^{1}State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China

^{2}State Key Laboratory of Mobile Network and Mobile Multimedia Technology, WDM System Department, ZTE Corporation, Beijing 100020, China

^{3}School of Physics Science and Information Engineering, Liaocheng University, Liaocheng 252000, China

An ultrasonic phase extraction method is proposed for co-cable identification without modifying transceivers in coherent optical transmission systems. To extract the ultrasonic phase, we apply an improved residual frequency offset compensation algorithm, an optimized unwrapping algorithm for mitigating phase noise induced by phase ambiguity between digital signal processing (DSP) blocks, and an averaging operation for improving the phase sensitivity. In a 64-GBaud dual-polarization quadrature phase shift keying (DP-QPSK) simulation system, the phase sensitivity of the proposed method reaches 0.03 rad using lasers with 100-kHz linewidth and a 60-kHz ultrasonic source, with only 400 k-points (kpts) stored data. Also verified by an experiment under the same transmission conditions, the sensitivity reaches 0.39 rad, with 3 kpts of data stored and no averaging due to the equipment limitation. The results have shown this method provides a better choice for low-cost and real-time co-cable identification in integrated sensing and communication optical networks.

With the rapid increase in the demand for high-speed data transmission, a large number of optical cables have been deployed in current communication networks^{[1-3]}. However, the specific location record of optical cables may be lost due to operator delivery and other reasons, potentially leading to the primary service path and secondary protection path deployed in the same cable, becoming a pair of shared risk optical fiber links (SROFLs)^{[2,4]}, also known as co-cable. In this case, external intrusions could cause service failures, which interrupt business in major networks^{[5]}. Therefore, co-cable identification is a very important part of optical network operation and maintenance (O&M).

Currently, the identification of co-cable issues mainly relies on traditional manual analysis or troubleshooting, which is inconvenient and inefficient^{[2,6]}. With the rapid development of the optical fiber sensing (OFS) technique^{[7]}, integrated sensing and communication (ISAC) optical networks^{[8]} show promising prospects in optical network O&M, including co-cable identification. In 2022, Zhao et al. and Li et al. proposed co-cable identification techniques based on OFS and AI, and verified their performance through field trials^{[2,9,10]}. However, these techniques require additional expensive OFS devices such as phase-sensitive optical time-domain reflectometers ($\varphi \text{-}\mathrm{OTD}\mathrm{Rs}$), the need to occupy extra communication fiber cores or wavelength-division-multiplexing (WDM) channels^{[11]}, and the launch of high-power probe pulses, which increases the cost of co-cable identification and may reduce communication efficiency.

Thanks to these works^{[12-16]}, the similarity between the OFS technique and coherent communication systems is completely illustrated, enabling sensing schemes directly using existing communication equipment. In 2022, Ip et al. proposed a novel distributed acoustic sensing (DAS) scheme over 489-km fiber using coherent transceivers with ultranarrow-linewidth lasers (UNLLs) and modified digital signal processing (DSP)^{[17]}. In 2023, our team proposed a post-processing residual frequency offset (RFO) compensation algorithm for coherent transceiver-based DAS without modifying its DSP, while also using UNLLs ($\sim 100\text{\hspace{0.17em}}\mathrm{Hz}$) due to the performance limitation of the proposed RFO compensation (RFOC) algorithm^{[18]}. In the same year, we proposed a co-cable identification scheme based on a digital receiver and artificial ultrasonic feature using lasers with 100-kHz linewidth^{[19]}. But in this scheme, the frequency offset estimation (FOE) is modified (referred to as the FOE-modified method in this article) due to the much larger phase noise and frequency drift of commercial lasers, and large storage cost is needed due to symbol-level processing, limiting the direct deployment in existing transceivers. Hence, there is currently no practical co-cable identification scheme that can be directly utilized and will not affect the coherent communication system, i.e., can be implemented without replacing the lasers with UNLLs and modifying DSP in coherent transceivers.

