## 4 Experiment Results and Discussion
### Communication Operation  
The analysis of a PolSK communication test signal is conducted, where the pair of EOMs generates two orthogonal polarization states to represent the data \"1\" and \"0\". In the experiment, EOM1 transmits \"01101\" and EOM2 transmits \"10010\". After modulation,  
Figure 5: Multi-point vibration positioning processing sequence. (**a**) Differential voltage signal; (**b**) time-delay spectrum showing corresponding positions associated with signal frequencies (identified from amplitude spectrum); (**c**) 3D relationship between vibration position, frequency, and amplitude.  
Figure 6: Vibration positioning accuracy from 100 repeated measurements. Inset: histogram of the positioning results with a Gaussian fitting.  
the information is transmitted through the optical fiber, and the communication signal received by the BPD of each detection end is shown in Figure 7. To decide between high and low levels, differential voltages greater than 40 mV are judged as \"1\", and those less than 40 mV are judged as \"0\". It is seen from Figures 7a and 7b that the periodic communication signals \"01101\" and \"10010\" can be clearly distinguished, corresponding to the modulation sequence \"01101\" from EOM1 and \"10010\" from EOM2, respectively. Due to the high extinction ratio of the modulation signal (static extinction ratio > 12 dB), even under the influence of vibrations, the communication signal can still maintain a relatively low bit error rate (BER).  
The BER can be estimated by analyzing the Q-parameter:  
\[BER=\frac{1}{2}erfc\bigg{(}\frac{Q}{\sqrt{2}}\bigg{)}, \tag{12}\]  
where the complementary error function (erfc) is defined as:  
\[erfc(x)=\frac{2}{\sqrt{\pi}}\int_{x}^{\infty}e^{-t^{2}}dt, \tag{13}\]  
The Q-parameter is defined as the ratio of the signal dynamic range to noise floor. A higher \(Q\)-parameter indicates a lower BER, given by:  
\[Q=\frac{V_{top}-V_{bottom}}{\sigma_{1}+\sigma_{2}}, \tag{14}\]  
where \(V_{top}\) and \(\sigma_{1}\) represent the signal amplitude and noise standard deviation for the high level, respectively, and \(V_{bottom}\) and \(\sigma_{2}\) represent the signal amplitude and noise standard deviation for the low level, respectively.  
The \(Q\)-parameter can also be expressed in decibels (dB), commonly denoted as \(Q_{dB}\), and is calculated by converting the linear scale into logarithmic scale. The conversion is as follows:  
\[Q_{dB}=20\text{log}_{10}\,Q, \tag{15}\]  
To analyze the stability and channel quality of the PolSK data transmission under vibrations, an eye diagram is plotted in Figure 8. In the eye diagram, the \"1\" level (\(V_{top}\)) and \"0\" level (\(V_{bottom}\)) represent the binary value of 1 or 0, respectively. The average value of the  
Figure 7: PolSK communication bit recovery under the influence of vibrations. (**a**) BPD1 signal (01011 sequence); (**b**) BPD2 signal (10100 sequence). Red line: recovery of original communication signal; blue line: BPD signal; black dashed line: decision threshold.  
high level (\(V_{top}\)) is 63.74 mV, with a standard deviation (\(\sigma_{1}\)) of 3.92 mV, while the average value of the low level (\(V_{bottom}\)) is 2.65 mV, with a standard deviation (\(\sigma_{2}\)) of 10.64 mV. According to Equations (12)-(15), the calculated \(Q_{dB}\) is 12.46 dB, and the estimated BER is \(1.359\times 10^{-5}\).