Spectral De-Aliasing Method of Micro-Motion Signals Based on a Complex-Valued U-Net Network
Round 1
Reviewer 1 Report
In the manuscript titled, "Spectral De-aliasing Method of Micro-motion Signals Based on a Complex-valued U-Net Network," the authors address the pivotal challenge of spectrum aliasing in radar technology pertaining to micro-motion signals. Leveraging the advanced capabilities of the U-Net network, particularly its complex-valued variant, this paper proposes a novel approach to de-alias the spectrum by employing zero interpolation. This method aims to enhance the sampling frequency and subsequently alleviate inherent issues associated with the Nyquist Sampling Theorem. Delving into the intricacies of transforming echoes from the time domain to the time-frequency domain through a sophisticated combination of zero interpolation and the Short-Time Fourier Transform (STFT), this work explores a complex landscape. This is further augmented by the innovative application of the complex-valued U-Net model to eliminate redundant frequency components. While this research offers several insightful contributions, there remain critical questions that warrant further exploration and elucidation.
1. How does your method differentiate from existing spectral de-aliasing techniques, making it superior in the context of micro-motion signal processing?
2. How does the complex-valued U-Net network enhance the accuracy and robustness of spectral de-aliasing?
3. What is the novelty in the introduction of zero interpolation for spectral de-aliasing?
4. After zero interpolation, how do you ensure that critical frequency components aren't erroneously removed?
5. Within the complex-valued U-Net network, which features of the network make it particularly adept at handling redundant frequency components caused by zero interpolation?
6. Is this method exclusively suitable for addressing the problem of micro-motion signal echo spectrum aliasing in narrowband radar, or does it also find broader applications in other radar systems or signal processing domains?
7. Has your method been validated or implemented in real-world radar systems?
8. Prior to the introduction of the complex-valued U-Net network for spectral de-aliasing, what were the main technical barriers or challenges?
9. When compared to traditional de-aliasing methods, what are the advantages and limitations of the method based on the complex-valued U-Net network?
10. In your opinion, what potential areas of improvement or research directions exist in the spectral de-aliasing method based on the complex-valued U-Net network?
11. With the increasing advancements in big data and AI technologies, what future research trends or challenges do you foresee in the realm of radar signal processing?
Author Response
Dear Reviewer:
Thank you for your insightful comments and constructive suggestions for our manuscript entitled “Spectral De-aliasing Method of Micro-motion Signals Based on a Complex-valued U-Net Network” Those comments are valuable and very helpful for revising and improving our paper. We have studied them carefully and have made corresponding corrections and modifications which we hope meet with approval.
A point-by-point reply to each comment is given in the following. For ease of reference, we use an independent reference set in each reply.
General Comment: In the manuscript titled, "Spectral De-aliasing Method of Micro-motion Signals Based on a Complex-valued U-Net Network," the authors address the pivotal challenge of spectrum aliasing in radar technology pertaining to micro-motion signals. Leveraging the advanced capabilities of the U-Net network, particularly its complex-valued variant, this paper proposes a novel approach to de-alias the spectrum by employing zero interpolation. This method aims to enhance the sampling frequency and subsequently alleviate inherent issues associated with the Nyquist Sampling Theorem. Delving into the intricacies of transforming echoes from the time domain to the time-frequency domain through a sophisticated combination of zero interpolation and the Short-Time Fourier Transform (STFT), this work explores a complex landscape. This is further augmented by the innovative application of the complex-valued U-Net model to eliminate redundant frequency components. While this research offers several insightful contributions, there remain critical questions that warrant further exploration and elucidation.
Answer: We thank you for the critical comments and helpful suggestions. We have taken all these comments and suggestions into account, and have made major corrections in this revised manuscript.
Comment 1: How does your method differentiate from existing spectral de-aliasing techniques, making it superior in the context of micro-motion signal processing?
Answer: The spectral de-aliasing techniques mainly rely on changes in sampling frequency to achieve spectrum de-aliasing. The frequency components are mainly fixed, that is, the frequency does not change over time, while micro-motion signals are generally time modulated signals like Figure 1 that change over time. Existing spectrum aliasing techniques cannot achieve the spectrum aliasing of such signals, and the method proposed in the paper can solve the spectrum aliasing problem of such signals. I have explained in introduction. ‘Spectrum aliasing is common in radar signals [29,30]. The spectral de-aliasing techniques mainly rely on changes in sampling frequency to achieve spectrum de-aliasing. The frequency components are mainly fixed, that is, the frequency does not change over time, while micro-motion signals are generally time modulated signals that change over time.’