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In this Letter, we propose an ultrasonic phase extraction method to identify co-cable issues in coherent optical transmission systems. Without modifying coherent transceivers and to extract the ultrasonic phase from the phase noise estimated by carrier phase estimation (CPE), we apply an improved fitting-based RFOC method, an unwrapping algorithm between DSP blocks to resist the phase ambiguity caused by the MSa/s-level sampling rate, and an averaging operation to improve the phase sensitivity. We compared this method with the FOE-modified method in a 64-GBaud dual-polarization quadrature phase shift keying (DP-QPSK) simulation system, and the proposed method maintains the phase sensitivity of 0.03 rad using 100-kHz-linewidth lasers and a 60-kHz ultrasonic source, while reducing storage cost by 5 orders of magnitude from 25.6 G-points (Gpts) to 400 k-points (kpts). In a verification experiment under the same condition as in simulation, the sensitivity reached 0.39 rad using only 3 kpts of stored data without averaging due to the limited oscilloscope storage, while there is no limitation in practical real-time communication systems. This method has shown its great compatibility with existing coherent transceivers and excellent performance, which implies that it better supports low-cost and real-time co-cable identification in O&M of future ISAC optical networks.

2. Principle

2.1. Principle of co-cable identification

This section will briefly illustrate the principle of ultrasound-assisted co-cable identification. Figure 1 shows a coherent optical transmission system with a service path (blue) and protection paths (red). We apply an ultrasonic excitation to a trench containing the optical fiber cables along the service path. Due to the photoelastic effect, the phase of transmitting the optical carrier and the amplitude of excitation are linearly related^{[20]}. So, the ultrasonic excitation can be recovered by extracting the ultrasonic phase in the coherent receiver. If the phase extracted from two paths simultaneously contains the applied ultrasonic phase (Cable 2 in Fig. 1), the co-cable issue is successfully detected.

Figure 1.Diagram of ultrasound-assisted co-cable identification (ODF: optical distribution frame).

The DSP in coherent optical communication systems^{[21,22]} is shown in Fig. 2(a), in which two steps are significant for extracting ultrasonic phase, i.e., FOE and CPE. The ultrasonic phase is included in the estimated phase noise by the CPE and will be affected by the accuracy of FOE. The phase after photoelectric conversion, FOE, and CPE within $k$th DSP block can be, respectively, expressed as^{[18,19]}$${\mathrm{\Phi}}_{\mathrm{Rx}}(t)={\varphi}_{M}(t)+{\varphi}_{\mathrm{FO}}(t)+{\varphi}_{u}(t)+{\varphi}_{\mathrm{LW}}(t)+{\varphi}_{I}(t),$$$${\mathrm{\Phi}}_{\mathrm{FOE}}(t)={\mathrm{\Phi}}_{\mathrm{Rx}}(t)-2\pi \xb7{f}_{\mathrm{est}}(k)\xb7t\phantom{\rule{0ex}{0ex}}={\varphi}_{M}(t)+{\varphi}_{\mathrm{RFO}}(t)+{\varphi}_{u}(t)+{\varphi}_{\mathrm{LW}}(t)+{\varphi}_{I}(t),$$$${\mathrm{\Phi}}_{\mathrm{CPE}}(t)={\varphi}_{u}(t)+{\varphi}_{\mathrm{RFO}}(t)+{\varphi}_{\mathrm{LW}}(t)+{\varphi}_{I}(t),$$where ${\varphi}_{M}(t)$, ${\varphi}_{\mathrm{FO}}(t)$, ${\varphi}_{\mathrm{LW}}(t)$, and ${\varphi}_{I}(t)$ represent the modulation phase (MP), the frequency offset (FO) induced phase noise, the laser phase noise, and the phase noise induced by the intensity noise, respectively. The ultrasonic phase ${\varphi}_{u}(t)$ is defined as $${\varphi}_{u}(t)={A}_{u}\text{\hspace{0.17em}}\mathrm{cos}(2\pi {f}_{u}t),$$where ${A}_{u}$ and ${f}_{u}$ are the amplitude and frequency of ultrasonic phase, respectively. ${f}_{\mathrm{est}}(k)$ is the estimated FO, and ${\varphi}_{\mathrm{RFO}}(t)$ is the RFO phase noise after FOE. It should be noted that we adjust ${\varphi}_{u}$ as the first item in Eq. (3) to facilitate the distinction between signal and noise in this work.

