1. Introduction

Coherent optical communication, already extensively commercialized in 100 G and beyond 100 G long-haul transmissions, is now expanding towards access networks and data center interconnects. Due to its ability to preserve the complete light field information during the demodulation process, it enables the potential for “communication-sensing” integration. Given the widespread deployment of coherent optical communication, this dual-function approach presents a promising avenue for enhancing the utility and efficiency of optical fiber networks.

Current seafloor sensing networks, while providing valuable data, are costly to deploy and maintain, which leads to an insufficient global coverage. By leveraging existing undersea fiber-optic networks, we can develop an integrated communication-sensing system. This approach not only mitigates the high costs and the challenge of expansive coverage but also enhances our ability to monitor and understand various natural phenomena like earthquakes and tsunamis [1]. Another pivotal application lies within the realm of power networks, where the safety and integrity of overhead line cables, a critical component, are often jeopardized by vibrations from high winds, improper construction activities, and lightning strikes. These threats underscore the need for a comprehensive, cost-effective solution capable of monitoring these threats and ensuring the stability of our power networks. Optical fiber sensing can also be used to monitor the structural health in urban, or monitor the underground embedded pipelines [2].

Traditional optical fiber sensing techniques are often built on reflective methodologies, such as Optical Time-Domain Reflectometry (OTDR), Bragg Grating Sensors, and Rayleigh, Raman, or Brillouin Scattering-based sensors. These techniques operate by sending a pulse of light down the fiber and analyzing the reflected light from points along the fiber, which can illuminate changes in environmental conditions like temperature, strain, and more [3]. However, these reflection-based techniques exhibit certain limitations. For one, the inherently weak signal strength of reflected light often results in a restricted operating range. In another aspect, the usage of light pulses could potentially interfere with the operation of communication systems. Additionally, these methods often require specialized light sources and detectors, coupled with complex signal processing, which can increase both the cost and complexity of the overall system.

In contrast, forward-propagating optical communication signal-based sensing methods circumvent many of these obstacles. These methods allow for channel estimation and phase estimation at the coherent receiver end, offering potential advantages in terms of coverage distance, sensitivity, and system complexity. As a result, forward-propagating techniques are gaining traction as an increasingly promising alternative in the realm of optical fiber sensing.

Because stress variations in optical fibers directly affect delay and phase, the Jones matrix of a lengthy fiber link depends on the cumulative effect of the fiber's birefringence that connects the transmitter and the receiver. Phase detection methods are generally more sensitive compared to simply monitoring the Jones matrix [4,5]. However, phase estimation is vulnerable to laser noise, even when using high-end lasers with a linewidth as low as a few tens of Hz. Conversely, polarization state estimation for sensing can be performed using lasers with a linewidth level of 100 kHz, which are routinely used in 100 G optical communication systems. This makes polarization state sensing a practical and cost-effective method for large-scale applications [6–9].

Existing literature has proposed the estimation of polarization state parameters by reading the equalization coefficients of adaptive equalizers, which are updated using the constant modulus algorithm (CMA) or other adaptive filtering algorithms [6,7]. However, this statistical-based coefficient update method not only exhibits slow response times but also struggles to accurately reflect subtle changes in the polarization state. Therefore, in our approach, we propose to directly calculate the polarization matrix using training data, which promises to offer a more accurate and responsive method for monitoring subtle changes in the polarization state.

In our previous work [10], we introduced a two-section equalizer architecture, which included two Finite Impulse Response (FIR) filters and a Direct Computation Butterfly Filter (DCBF). This unique architecture demonstrated superior fast-tracking capabilities compared to adaptive filter-based architectures, making it uniquely effective for sensing rapid polarization changes induced by phenomena such as lightning strikes.

In this paper, we extend our investigation to the polarization state changes caused by optical fiber vibrations. We established an experimental platform for studying optical fiber vibrations based on piezoelectric ceramics. Under these conditions with relatively slow polarization changes, both DCSA and the existing adaptive filter-based sensing architectures (AFSA) are capable of tracking these changes. However, The DCSA is predicted to offer superior performance in terms of sensitivity, and noise resistance compared to the AFSA. Furthermore, by recovering the tune of a song played near the optical fiber from changes in the polarization state, we demonstrated the correspondence between polarization state changes and acoustic vibrations.

