Impact of Terminal Noise on Polarization Rotation Vector for Sensing Applications

This paper investigates how terminal noise affects polarization rotation estimates derived from receiver equalizer coefficients in coherent transponders, and how it can obscure stochastic polarization drift used for sensing applications. The study analyzes Jones-matrix time series from two deployed receivers in the Sparkle Mediterranean link MedNautilus (approximately 2000 km and 450 km) and compares them with a laboratory back-to-back reference. Power Spectral Density (PSD) analysis reveals a low-frequency random-walk regime and a high-frequency white-noise floor, separated by a link-dependent corner frequency. The rotation innovation variance increases with link length, while the longest field link also shows elevated white noise consistent with accumulated amplifier and terminal contributions. Additionally, harmonic spectral components are observed, indicating a transponder-related artifact that should be considered in practical sensing applications.

The paper reviews theoretical modeling of ideal polarization dynamics, including the Jones formalism and Stokes formalism, and discusses the waveplate model and hinge model of PMD. The model proposed in Ref. [2] captures the time evolution of polarization by modeling the Jones matrix as a sequence of random matrices, emulating a random walk on the Poincaré sphere. The time evolution is formulated as Jk = J(ϕ̇k)Jk−1, where J(ϕ̇k) = exp(−i ϕ̇k/2 · σ) is the random innovation matrix parameterized by a random vector ϕ̇k drawn from a zero-mean Gaussian distribution with variance σp2 = 2π∆pT, where T is the symbol interval and ∆p defines the polarization linewidth parameter.

Data were collected from operational coherent transponders deployed in two cable routes of Sparkle networks in the Mediterranean Sea: the CAT cable (2000 km) and the GEN cable (450 km), as well as a lab transponder in back-to-back mode with a received OSNR of 38 dB at 800 Gbps. All data were stored at a 2 Hz sampling rate without anti-aliasing filtering. The PSD of the Jones rotation vector was computed from 24 hours of continuous measurements using the preprocessing method proposed by A. Mecozzi et al. The results show a low-frequency random-walk regime and a white-noise floor at higher frequencies, with corner frequencies of 70 mHz for CAT, 60 mHz for GEN, and 20 mHz for Lab. The estimated σp2 values are 1.6 × 10−5 rad2 for CAT, 1.6 × 10−6 rad2 for GEN, and 4.5 × 10−7 rad2 for Lab, showing a clear correlation with cable length. The white-noise variances are 9.3 × 10−3 rad2 for CAT, 8.3 × 10−4 rad2 for GEN, and 9.0 × 10−4 rad2 for Lab.

The CAT transponder exhibits approximately 10 times and 35 times larger rotation-angle innovation variance compared to the GEN and Lab transponders respectively. Although the CAT route is only slightly more than four times longer than the GEN route, it exhibits more than four times higher noise levels, attributed to the larger number of terminal points along the CAT route where the cable comes to the surface and undergoes more environmental noise. The white-noise contribution remains similar for GEN and Lab transponders (8.5 × 10−4), but the CAT link exhibits a white-noise level nearly one order of magnitude higher, potentially originating from Amplified Spontaneous Emission (ASE) noise, laser phase noise, polarization tracking convergence error, quantization noise, and Carrier Phase Estimation (CPE) error.

The paper also shows the evolution of the SOP on the Poincaré sphere for an arbitrary input state across all three datasets over a 6-hour interval, along with the corresponding rotation vector total PSD computed over a 24-hour record. Harmonic structures appear in the polarization PSD, clearly visible in the Lab dataset but partially obscured in field data due to PSD smoothing. These harmonics are attributed to strong transponder-related polarization oscillations, transformed by nonlinear effects of polarization transformation in the large signal regime that generate multiple vanishing discrete tones spaced by a fundamental perturbation frequency.

The theoretical model was evaluated using the σp2 mapping to generate a pure random-walk process on SU(2). A single parameter, σp2, governs the stochastic evolution of polarization rotations in three-dimensional space with three degrees of freedom. Mapping an input Stokes vector to an output Stokes vector through this rotation reduces the observable degrees of freedom by one. The paper distinguishes between intrinsic polarization noise (arising from native stochastic evolution of the optical field in transmission) and extrinsic noise contributions (originating from other sources and mapped into the SU(2) representation through the receiver processing chain).