Figure 2.DSP in ultrasound-assisted co-cable identification: (a) coherent DSP and (b) proposed FUA-UPE method.

According to the Nyquist–Shannon sampling theorem and to ensure the accuracy of subsequent processing, we only need to sample the kHz-level ultrasonic phase at a sampling rate of approximately MSa/s. As shown in the upper part of Fig. 2(a), there is only one phase data estimated by CPE and one FO estimated by FOE within one DSP block stored and waiting for subsequent processing. Here, we give the phase stored by DSP of the $k$th block, $${\mathrm{\Phi}}_{\mathrm{CPE}}(k)={\varphi}_{u}(k)+{\varphi}_{\mathrm{RFO}}(k)+{\varphi}_{\mathrm{LW}}(k)+{\varphi}_{I}(k),$$where ${\varphi}_{*}(k)={\varphi}_{*}({\tau}_{s})$ and ${\tau}_{s}$ is the sampling time for the $k$th block. In order to better explain the subsequent method and clearly show the results, we perform a differencing operation on the sampled phase, which will be expressed as $\mathrm{d}{\mathrm{\Phi}}_{*}(k)={\mathrm{\Phi}}_{*}(k+1)-{\mathrm{\Phi}}_{*}(k)$, and the ultrasonic phase becomes $$\mathrm{d}{\varphi}_{u}(k)=2\pi {f}_{u}\mathrm{\Delta}t\xb7{A}_{u}\text{\hspace{0.17em}}\mathrm{cos}(2\pi {f}_{u}\xb7k\mathrm{\Delta}t),$$where $\mathrm{\Delta}t$ is the sampling time interval. Then, we will conduct a detailed derivation of the method for extracting the ultrasonic phase from ${\mathrm{\Phi}}_{\mathrm{CPE}}(k)$.

2.2. Principle of ultrasonic phase extraction

To extract ultrasonic phase from downsampled phase noise ${\mathrm{\Phi}}_{\mathrm{CPE}}(k)$ without modifying the coherent transceivers, we propose a fitting-unwrapping-averaging ultrasonic phase extraction (FUA-UPE) method mainly including fitting-based RFOC (F-RFOC), unwrapping inter blocks (UIBs), and averaging after differencing operation, which is shown in Fig. 2(b).

2.2.1. Fitting-based residual frequency offset compensation

In 2007, Leven et al. proposed an FOE algorithm based on the typical Viterbi–Viterbi (V–V) algorithm^{[23]}, whose estimation error (named the residual frequency offset) caused by intensity noise and block size has been analyzed^{[24]}. Due to its low complexity and relatively high accuracy, it is widely used in practice. However, the phase noise caused by RFO is fatal to the phase-based sensing scheme. The orange curve in Fig. 3(a) still has spectrum aliasing, which explains why RFO induces large noise. The proposed F-RFOC is used to reduce the noise caused by RFO. An intuitive explanation of F-RFOC is shown in Fig. 3(b). The proposed F-RFOC attempts to fit the real FO of the signal and accurately move the signal spectrum to the baseband. Without signal aliasing, the phase noise of the signal can be eliminated.

Figure 3.Signal spectrum with residual frequency offset: (a) with V–V FOE and (b) with V–V FOE and proposed F-RFOC. (Δf: frequency offset center; F: sampling rate; FORL: FO reloading; FORC: FO re-compensation.).

The F-RFOC includes 3 steps, i.e., FO reloading (FORL), FO fitting (FOF), and frequency offset re-compensation (FORC). The principle of these steps has been illustrated^{[18]}, and more details will be given in this section.

