High-Stability PGC-EKF Demodulation Algorithm Integrated with a Phase Delay Compensation Module

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

 

This paper proposes a PGC-PDC-EKF joint algorithm that combines phase delay compensation (PDC) with an extended Kalman filter (EKF) to effectively eliminate the nonlinear distortion caused by modulation depth (C value) drift and carrier phase delay (θ) in the phase-generated carrier (PGC) demodulation scheme. The paper has certain innovation and practical value, but the lack of a direct comparison between the theoretical predictions and experimental outcomes of the PGC-PDC-EKF algorithm is a major shortcoming. This comparison is essential to validate the accuracy of the theoretical model and to understand any discrepancies that may arise in practical implementation.

 

 

Comments on the Quality of English Language

• The overall writing logic is clear. Starting from the introduction, the research background and the shortcomings of existing algorithms are described, leading to the proposed algorithm. Then, the theory, simulation analysis, and experimental results are presented in sequence, and finally, the conclusions are drawn. 

Author Response

Comment1: 

This paper proposes a PGC-PDC-EKF joint algorithm that combines phase delay compensation (PDC) with an extended Kalman filter (EKF) to effectively eliminate the nonlinear distortion caused by modulation depth (C value) drift and carrier phase delay (θ) in the phase-generated carrier (PGC) demodulation scheme. The paper has certain innovation and practical value, but the lack of a direct comparison between the theoretical predictions and experimental outcomes of the PGC-PDC-EKF algorithm is a major shortcoming. This comparison is essential to validate the accuracy of the theoretical model and to understand any discrepancies that may arise in practical implementation.

Response 1:

Thanks to the reviewer for the comprehensive and helpful comment.

This work fully evaluates the effectiveness of the PGC-PDC-EKF algorithm through a combination of simulated data and experimental verification. In the simulation, the amplitude and frequency of the modulated carrier signal and the frequency of the signal to be measured are consistent with the experimental settings to ensure that the simulation results are representative. In addition, the interference optical path and modulation demodulation system were built to verify the performance of the algorithm under actual conditions. The experimental results are generally consistent with the simulation results, verifying the accuracy of the theoretical model. The difference between the two mainly comes from the performance differences of the optical and electrical devices used in the experiment, such as the stability of the light source, the linearity of the modulator, and the bit width limitations of the analog-to-digital converter and the digital to analog converter. In practical applications, the same optical path and device configuration as the experiment are usually used, so the difference between experimental results and actual implementation is relatively small.

 

Comment2: The overall writing logic is clear. Starting from the introduction, the research background and the shortcomings of existing algorithms are described, leading to the proposed algorithm. Then, the theory, simulation analysis, and experimental results are presented in sequence, and finally, the conclusions are drawn. 

Response 2:

Thank you for the reviewer's affirmation of the logical structure of the article.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The authors demonstrated an improved PGC-Arctan demodulation scheme by combining PDS and EKF technique. Where, the nonlinear distortion caused by C value drift and phase has been effectively eliminated. The system stability and the algorithms feasibility were verified by simulation and experiment. This manuscript is well-written. I recommend a minor revision before its possible publication in Photonics SI.

The performance of the proposed method should be compared to reported related-works or present products. Its merit should be explained clearly.

Author Response

The authors demonstrated an improved PGC-Arctan demodulation scheme by combining PDS and EKF technique. Where, the nonlinear distortion caused by C value drift and phase has been effectively eliminated. The system stability and the algorithms feasibility were verified by simulation and experiment. This manuscript is well-written. I recommend a minor revision before its possible publication in Photonics SI.

Comment1: 

The performance of the proposed method should be compared to reported related-works or present products. Its merit should be explained clearly.

Response 1:

Thanks for the reviewer’s suggestion.

The present products are primarily used in military and civilian equipment. Military products have confidentiality, while civilian products generally adopt the traditional PGC-Arctan demodulation algorithm. In Sections 3.2 and 4.3 of the work, the proposed PGC-PDC-EKF algorithm is compared with the latest demodulation algorithms through simulation analysis and experimental validation, including PGC-Arctan, PGC-Arctan-HP, PGC-ODR-ATAN, Four-Component, and PGC-EKF algorithms. The results show that the proposed algorithm outperforms other algorithms in terms of signal-to-noise and distortion ratio (SINAD), total harmonic distortion (THD), and relative amplitude error (RAE), especially in harmonic and noise suppression. Furthermore, the algorithm has significant advantages in engineering implementation, is easy to implement on hardware platforms, and has promising prospects for engineering applications.

 

See changes made in Paragraph 8, Section 3.2, Page 8. 

The performances of different demodulation algorithms are shown in Figure 5. The SINAD of the PGC-PDC-EKF is higher than 80.67 dB, THD is lower than -80.65 dB, and RAE is lower than 0.36 %. Compared to the PGC-Arctan scheme, the PGC-PDC-EKF shows a considerable performance advantage with a 9.73 dB improvement in SINAD and a 9.715 dB reduction in THD. The proposed algorithm outperforms other algorithms in terms of SINAD, THD and RAE, especially in harmonic and noise suppression. The simulation results show that the proposed algorithm has a stable performance with a phase delay in the range of 0 to p.

 

See changes made in Paragraph 4, Section 4.3, Page 12. 