Following this, by implementing a bidirectional transmission setup using two coherent devices, we were able to compare data from both ends and determine the distance difference between the two ends during a vibration event, thus enabling us to accurately locate the source of the vibration.

Our technique was further validated through field tests by inducing vibrations with machines and observing natural movements of the cable. These findings reinforce its validity for various practical applications.

2. Proposed method

In the practical ultra-high voltage AC power grid construction, the long haul systems over Optical Ground Wire (OPGW) span seldom exceed 500 km. Morever, although fibers during 1980s has large PMD parameter often exceeding 1ps/km^1/2, the modern fibers installed have very small PMD parameter (< 0.1 ps/km^1/2) [11]. Given these conditions, the impact of PMD and Polarization Dependent Loss (PDL) can be considered negligible. Therefore, for the purposes of our analysis, we approximate the polarization as an orthogonal matrix.

At the receiver end, as depicted in Fig. 1, we adopt the two-stage equalizer architecture identical to the one used in [10]. After coherent demodulation and the first stage of Finite Impulse Response (FIR) filtering, the signal after the elimination of Inter-symbol Interference (ISI) can be represented as

Here $\textrm{E}_{\textrm{IM}}^\textrm{X}$ and $\textrm{E}_{\textrm{IM}}^\textrm{Y}$ are the two FIR’s output, TX/TY is transmitted symbol, $\Delta \textrm{f}$ is the frequency offset, $\Phi $ is the common phase offset of the two polarization, A/B is Jones matrix element, * denotes conjugate. Utilizing the method from paper [10], we design two training symbols as a group. The two transmitted (TX) symbols are chosen randomly from the set {1,j,-1,-j}. The two TY symbols are then chosen such that TY(2n) equals ± TX(2n) and TY(2n + 1) equals ± j × TX(2n + 1).

 

Fig. 1. Schematic diagram of the two-stage equalizer. The second stage features a forward MIMO for polarization resolution, with polarization directly calculated. An adaptive equalization MIMO is also depicted for comparative analysis.

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After the conjugate product of $\textrm{E}_{\textrm{IM}}^{\textrm{X/Y}}$ signal, the obtained result can be expressed as

Then A² and B² are obtained.

Our FPGA's system clock operates at an approximate frequency of 180 MHz, hence, the State of Polarization (SOP) is updated at this rate. However, due to the memory depth limitation of 128 K in our FPGA debugging tool, direct sampling at 180 MHz would provide a frequency resolution of just 1.4 K (calculated as 180 M/128 K). Such a resolution is inadequate for detecting low-frequency disturbances, such as acoustic vibrations. To address this, we accumulate 2^N instances of A² and B² for reading, resulting in what we refer to as the ‘Accumulated Polarization Signal’ (APS). The actual sampling rate of APS is 180/2^N MHz. Thus, by employing this methodology, our frequency resolution is enhanced to 1.4 K/2^N. To detect disturbances at even lower frequencies, we can opt for a larger value of N, further improving the resolution. Taking N = 12 as an example, this equals to a signal with sampling rate of 44 kHz. The accumulation of all A² and B² values serves to filter the signal and reduce noise.

Moreover, the APS signal can be considered as a combination of a DC component and a varying component, which can be represented by the equation:

Here, APS_A_DC and APS_B_DC refer to the average level of the APS signal, and ΔAPS_A and ΔAPS_B denote the variation in the APS signal over time, which corresponds to the external vibration signal. This means that these variations can be used to measure or represent the external vibrations affecting the system, or to infer information about the external environment disturbances. The changes in APS could be due to several factors such as mechanical stresses, temperature fluctuations, or acoustic vibrations. When ΔAPS_A/B is significantly smaller than APS_A/B_DC, the third term in the expansion of Eqs. (4), (5) is much smaller than the second term. Therefore, after removing the constant component (the first term), the filtered APS_A²/B² signals can be directly used to indicate external disturbances, which contain the vibration signal, its harmonics, and other line disturbances. This approach greatly simplifies the computation process.

As anticipated, by transforming the filtered APS Signals into the frequency domain, we can observe distinct disturbance signals that stand out above the background noise. In scenarios where multiple sources of disturbance, each exhibiting unique frequencies, coexist, these individual disturbance signals can be effectively differentiated in the frequency domain.