First, we should reload the FO-induced phase noise to obtain the phase before FOE but without MP. This is because the phase after FOE is discontinuous. Actually, the FO within each DSP block is variable and continuous, but the FOE of each DSP block compensates it according to an averaged FO value, which causes the mentioned discontinuity. The phase after FORL can be expressed as $${\mathrm{\Phi}}_{\mathrm{FORL}}(k)={\mathrm{\Phi}}_{\mathrm{Rx}}(k)-{\varphi}_{M}(k)\phantom{\rule{0ex}{0ex}}={\mathrm{\Phi}}_{\mathrm{CPE}}(k)+2\pi \xb7{f}_{\mathrm{est}}(k)\xb7{\tau}_{s}\phantom{\rule{0ex}{0ex}}={\varphi}_{u}(k)+{\varphi}_{\mathrm{FO}}(k)+{\varphi}_{\mathrm{LW}}(k)+{\varphi}_{I}(k).$$

Then, we fit the FO estimated by block-level FOE to obtain continuous FO values at the symbol level. The fitting algorithm must be replaced according to the actual conditions, as the FO of lasers will vary with the manufacturing and the environment. With the suitable fitting function $\mathrm{Fitting}[\xb7]$, the fitted angular frequency is $${\widehat{\omega}}_{\mathrm{fit}}(m)=\mathrm{Fitting}[2\pi \xb7{f}_{\mathrm{est}}(k)]=\mathrm{\Delta}\omega (m)+{\omega}_{\mathrm{err}}(m),$$where $m$ is the symbol-level index, $\mathrm{\Delta}\omega (m)$ is the real angular FO, and ${\omega}_{\mathrm{err}}(t)$ is the fitting error. Then, the more accurate FO-induced phase noise is calculated by summing the fitting result within a DSP block, and it can be expressed as $${\widehat{\varphi}}_{\mathrm{fit}}(k)=\sum {\widehat{\omega}}_{\mathrm{fit}}(m)\xb7\frac{1}{{R}_{\text{Symbol}}},$$where ${R}_{\text{Symbol}}$ is the symbol rate.

Finally, we recompensate the FO-induced phase noise with the fitted phase noise, and the phase to be further analyzed is expressed as $${\varphi}_{\mathrm{RFOC}}(k)={\mathrm{\Phi}}_{\mathrm{FORL}}(k)-{\widehat{\varphi}}_{\mathrm{fit}}(k)\phantom{\rule{0ex}{0ex}}={\varphi}_{u}(k)+{\varphi}_{\mathrm{LW}}(k)+{\varphi}_{I}(k)+{\varphi}_{\mathrm{err}}(k),$$where ${\varphi}_{\mathrm{err}}(k)$ is the error phase noise and ${\varphi}_{\mathrm{err}}(k)\ll {\varphi}_{\mathrm{RFO}}(k)$.

2.2.2. Unwrapping inter-blocks and averaging

According to the analysis above, we actually made an implicit assumption that we have performed symbol-level unwrapping of the phase after CPE so that it is continuous. In practice, there is no unwrapping between blocks in traditional DSP, which causes the phase between blocks to be discontinuous, as shown in Fig. 4(a). This step aims to recover the continuous phase noise as shown in Fig. 4(b).

Figure 4.Phase ambiguity between DSP blocks: (a) without and (b) with proposed UIB.

