Frequency-division multiplexing (FDM) could effectively expand the high-frequency response capability of the phase-sensitive optical time-domain reflectometry (W-OTDR) system. However, the redistribution of the probe pulse energy into bilateral bands by Mach-Zehnder modulators significantly degrades the signal-to-noise ratio (SNR). A multiplex random coding (MRC) method is proposed for compensating the probe energy loss, which deploys distinct random coding pulses per channel to achieve SNR gain. Experimental results demonstrate that by using a five-channel sensing system, the SNR of the restored sinusoidal acoustic signals with a frequency of 15 kHz can reach 29.89 dB over a 10.438 km optical fiber. Compared with the conventional FDM W-OTDR system, the RMSE value of the demodulated signal at 45 km in a static environment decreased by 67.77 %. Furthermore, over a 48.536 km optical fiber, the SNR of the restored 1 kHz sinusoidal acoustic signal is improved by 9.37 dB, and the strain resolution is reduced from 120 p epsilon/ Hz to 31 p epsilon/ Hz. Compared with other FDM W-OTDR systems employing coding techniques, the scheme exhibits superior sensing performance. This method provides a potential solution for practical engineering applications of distributed acoustic sensing technology based on W-OTDR, particularly in detecting weak signals at high frequencies over a long distance.
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