As shown in Fig. 2, we can calculate the distance difference from the disturbance source to each end by transmitting light signals bi-directionally using two coherent devices (named as the West and East devices), and comparing the time difference of the disturbance signals arriving at both ends. The exact location of the disturbance source can then be determined after combining this with the known distance between the two ends. The time difference can be calculated by performing a correlation operation on the disturbance signals in the time domain from both ends. Alternatively, calculating the phase difference of the signals in the frequency domain, the distance difference can be represented as

Here, ΔL represents the distance difference, Φ_West and Φ_East represent the phases of the recovered signals, C is the speed of light in vacuum, n is the refractive index, f₂ and f₁ can be any of the positive or negative frequencies of the disturbance signal or its harmonics.

 

Fig. 2. The setup of source localization experiment

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Although theoretically, correlation peaks would appear at intervals of c/n(f₂-f₁), introducing ambiguity in distance determination, in practical scenarios this ambiguity can often be resolved by considering specific application conditions. For rapid polarization rotations, such as those caused by lightning strikes, there are distinct start and end moments, which allow us to compute the time difference of arrival at both ends directly. Thus, when employing the correlation method or phase comparison for localization, the disturbances we typically deal with are of low frequency. In these situations, due to the long intervals, even if ambiguities do occur, they are relatively very few and can be resolved by integrating other information. The sine wave was chosen for its simplicity to demonstrate our method, but real-world vibrations are more intricate. By decomposing these complex vibrations into individual frequencies, our equation can be applied to each, yielding insights into the vibration's nature and position.

As a prerequisite for this approach, synchronization of timing between both ends is essential. While GPS can be used to achieve this, another alternative is the implementation of a master-slave mode. In this configuration, one end sends a unique sequence to the other end, thereby ensuring that the sampling process begins simultaneously at both ends. Notably, this method not only ensures synchronization but also circumvents the potential issues associated with GPS availability or reliability.

3. Laboratory experimental setup

To evaluate the performance of the integrated communication and sensing system proposed in this study, we first conducted tests in a laboratory environment, using a 10 G coherent transceiver product as our reception platform, as illustrated in Fig. 2. The FPGA utilized was an Altera GSMD8K2, responsible for generating the modulating signal through four SerDes. A pair of training symbols was inserted every 32 symbols, resulting in an insertion ratio of 1/16. On the receiving side, we implemented the two-section equalizer proposed in paper [10]. The initial two FIR filters, updated by the adaptive algorithm, counteract the effects of slowly varying ISI, whereas the subsequent training-based feed-forward 1-tap 2 × 2 MIMO directly computes the polarization.

A piezoelectric ceramic actuator was used to simulate the source of vibration, driven by a sinusoidal signal with a 5 V amplitude produced by a signal generator. The actuator was located on the western side of the transmission line, 15.2 km from the western end and 39.9 km from the eastern end.

Due to the debug depth limit of the FPGA, the total length of the sample data was restricted to 128 K. The accumulation number for the APS signal was chosen based on the frequency of the tested vibration signal. During the tests, N was set to 12 when f_vibra>=1KHz, N was 15 when 31.25Hz < f_vibra < 1KHz, and N was 18 when f_vibra < 31.25 Hz. Choosing larger values for N allows for the extension of the signal acquisition window, thus enhancing the resolution of low-frequency vibration signals.

For comparison, we also implement an adaptive algorithm in the second stage Multiple-Input Multiple-Output (MIMO) system with FPGA, with functionality represented in the bottom part of Fig. 1. The functionality of the MIMO can be represented as

Here $\textrm{E}_{\textrm{out2}}^{\textrm{X/Y}}$ represent the outputs of the adaptive MIMO, and Hxx_Adapt, Hxy_Adapt, Hyx_Adapt, and Hyy_Adapt are the coefficients of the adaptive MIMO. The coefficients can be updated based on a gradient-based algorithm [12]. When using the Constant Modulus Algorithm (CMA), the corresponding error equation for this algorithm can be represented as:

Here ${\textrm{D}_{\textrm{X}}}$ and ${\textrm{D}_{\textrm{Y}}}$ are decided data, $\Delta \textrm{f}$ is the estimated frequency offset used for compensation, ${\Omega _{\textrm{X}}}$ and ${\Omega _{\textrm{Y}}}$ is the estimated phase offset.