The stored phase within a block includes an estimated phase at the middle of a block, and a head and a tail phase of the same block [marked as ${\varphi}_{\text{head}/\text{tail}}(k)$]. Then by subtracting ${\varphi}_{\text{head}/\text{tail}}(k)$ we can get the phase difference between two adjacent blocks, which is expressed as $${\varphi}_{\text{diff}}(k)={\varphi}_{\text{head}}(k+1)-{\varphi}_{\text{tail}}(k).$$

As the symbol-interval phase noise can be seen as continuous at kHz level, which means ${\varphi}_{\text{diff}}(k)$ should be within the range of $-\pi \text{to}+\pi $, implying a general unwrapping should be applied. Then the unwrapped phase is expressed as $${\varphi}_{\mathrm{unrp}}(k)=\mathrm{Unwrap}[{\varphi}_{\text{diff}}(k)],$$where $\mathrm{Unwrap}[\xb7]$ means general unwrapping algorithm. Then, the unwrapping period can be obtained by computing the difference between Eqs. (12) and (11), $${\varphi}_{\mathrm{prd}}(k)={\varphi}_{\text{unrp}}(k)-{\varphi}_{\text{diff}}(k).$$

It should be noticed that, although the phase is discontinuous between blocks, it is continuous within the block. So, the unwrapping periods of ${\varphi}_{\text{head}/\text{tail}}(k)$ and the sampled phase are the same. The final step is to unwrap the estimated phase according to Eq. (13). As mentioned above, this step is to solve the inter-block discontinuity of the phase after FORL, so FORL should also contain ${\varphi}_{\text{head}/\text{tail}}(k)$, and the UIB compensation should be applied to ${\mathrm{\Phi}}_{\mathrm{FORL}}(k)$. It is expressed as $${\varphi}_{\mathrm{UIB}}(k)={\mathrm{\Phi}}_{\mathrm{FORL}}(k)+{\varphi}_{\mathrm{prd}}(k).$$

The last step of FUA-UPE is averaging aided by resampling and differencing operation. The phase noise of the laser obeys the Wiener process, and the differenced phase obeys Gaussian distribution, which means it can be eliminated by averaging. Since the excitation applied in this Letter is a single-frequency ultrasonic signal, the averaging operation will also cause the amplitude of the ultrasonic phase to be reduced. Therefore, a resampling is needed for the sampled phase before the differencing operation so that the initial phase of each group of phase to be averaged is synchronized.

So far, the phase noise caused by the RFO, the phase ambiguity between DSP blocks, and the lasers has been eliminated.

2.3. Storage cost analysis

This section will analyze the storage cost for the FOE-modified method and the FUA-UPE method. For the FOE-modified method, since the transmitting data need to be processed, all symbols need to be stored at multiple sampling rates. Suppose that the number of multiplexed polarization is ${N}_{\mathrm{Pol}}$, the symbol rate of one polarization is ${R}_{\text{Symbol}}$, the sampling rate is SR in sample-per-symbol (SPS), and the sampling time window is ${T}_{\text{Sample}}$. Then the storage cost for the FOE-modified method can be given by $${S}_{\mathrm{FOE}}={N}_{\mathrm{Pol}}\times {R}_{\text{Symbol}}\times \mathrm{SR}\times {T}_{\text{Sample}}.$$

For the FUA-UPE method, the amount of data stored depends on the symbol rate ${R}_{\text{Symbol}}$ and DSP block size ${L}_{\text{Block}}$, and the sampling time window is ${T}_{\text{Sample}}$, i.e., the block number ${N}_{\text{Block}}$, and the number of data points stored in each block, which is 3 phase points and 1 frequency point in this method. Hence, according to the previous analysis, the storage cost for the FUA-UPE method can be expressed as $${S}_{\mathrm{FUA}}={N}_{\text{Block}}\times 4=\frac{{R}_{\text{Symbol}}\times {T}_{\text{Sample}}}{{L}_{\text{Block}}}\times 4.$$

As shown in Table 1, when the transmission is dual-polarization multiplexing and the sampling rate is 2 SPS, the reduction in required storage is expressed by the following expression: $${R}_{S}=\frac{{S}_{\mathrm{FOE}}}{{S}_{\mathrm{FUA}}}=\frac{{N}_{\mathrm{Pol}}\times \mathrm{SR}\times {L}_{\text{Block}}}{4}={L}_{\text{Block}}.$$

Since the typical block size of the coherent DSP is kSymbols to MSymbols, the storage consumption of the FUA-UPE method is reduced by 3–6 orders of magnitude.

