## 3 Experiments and Results  
As shown in Figure 4, the experimental setup utilizes a narrow-linewidth laser (TeraXion, SFFL-N-34 (Quebec City, QC, Canada)) with a central wavelength of 1550.2387 nm and a linewidth of 1.035 KHz. The laser output is split into local light and signal light using a 10:90 coupler. The signal light is intensity-modulated into an OFDM-NLFM signal using an electro-optic modulator (EOM, JDSU, X5 (Singapore)). This signal consists of 4 subcarriers, each with an NLFM signal with a sweeping bandwidth of 20 MHz. An acousto-optic modulator (AOM, Gooch & Housego, T-M080 (Ilminster, UK)) is used for sideband suppression and a frequency shift of 80 MHz. The modulated pulse light is then amplified by an erbium-doped fiber amplifier (EDFA). It passes through a circulator and then enters a grating filter to filter out the amplifier's spontaneous emission noise. Subsequently, the light enters another circulator and travels through approximately 16.3 km of optical fiber. At around 14.3 km, the first piezoelectric transducer (PZT) with 5 m of wound optical fiber is positioned. Following this, it is connected to a 2 km-long optical fiber spool. A second PZT, which also has 5 m of wound optical fiber, is placed. Finally, there is a remaining 20 m of tail fiber at the end. The fiber generates backward Rayleigh scattering signals. These signals, along with the local light, are combined in the circulator. The beating frequency signal is detected using a balanced photodetector (BPD, MBD-200M-A) with a bandwidth of 200 MHz. The converted electrical signal first passes through a high-pass filter with a cutoff frequency of 80 MHz. It is then mixed with an 80 MHz sine wave and subsequently goes through a low-pass filter with a cutoff frequency of 120 MHz. Afterward, the signal is sampled by an acquisition card, with a sampling rate of 250 MSa/s. The acquired data are processed using a PC, where each frequency band is down-converted separately,  
Figure 4: Experimental setup. followed by low-pass filtering and matched filtering. This process extracts the amplitude for positioning and simultaneously extracts the phase to reconstruct the vibration waveform. When the subcarrier spacing is less than 1 times the sweep bandwidth, the received signal's positioning SNR and spatial resolution degrade. A 9.8 kHz 1 Vpp sine wave drive voltage is still applied to the PZT, with a sweep bandwidth of 20 MHz, theoretically achieving a spatial resolution of 10 m. As an example, considering a subcarrier spacing equal to 0.75 times the sweep bandwidth, the bandwidth occupied by the four frequency components should be 20 \(\times\) 0.75 \(\times\) 3 + 20 = 65 MHz, as shown in Figure 5:  
The dynamic range of the received signal after matched filtering is approximately 15 dB. The vibration position is determined using a moving differential method, and the result is shown in Figure 6a. A peak appears at 16.3 km in Figure 6a, indicating the location of the applied 9.8 kHz sine wave vibration. The SNR for this positioning is approximately 5 dB. As shown in Figure 6b, the moving differential peak of the tested optical fiber at 16.3 km is amplified. The indicated spatial resolution is approximately 11 m, which has decreased by about 1 m compared to the theoretical value. The curves 1, 2, 3, and 4 in Figure 7a represent the results of separate phase demodulating signals from four different frequency bands. Specifically, curve 1, which is represented  
Figure 5: The power spectrum of the OFDM-NLFM pulse when the center frequencies of the subcarriers are spaced by 0.75 times the sweep bandwidth. Figure 6: (**a**) The result of the moving differential after matched filtering of the received signal; (**b**) spatial resolution. by the blue curve, shows the time-domain waveform of the signal in the 0-20 MHz frequency band after phase demodulation. Curve 2, which is represented by the red curve, represents the time-domain waveform of the signal in the 15-35 MHz frequency band after phase demodulation.