For Hxx_Adapt, Hxy_Adapt, Hyx_Adapt, and Hyy_Adapt, we adopted the same methodology as with APS_A² and B², namely, accumulating 2^N instances for reading. As a result, their sampling frequency is 180/2^N MHz. These signals are correspondingly named as APS_Hxx_Adapt, APS_Hxy_Adapt, APS_Hyx_Adapt, and APS_Hyy_Adapt. The selection of N is consistent with what was previously mentioned for APS_A² and APS_B².

In the vibration source localization experiment, as depicted in Fig. 2, we achieve bidirectional transmission through an optical circulator. The signals sent from the West and East ends operate at wavelengths of 1550.12 nm and 1549.12 nm, respectively. We initiate the sampling at the East end by sending a special sequence from the West end. Then the West end waits for an interval equivalent to the optical signal transmission delay before starting simultaneously with the East end. The delays in the optical fiber path are considered known quantities, which can be determined using an OTDR during the setup of the line or through a loop-back test.

4. Laboratory experiment result and discussion

Figure 3 illustrates the representation of the APS and APS_adapt signals in the complex plane when subjected to a 4 kHz sinusoidal disturbance generated by the piezoelectric ceramic actuator. Additionally, Fig. 4 shows the real and imaginary parts of the APS and APS_adapt signals under the same conditions. Because APS and APS_Adapt are sampled simultaneously, a length of 128 K couldn't be chosen due to memory limitations, the sample points span a length of 64 K. With N = 12 and a sampling frequency of 44KHz (calculated as 180 MHz/2¹²), this results in a sampling duration of 1.45 seconds. It is evident that the APS signal remains relatively constant, while the APS_adapt signal, influenced by the adaptive filter, exhibits a drift over time. Observing Eq.7, it can be seen that the simultaneous rotation of Hxx and Hxy only causes the output signal to rotate in the complex plane, without changing its magnitude. According to the presented equation (8-9), the Constant Modulus Algorithm (CMA) remains valid [12]. Furthermore, as shown in equation (10-11), the rotation of the MIMO output in the complex plane is compensated through carrier recovery when employing the Least Mean Squares (LMS) algorithm based on decision feedback. In both scenarios, the simultaneous rotation of Hxx and Hxy cannot be detected by the error function, making it an unavoidable occurrence.

 

Fig. 3. Complex plane representation of the APS and APS_adapt signals: (a) APS_A² and APS_B², (b) APS_Hxx_Adapt and APS_Hxy_Adapt, (c) APS_S23_Adapt

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Fig. 4. Representation of the real and imaginary parts of the APS and APS_adapt signals (a) real and imaginary parts of the APS_signal (b) real and imaginary parts of the APS_Adapt_signal (c) real and imaginary parts of the APS_Adapt_S23_signal

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This drift introduces noise, particularly in the low-frequency range. By performing an FFT transformation on the APS and APS_AdaptF signals obtained under 4 kHz disturbance conditions and examining their modulus, it becomes evident, as shown in Fig. 5, that APS_AdaptF exhibits stronger noise. Particularly in the lower frequency domain, the noise significantly outweighs any potential vibration signals.

 

Fig. 5. Representation of FFT of the APS and APS_adapt signals without DC component. (a) |fft(APS_A²)| (red) and |fft(APS_B²)| (blue); (b) |fft(APS_Hxx_Adapt)| (red) and |fft(APS_Hxy_Adapt)| (blue); (c) |fft(APS_S23_Adapt); (d)20log10(|fft(APS_A²)|) (red) and 20log10(|fft(APS_B²)|) (blue), in dB; (e) 20log10(|fft(APS_Hxx_Adapt)|) (red) and 20log10(|fft(APS_Hxy_Adapt)|) (blue), in dB; (f) 20log10(|fft(APS_S23_Adapt|), in dB.

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In Fig. 5, many tones cannot be attributed to the harmonics of 4 K Hz, it underscores the complexity of the relationship between changes in the optical fiber's SOP state and external disturbances. Such complexity necessitates further investigation. Some of these tones may not even be related to disturbances at all. In the processing of this article, they are all treated as noise.