3. Results

We first demonstrate the performance of the FUA-UPE method and compare storage consumption with the FOE-modified method. Then, we also verify the performance of the FUA-UPE method through experiments. It should be noted that, since the current integrated transceiver does not support the output of DSP intermediate results, the experiment was conducted in the laboratory. At the same time, because of the storage limitation of the laboratory oscilloscope, it cannot meet the verification needs of the FUA-UPE method. Hence, the comparison of storage cost is completed through simulation. Also, the sampling time window of the verification experiment is limited, and there is no averaging step in the FUA-UPE method. Even so, the results have demonstrated the excellent performance and good compatibility of the FUA-UPE method with the existing transceivers.

3.1. Simulation results

The section will show the performance of the FUA-UPE method mainly through the phase signal-to-noise ratio (SNR), the phase sensitivity, and the storage cost. The phase sensitivity^{[25,26]} represents the minimum detectable phase, which is defined as the noise level in the power spectrum density (PSD), and can be calculated by^{[19]}$${\mathrm{PSD}}_{\varphi}=\frac{2{\pi}^{2}{f}_{u}^{2}{A}_{u}^{2}{T}_{\text{Sample}}}{{({R}_{\text{Symbol}}/{L}_{\text{Block}})}^{2}}.$$

The DSP flow with the FUA-UPE method is illustrated in Fig. 2. The Gram–Schmidt orthogonalization procedure (GSOP), chromatic dispersion compensation (CDC), constant modulus algorithm (CMA), V–V FOE, and blind phase search (BPS) algorithm are used for decoding the transmitting symbols. The main parameters of simulation setup and DSP are shown in Table 2. It should be noted that the linewidth of the lasers is set as 100 kHz, and as illustrated in Section 2.2.1, the fitting function should be optimized for the laser and the environment, so the chosen function in this simulation and further experimental verification is given by $$f(t)=\alpha t+\beta \text{\hspace{0.17em}}\mathrm{sin}(2\pi \xb7\gamma \xb7t+\theta ),$$where $\alpha $, $\beta $, $\gamma $, and $\theta $ are the parameters that should be determined by fitting. For the FOE-modified method, the system setup and simulation parameters are consistent with the above, and the DSP flow is described in detail in Ref. [19], which is already optimized for this system.

The simulation results are shown in Fig. 5. The blue curve in Fig. 5(a) is the FO estimated by FOE in each DSP block within a 1-ms time window, which is one of 100 groups of data, and the orange curve is the FO fitted by F-RFOC. It can be seen that, even though the number of fitting data points is reduced from 6.4 Gpts (only data of X-polarization in 1 SPS) to 100 kpts, the FO of the system is still well fitted. Also, it can be seen from Fig. 5(b) that the estimation error of FO is reduced by 2 orders of magnitude by F-RFOC and is recovered to be continuous. Figure 5(c) shows the phase extracted by the FOE-modified method and the FUA-UPE method. This shows that the two methods recover the differenced phase with an amplitude of approximately 0.4 rad, which is consistent with the theoretical value of 0.38 rad according to Eq. (6). It is further verified in Fig. 5(d) that, from the PSD, the SNR reaches 28.7 dB, and the noise level near the ultrasonic frequency is about $-72\text{\hspace{0.17em}}\mathrm{dB}$, which means the sensitivity reaches 0.03 rad according to Eq. (18). Compared with the FOE-modified method, the amount of stored data is reduced by 5 orders of magnitude, and there is no performance loss in the FUA-UPE method.

Figure 5.Result of simulation: (a) frequency offset, (b) estimation error of frequency offset, (c) extracted phase, and (d) PSD of extracted phase.

