal (Vo) and a frequency of a received signal (Vrx); a transceiver coupled to the output terminal and the second injection terminal of the frequency multiplier, and configured to transmit the output signal (Vo), and receive the received signal (Vrx), wherein the transceiver is configured to update the second injection signal by the received signal (Vrx); and a demodulator (240, 540, 640, 740, 840, 940) coupled to the output terminal of the frequency multiplier, and configured to perform a demodulation operation so as to generate a displacement signal (Vd) according to the output signal (Vo). an oscillation source (210, 710, 1010) configured to generate a first injection signal having a first frequency (fi); a frequency multiplier comprising: a first injection terminal configured to receive a first injection signal having a first frequency; an output terminal configured to output an output signal (Vo); and a second injection terminal configured to receive a second injection signal having a second frequency; wherein the frequency multiplier outputs the output signal (Vo) having an initial frequency equal to a multiple of the first frequency by injection locking, a frequency of the output signal (Vo) is updated by injection pulling to be a sum of a previous frequency of the output signal (Vo) and a difference frequency (fd), and the difference frequency (fd) is equal to a difference between the previous frequency of the output signal (Vo) and a frequency of a received signal (Vrx); a first injection terminal configured to receive a first injection signal having a first frequency; an output terminal configured to output an output signal (Vo); and a second injection terminal configured to receive a second injection signal having a second frequency; wherein the frequency multiplier outputs the output signal (Vo) having an initial frequency equal to a multiple of the first frequency by injection locking, a frequency of the output signal (Vo) is updated by injection pulling to be a sum of a previous frequency of the output signal (Vo) and a difference frequency (fd), and the difference frequency (fd) is equal to a difference between the previous frequency of the output signal (Vo) and a frequency of a received signal (Vrx); a transceiver coupled to the output terminal and the second injection terminal of the frequency multiplier, and configured to transmit the output signal (Vo), and receive the received signal (Vrx), wherein the transceiver is configured to update the second injection signal by the received signal (Vrx); and a demodulator (240, 540, 640, 740, 840, 940) coupled to the output terminal of the frequency multiplier, and configured to perform a demodulation operation so as to generate a displacement signal (Vd) according to the output signal (Vo).