The SINAD of the improved PGC demodulation algorithm achieves gains of 18.03 dB, 7.83 dB, 14.74 dB, 13.89 dB, and 6.05 dB, compared with PGC-Arctan, PGC-Arctan-HP, PGC-ODR-ATAN, Four-Component and PGC-EKF, respectively. The THD achieves gains of -26.04 dB, -12.51dB, -20.81 dB, -19.75 dB, and -7.42 dB. PGC-PDC-EKF has the smallest RAE of 0.0374%, which is approaching 0, indicating that the demodulated signal is closest to the original signal. Based on the achieved results, PGC-PDC-EKF confirms its superiority over the basic PGC-Arctan algorithm and the other demodulation algorithms in all three metrics.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This work aims to conduct a High stability PGC-EKF demodulation algorithm integrated with a phase delay compensation module. While the paper is generally well-written, there are several areas requiring clarification:

1.       How does the performance of the proposed PGC-PDC-EKF algorithm compare to other state-of-the-art algorithms in terms of computational complexity and real-time applicability?

2.       What specific measures were taken to assess the algorithm's resilience to different types of noise in the experimental setup?

3.       Is the proposed method scalable for larger systems or more complex sensor networks? If so, what modifications would be necessary?

4.       How does the proposed algorithm perform under varying environmental conditions, such as temperature fluctuations or mechanical vibrations?

 

5.       Could you provide more details about the experimental setup, such as the type of optical fiber used, the fiber's length, and the interferometric sensor's specific configuration?

Author Response

This work aims to conduct a High stability PGC-EKF demodulation algorithm integrated with a phase delay compensation module. While the paper is generally well-written, there are several areas requiring clarification:

Comment1: 

How does the performance of the proposed PGC-PDC-EKF algorithm compare to other state-of-the-art algorithms in terms of computational complexity and real-time applicability?

Response 1:

The editor’s suggestion is thoughtful.

The PGC-PDC-EKF algorithm proposed in this work combines the carrier phase delay compensation (PDC) module with the extended Kalman filter (EKF) algorithm. In terms of computational complexity, the PDC module is low in arithmetic and can quickly accomplish the carrier phase delay compensation. Although the EKF algorithm requires more computation than other algorithms, the parallel processing of the EKF algorithm can be realized on the high-speed signal processing platform FPGA, and the operation can be completed in microseconds, which ensures its excellent real-time performance and responsiveness in practical engineering applications.

Comment2: 

What specific measures were taken to assess the algorithm's resilience to different types of noise in the experimental setup?

Response 2:

We thank the reviewer for the comment.

In the experimental setup, we utilize the same experimental environment and hardware platform to analyze and compare the collected interference signals using multiple demodulation algorithms. In this paper, signal-to-noise and distortion ratio (SINAD) are used as the evaluation metrics to quantify the impact of noise on the demodulation performance. From the experimental results in Figure 5(a) of the paper, it can be seen that the proposed PDC-EKF algorithm has the highest SINAD of 80.67 dB, which is significantly better than other demodulation algorithms. This indicates that the PDC-EKF algorithm has an obvious advantage in anti-noise performance and can more effectively suppress the interference of noise on demodulation accuracy.

 

Comment3:  

Is the proposed method scalable for larger systems or more complex sensor networks? If so, what modifications would be necessary?

Response 3:

Thanks to the reviewer for the comprehensive and helpful comments.

The proposed method can be extended to larger systems or more complex sensor networks. To achieve expansion, it is necessary to make appropriate adjustments to the optical signal processing and sensor network structure. To meet the requirements of complex sensor networks, continuous light needs to be converted into pulsed light. In wavelength division multiplexing sensing networks, optical signals of different wavelengths are combined and transmitted through a multiplexer, and an electro-optic modulator is added after the phase modulator to convert the phase modulated optical signals into pulsed light for transmission in the network. At the receiving end, wavelength division multiplexing technology is used to separate optical signals of different wavelengths and input them into the corresponding optoelectronic converters. After photoelectric conversion, the electrical signal is converted into a digital signal by an analog-to-digital converter, and the proposed algorithm is used to independently process the data from each sensor. Through the above adjustments, the proposed method can maintain efficient demodulation performance in complex sensor networks.

Comment4:  

How does the proposed algorithm perform under varying environmental conditions, such as temperature fluctuations or mechanical vibrations?

Response 4:

We thank the reviewer for the comment.

Temperature fluctuations and mechanical vibrations may cause changes in modulation depth and carrier phase delay in interference signals. However, the PGC-PDC-EKF algorithm proposed in this work exhibits high robustness to these two variations. The PDC module can quickly and accurately compensate for carrier phase delay, ensuring the stability of the demodulation process. Meanwhile, the EKF algorithm effectively suppresses the nonlinear distortion of the demodulated signal caused by modulation depth drift by dynamically updating the state estimation. Therefore, the proposed algorithm can maintain efficient and stable performance under complex environmental conditions such as temperature fluctuations or mechanical vibrations.

Comment5: 

Could you provide more details about the experimental setup, such as the type of optical fiber used, the fiber's length, and the interferometric sensor's specific configuration?

Response 5:

We thank the reviewer for the comment.

The fiber used in the experiment is a regular single-mode fiber, and the interferometric sensor adopts a Michelson interferometer structure with an arm length difference of 0.8 meters. This configuration aims to ensure that the sensor has sufficient sensitivity and resolution, while maintaining good stability and anti-interference performance.

See changes made in Paragraph 1, Section 4, Page 10. 

The modulation carrier signal is output from the Field-Programmable Gate Array (FPGA) and amplified by the High voltage amplifiers (HVA), respectively. The interferometric sensor adopts a MI structure with an arm length difference of 0.8 m and is covered with acoustic cotton to isolate external vibrations and ambient noise.

Author Response File: Author Response.pdf