The system setup of experimental verification is shown in Fig. 6. There is a 120-GSa/s arbitrary waveform generator (AWG, Keysight 8194A) generating 4-channel 64-Gbps data flows, driving an optical multi-format transmitter (OMFT, ID Photonics OMFT-x-0x-FA) to send 64-GBaud DP-QPSK signal to the100-km fiber link. An optical modulation analyzer (OMA, Keysight N4391B) is used to receive and demodulate the optical signal, before which there is an erbium-doped fiber amplifier (EDFA) to adjust the received optical power (ROP). The link optical SNR (OSNR) is controlled through adjusting the launch power by an EDFA and a variable optical attenuator (VOA) and is monitored by an optical spectrum analyzer (OSA) through a 1:9 coupler. The OSNR is controlled at 20% forward error correction (FEC) threshold, leaving a margin of 1 dB. In the middle of the fiber link, we use a piezoelectric transducer (PZT) driven by another AWG to apply the ultrasonic excitation. The phase change produced by this ultrasonic signal is $\sim 1\text{\hspace{0.17em}}\mathrm{rad}$. Because of the storage limitation (up to 200 MSa/channel), the oscilloscope inside OMA stores 192 MSa of data for offline processing with a sampling rate of 256 GSa/s, whose sampling time window is 750 µs. This means that the PSD resolution becomes 1.33 kHz with only one group of phase (no averaging operation) and the storage cost becomes 3 kpts. The other parameter settings are the same in the simulation and have been shown in Table 2.

Figure 7 shows the results of the verification experiment, including the fitted FO and the PSD of the extracted phase. Different from the simulation, we cannot obtain the real FO of the lasers, so the FO in Fig. 7(a) only includes the FOE estimated curve and the fitted curve. This result can further verify that the FO setting used in the simulation is consistent with the real world and also shows that the fitting function we choose can correctly restore the laser FO. In Fig. 7(b), we demonstrate the PSD of the extracted phase directly estimated by CPE (without the FOE-modified method and the FUA-UPE method) and processed by the FUA-UPE method. Due to the mentioned limitation of oscilloscope storage, the phase is not processed by averaging operation, so the noise floor remains at a relatively high level. The SNR reached 6.3 dB, and the sensitivity reached 0.39 rad with a noise level of $-51\text{\hspace{0.17em}}\mathrm{dB}$. Compared with the result estimated by CPE, the noise floor has indeed dropped, and the ultrasonic phase with a theoretical PSD of $-43\text{\hspace{0.17em}}\mathrm{dB}$ is correctly restored. The experimental results also verified the feasibility and the performance of FUA-UPE.

Figure 7.Result of experiment: (a) frequency offset and (b) PSD of extracted phase.

The comprehensive analysis of cutting-edge co-cable identification schemes is summarized in Table 3. The OFS-based scheme is relatively balanced. The FOE-modified method is an innovative attempt, and the FUA-UPE method improves its ease of integration, contributing to the practical deployment of the ultrasound-assisted co-cable identification scheme. However, this method needs intermediate results in the coherent transceiver, which means the transceiver should open the related interface. Also, fiber optic sensing schemes using coherent transceivers require bidirectional transmitting signals for localization^{[17]}, which is not considered in this work. We will further research in the future.

Table 3. Comparison of Existing Co-Cable Identification Schemes

Table 3. Comparison of Existing Co-Cable Identification Schemes

Scheme

Performance

Cost

Ease of Integration

OFS-based

High

Medium

Medium

FOE-modified

High

Low

Low

FUA-UPE

High

Low

High

4. Conclusion

An ultrasonic phase extraction method without modifying coherent transceivers has been proposed for co-cable identification in coherent optical transmission systems. The proposed method can extract the ultrasonic phase by eliminating the phase noise caused by the RFO and the unwrapping, and improving the phase sensitivity. The method has been verified in a 64-GBaud DP-QPSK simulation system that, compared with our previous work, reached a phase sensitivity of 0.03 rad, and there is no performance loss while reducing storage cost by 5 orders of magnitude. Also verified by an experiment, the sensitivity reached 0.39 rad with only 3 kpts of data stored. The proposed method shows great potential for low-cost and real-time co-cable identification in future ISAC optical networks.

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