To quantitatively measure the performance of different methods, we employed a signal-to-noise ratio (SNR) estimation approach. Initially, we isolated our vibration frequency signal, referred to as Signal_band1, by using a 10/2^(N-12) Hz bandwidth. Subsequently, we applied a 100/2^(N-12) Hz bandwidth with the same center frequency to filter out Signal_band2. By calculating the power of both signals, we obtain the difference between them, which represents the noise power within the 100/2^(N-12) Hz bandwidth. The SNR is defined as follows:

The unit is in decibels (dB), and the numerator is multiplied by 10 to offset the effect of bandwidth size.

When comparing the signal-to-noise ratio (SNR) of the APS and APS_Hxx/Hxy_adapt signals, a significant difference is observed, ranging from 15 to 25 dB, which makes a detailed graphical comparison unnecessary. Taking into account the simultaneous rotation of Hxx and Hxy, we propose that the noise resulting from this rotation can be mitigated by multiplying Hxx and the conjugates of Hxy. This processed signal, referred to as APS_S23_adapt because it bears resemblance to the S2 and S3 elements of the Stokes vector, exhibits a point-like representation in the complex plane, as observed in Fig. 3(c). Upon performing FFT transformation and comparing Fig. 5(c) with Fig. 5(a), it becomes apparent that the difference between them is already challenging to discern visually for a 4 kHz vibration.

In subsequent tests, we conducted SNR evaluations of the APS-signal and APS_S23_adapt using the method described by Eq. (12). The evaluations were performed across a range of frequencies, including 0.98 Hz, 1.95 Hz, 3.09 Hz, 7.81 Hz, 15.63 Hz, 31.25 Hz, 62.5 Hz, 125 Hz, 250 Hz, 500 Hz, 1 KHz, 2 KHz, 4 KHz, and 8 KHz. As shown in Fig. 6, the results indicated that in the frequency range of 250 Hz to 4 KHz, both signals demonstrated comparable performance, with minimal fluctuations in the measured SNR values within 1 dB. However, when the vibration frequency reached 8 KHz, the APS-signal exhibited a significant advantage, with an SNR improvement of up to 17 dB. This improvement can be attributed to the limited ability of the adaptive equalizer to effectively track vibrations at this higher frequency. The degradation of the Bit Error Rate (BER) of the coherent transceiver at 8 KHz further supports this observation.

 

Fig. 6. Representation SNR of the APS and APS_adapt signals

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Furthermore, at frequencies lower than or equal to 125 Hz, while being greater than 1 Hz, the APS-signal showed a fluctuation of 1-2 dB and the APS_S23_adapt showed a fluctuation of 2-3 dB in the measured SNR values. To ensure accuracy, the average of three measurements was calculated. In this frequency range, the APS-signal exhibited a 3 to 10 dB advantage over the APS_S23_adapt. It can be inferred that the conjugate multiplication employed in the calculation of APS_S23_adapt does not completely eliminate the low-frequency noise, contributing to the observed advantage.

When the disturbance frequency was lower than 1 Hz, it was not possible to clearly observe the corresponding disturbance frequency signal, possibly due to the specific characteristics of the piezoelectric ceramic actuator used in our experiments.

These findings demonstrate the performance differences between the APS-signal and APS_S23_adapt across various frequencies, highlight the advantages of the APS-signal.

In the localization experiment, the vibration location was tested using an Optical Time Domain Reflectometer (OTDR), and it was determined to be 15.2 km from the West end and 39.9 km from the East end, resulting in a distance difference of 24.7 km. Using a disturbance frequency of 1KHz and the method described by Formula 6, calculations were performed to estimate the distance difference between the two ends. In the formula, f₂ and f₁ are chosen as the positive and negative frequencies of the disturbance signal or its harmonics.

We performed the tests 20 times to ensure the reliability of our results. The mean and the standard deviation of the estimated distances, obtained from these tests, are presented in Table 1. In the table, ‘Variance’ computes the deviations from the ‘true’ values determined through commercial OTDR testing as a reference point.

Table 1. Estimated Distance Difference Using Positive Frequencies (f2) and Negative Frequencies (f1) of the Disturbance Signal or Its Harmonics

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As can be observed, except for the results of the second harmonic, the variance for most test results is about 1∼2 km. This indicates that both the signal corresponding to the disturbance frequency itself and its harmonics in the polarization state variation signal can be used for localization. The results of the second harmonic appear relatively poorer, possibly due to its smaller magnitude (unitless) compared to the first and third harmonics. which average at 42, 369, and 168, respectively.