The conclusion states that terminal-induced polarization noise is considerable for SOP sensing using coherent transponders. Analysis of field and laboratory data revealed polarization dynamics consisting of a low-frequency random walk and a higher-frequency noise floor, with noise levels increasing for longer links. The results highlight the need to identify and mitigate terminal noise sources to improve sensing sensitivity and further enable the use of existing submarine telecommunication cables for large-scale environmental and geophysical monitoring. The paper also notes that after possible removal of the white-noise floor, detection sensitivity would be fundamentally limited by random-walk polarization dynamics, with an improvement in sensitivity of up to 20 dB achievable at frequencies approaching the Nyquist limit of sampling.

Improvements to AI Systems:

1. Noise-Aware Polarization Drift Estimation:

• Improvement: Integrate the paper’s PSD-based model (low-frequency random walk + white-noise floor with link-dependent corner frequency) into AI-based polarization tracking algorithms. Use the measured σp2 and white-noise variance as priors to separate intrinsic drift from terminal/amplifier noise.

• Capability: An AI system can now estimate true geophysical strain or temperature changes from submarine cable SOP data with reduced false positives, by explicitly modeling and subtracting terminal-induced noise.

2. Adaptive Filtering for Sensing Applications:

• Improvement: Train a neural network or Kalman filter to dynamically adjust its noise covariance matrix based on the detected corner frequency and link length (e.g., using the observed 70 mHz for CAT vs. 20 mHz for Lab).

• Capability: The AI can automatically tune its smoothing bandwidth to maximize signal-to-noise ratio for slow environmental events (e.g., seismic waves) while rejecting high-frequency transponder artifacts.

3. Harmonic Artifact Detection and Removal:

• Improvement: Implement a spectral analysis module that identifies the harmonic structures (discrete tones) caused by transponder-related polarization oscillations, as shown in the Lab PSD. Use pattern recognition to flag and filter these components before feeding data to downstream AI models.

• Capability: The system can clean field data in real time, improving the reliability of polarization-based sensing without requiring manual inspection of spectral peaks.

4. Link-Length Scaling Prediction:

• Improvement: Build a regression model (e.g., Gaussian process) that predicts σp2 and white-noise variance as a function of cable length and number of terminal points, using the paper’s data (CAT 2000 km, GEN 450 km, Lab back-to-back).

• Capability: For new or unmeasured submarine cables, the AI can estimate expected noise floors and corner frequencies, enabling pre-deployment sensitivity assessments for environmental monitoring.

5. Theoretical Model Calibration for Simulation:

• Improvement: Use the paper’s Jones-matrix random-walk model (Jk = exp(−i ϕ̇k/2 · σ) Jk−1) with calibrated σp2 values to generate synthetic training data for AI models. Include both intrinsic and extrinsic noise contributions as separate channels.

• Capability: AI systems can be trained on realistic polarization dynamics, including terminal noise, improving their robustness when deployed on real field data—especially for anomaly detection or event classification.

6. Optimal Sampling and Sensitivity Enhancement:

• Improvement: Implement an AI-driven adaptive sampling strategy that uses the paper’s finding that sensitivity improves by up to 20 dB near the Nyquist limit after white-noise removal. The AI can decide when to increase sampling rate or apply denoising based on detected noise regime.

• Capability: The system can autonomously switch between high-sensitivity (low-noise) and high-robustness (noise-tolerant) modes, maximizing detection of weak geophysical signals while avoiding false alarms from terminal artifacts.

7. Multi-Sensor Fusion with Noise Characterization:

• Improvement: Develop a fusion AI that combines SOP data from multiple cables (e.g., CAT and GEN) with known noise profiles to jointly estimate environmental events, weighting each cable by its signal-to-noise ratio derived from the paper’s variance metrics.

• Capability: The system can produce a more accurate, spatially resolved map of strain or temperature changes across a network, with confidence intervals that reflect each link’s intrinsic noise limitations.

8. Real-Time Noise Source Attribution:

• Improvement: Train a classifier to distinguish between ASE noise, laser phase noise, polarization tracking convergence error, and quantization noise based on the shape of the PSD (e.g., white-noise level, corner frequency, harmonic presence).

• Capability: The AI can diagnose which terminal component is degrading sensing quality, enabling proactive maintenance or algorithmic compensation (e.g., adjusting equalizer coefficients) to restore sensitivity.