In a demonstrative experiment, a mobile phone was placed close a bundle of optical fibers with 15 km length, and a piece of music was successfully reconstructed from the changes in the polarization state. Due to the FPGA debug tool's memory depth constraint of 128 K, we could recover only a few dozen seconds from the song, even though we employed a sampling rate of 5.4KHz (180 MHz/2¹⁵) to retrieve a longer music segment. Despite the presence of significant background noise, the melody is clearly heard and discernible. Fig7.a illustrates the waveforms of the original music and the recovered music spanning 24 seconds, while Fig7.b shows the corresponding frequency spectrum. Because frequencies below 20 Hz are not audible to the human ear, they are filtered out in the recovery process. Then we calculate the correlation between the recovered signal and the original. To reduce the noise, frequency component above 1.5kHz are also filtered out. The reason for selecting 1.5kHz is that reducing the filter bandwidth further would significantly impact the auditory perception of the recovered sound, thus affecting the quality of the music. Filtering was applied to both the original and recovered signals. Fig7.c presents the result of a sliding correlation between the 32-second original music waveform and its recovered counterpart using a 24-second window, subsequently taking the absolute value. As depicted in Fig. 7, while the time-domain waveforms of the original and recovered music aren't visually similar, their correlation shows prominent peaks. The low peak value of 0.35 indicates a moderate correlation and suggests that the recovered signal doesn't perfectly mirror the original, warranting further analysis. This scenario might be comparable to the effects seen in optical fiber when external forces act upon them, akin to wind-induced overhead cable sway or undersea cables affected by seismic activities.

 

Fig. 7. Comparison of waveforms between the recovered music and the original music obtained from the polarization state recovery. (a) Time domain waveform: original music (top) and recovered music (bottom). (b) Frequency spectrum of original music (top) and recovered music (bottom). (c) Correlation between the two waveforms. (d) Playing music using a mobile phone near the optical fiber.

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This experiment not only demonstrated the wide-ranging information extraction capabilities of the proposed APS-signal but also underscored the potential of this approach in capturing high-frequency components, a task that would be very challenging using adaptive coefficients.

5. Field test

To measure the impact of realistic cable movement on the polarization state, we conducted our field experiments at the State Grid Key Laboratory of Power Transmission Line Galloping Prevention and Control Technology. The experimental site is located in Jian Mountain, Xinmi, Henan. At this site, a section of overhead cables, which had been decommissioned due to frequent tripping trouble, was utilized as a research base for studying the movement of both overhead cables and optical fibers.

As depicted in Fig. 8, we utilized a robotic system to generate controlled cable movements at a constant frequency. The optical fiber was firmly attached to the oscillating cable and connected back to the transmitting end. The frequencies of the cable movements were set in the range of 0.3 Hz to 1.6 Hz, with a step size of 0.1 Hz. After establishing the communication link, we monitored the APS signal and obtained its temporal and frequency domain representations. The following Fig. 9(a)-(d) depicts the APS signals when the machine vibrates at a frequency of 1 Hz or remains stationary:

 

Fig. 8. The photograph of the machine induced cable oscillation experiment

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Fig. 9. Complex plane representation of the APS signals: (a) 1 Hz vibration, (b) no vibration. Subfigures (c) and (d) show the real and imaginary parts of the APS signal under 1 Hz vibration and no vibration, respectively.

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It is evident that when the machine oscillates at a frequency of 1 Hz, the polarization state also exhibits periodic changes at the same frequency. On the other hand, when the machine stops oscillating the cable, the polarization state remains relatively constant. This observation clearly indicates that the changes in the polarization state directly correspond to the frequency of the cable oscillation. In Fig. 10, the frequency spectrum plot further supports this finding. When the cable is oscillating, we can observe the corresponding 1 Hz polarization state variation signal and its harmonics. However, when the cable is not oscillating, the amplitude of the polarization state signal in the frequency spectrum plot is significantly lower, by approximately two orders of magnitude, compared to when the cable is oscillating. Although tones are faintly observable in Fig. 10(d) when using a y-axis matching its amplitude, their magnitudes are considerably smaller than the major components observed in Fig. 10(a/b) due to shaking, indicating that they might arise from intrinsic system disturbances.

 

Fig. 10. Frequency spectrum analysis of the APS signals without DC component under 1 Hz vibration or without vibration: (a) Magnitude spectrum |fft(APS_A2)| with 1 Hz vibration, (b) Magnitude spectrum |fft(APS_B2)| with 1 Hz vibration, (c) Magnitude spectrum |fft(APS_A2)| and |fft(APS_B2)| without vibration using the same vertical scale, (d) Magnitude spectrum |fft(APS_A2)| and |fft(APS_B2)| without vibration using individual amplitude-matched vertical scales.

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Subsequently, we conducted tests on an actual overhead optical cable, which has a length of 3 km and was supported by 10 towers. Towers 1, 3, 6, 9, and 10 were suspension towers, while the remaining towers were straight-line towers. At this time, according to the weather report, the wind speed was at level 5, and the overhead cable is visibly swaying. We were able to observe continuous changes in the polarization state during this period. Additionally, we test the polarization signal by deliberately striking the overhead cable with a long pole. The signal is depicted in the figure below:

From the complex plane representation of the signals in Fig. 11(a)-(b), it can be observed that under continuous cable movement, the polarization state of the optical fiber undergoes continuous changes, making it difficult to differentiate whether it was struck or not. However, as shown in Fig. 11(c)-(d), when the two complex signals are converted into four real signals, particularly the imag(APS_A2) signal, periodicity becomes apparent when the cable is struck. From the frequency spectrum in Fig. 12, more prominent frequency signals at 0.58 Hz are observed, further supporting our observation. We interpret this as our system detecting the overall polarization variation of the entire line. In the case of suspended optical cables, similar to a pendulum, there is an inherent oscillation frequency. When multiple sections of the cable are subjected to wind-induced movements, it is difficult for a dominant frequency oscillation signal to emerge. However, when struck, the inherent frequency oscillation at the impacted position becomes significantly stronger compared to other locations. This further emphasizes the need for advanced processing techniques, like machine learning, to manage the complex scenarios encountered with real-world overhead fiber cables. Machine learning algorithms can be trained to analyze and classify the different patterns and variations in the polarization signals, enabling more accurate detection and characterization of cable movements, including distinguishing between wind-induced vibrations and external disturbances such as knocking.

 

Fig. 11. Complex plane representation of the APS signals for the actual overhead cable: (a) APS signal under wind-induced vibration, (b) APS signal under wind-induced vibration plus knocking. Subfigures (c) and (d) show the real and imaginary parts of the APS signal under wind-induced vibration without knocking or with knocking, respectively.

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Fig. 12. Representation of FFT of the APS signals without DC component (a) |fft(APS_A²)| under wind-induced vibration (b) |fft(APS_B²)| under wind-induced vibration, Subfigures (c) and (d) show |fft(APS_A²)| and |fft(APS_B²)| under wind-induced vibration with knocking, respectively.

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6. Conclusion

In this paper, we proposed a novel architecture called the Direct-Computation-Sensing Architecture (DCSA) for accurately detecting and monitoring polarization state changes induced by optical fiber vibrations. Compared to adaptive filter-based sensing architectures, DCSA provides a more responsive and accurate method by directly calculating the polarization matrix using training data. To validate the performance of DCSA, we conducted experiments using a piezoelectric ceramic actuator to induce controlled fiber vibrations. By calculating the signal-to-noise ratios (SNR) between DCSA and AFSA signals, we confirmed that DCSA not only exhibits strong tracking capabilities for high-frequency signals, but also demonstrates significant SNR advantages for low-frequency signals below 125 Hz.

Furthermore, we implemented a bidirectional transmission setup to accurately locate the source of vibrations by comparing data from both ends. Additionally, we successfully recovered the melody of a song played near the optical fiber by analyzing the polarization changes. The results of our experiments demonstrated a direct correspondence between the polarization state changes and the frequency of cable oscillation.

In field tests involving both machine-induced vibrations and natural cable movements, we further validated the effectiveness of our approach. The integration of communication and sensing functionalities into optical fiber networks shows great potential for enhancing their utility and efficiency across various applications, such as seafloor sensing networks and the monitoring of overhead power cables.