Figure 1. the time-frequency result of a micro-motion signal
- Borys, A. The Problem of Aliasing and Folding Effects in Spectrum of Sampled Signals in View of Information Theory. International Journal of Electronics and Telecommunications 2022, 68, 315–322, doi:10.24425/ijet.2022.139884.
- Jana, S.; Rakshit, G.; Maitra, A. Aliasing Effect Due to Convective Rain in Doppler Spectrum Observed by Micro Rain Radar at a Tropical Location. Advances in Space Research 2018, 62, 2443–2453, doi:10.1016/j.asr.2018.07.010.
Comment 2: How does the complex-valued U-Net network enhance the accuracy and robustness of spectral de-aliasing?
Answer: The paper enhances the accuracy and robustness of spectral de-aliasing by modifying the network structure and dataset. When training the model, the accuracy and robustness of the network structure are mainly judged through two indicators: SSIM and PSNR. By modifying the number of network layers and convolution kernel size, a network structure with good robustness and accuracy will be selected. Based on the characteristics of the micro-motion signal, a dataset corresponding to the type of target is generated to improve the accuracy of spectral de-aliasing.
Comment 3: What is the novelty in the introduction of zero interpolation for spectral de-aliasing?
Answer: The zero interpolation is the foundation for Complex-valued UNet networks to eliminate excess frequency components and achieve spectrum aliasing resolution. The paper uses the zero interpolation to increase the sampling frequency, resulting in the appearance of aliased frequency components, but also generating other frequency components. The Figure 2(a) shows the time-frequency results of spectrum aliasing. The time-frequency results of the signal after interpolating once of zeros in Figure 2(b).
(a) (b)
Figure 2. Time-frequency results of micro-motion signal after using zero interpolation. (a) the Result when the sampling frequency does not meet the Nyquist Sampling Theorem. (b) the Result after interpolating once of zeros.
Comment 4: After zero interpolation, how do you ensure that critical frequency components aren't erroneously removed?
Answer: Zero interpolation will not eliminate the original frequency component, but will only add new frequency components. The frequency components of micro-motion signals are generally a sinusoidal signal modulated by time, so there is a connection between the signals at each moment in the time-frequency results. In general, using a U-Net network can determine this connection well, the critical frequency components aren't erroneously removed.
Comment 5: Within the complex-valued U-Net network, which features of the network make it particularly adept at handling redundant frequency components caused by zero interpolation?
Answer: U-Net shows great potential in applications such as semantic segmentation, target segmentation and detection, particularly in image segmentation [1,2]. The micro-motion signal is a complex-valued signal, and after using STFT, the time-frequency domain of the signal is also complex-valued. The use of complex U-Net networks can fully utilize the information contained in signals. Removing redundant frequency components caused by zero interpolation is actually a semantic segmentation problem in time-frequency results, and complex U-Net networks have advantages in this problem.
- Schmidhuber, J. Deep Learning in Neural Networks: An Overview. Neural Networks 2015, 61, 85–117, doi:10.1016/j.neunet.2014.09.003.
- Ronneberger, O.; Fischer, P.; Brox, T. U-Net: Convolutional Networks for Biomedical Image Segmentation. In Proceedings of the Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015; Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F., Eds.; Springer International Publishing: Cham, 2015; pp. 234–241.
Comment 6: Is this method exclusively suitable for addressing the problem of micro-motion signal echo spectrum aliasing in narrowband radar, or does it also find broader applications in other radar systems or signal processing domains?
Answer: Thank you for pointing this out. This method can be applied to narrowband and broadband radars. Based on the characteristics of the corresponding radar, a corresponding dataset is generated, which could be used for de aliasing of micro-motion signals. At the same time, this method can also be used for spectrum aliasing of multiple micro-motion signals, which is also the direction of this research. Thank you for your suggestion and pointing me out the next research direction.
Comment 7: Has your method been validated or implemented in real-world radar systems?
Answer: Thank you for pointing this out. At present, the method has been experimentally validated using small radars in the laboratory, but has not yet been validated and implemented in mature radar systems.
Comment 8: Prior to the introduction of the complex-valued U-Net network for spectral de-aliasing, what were the main technical barriers or challenges?
Answer: I think the main challenge is that the frequency components contained in the micro motion signal are time-varying, so it is difficult to achieve the de aliasing of the micro motion signal using conventional methods of de aliasing. Figure 1 shows the characteristics of the frequency variation of such signals over time.
Comment 9: When compared to traditional de-aliasing methods, what are the advantages and limitations of the method based on the complex-valued U-Net network?
Answer: Compared to traditional de-aliasing methods, the method can solve the problem of conventional signal spectral aliasing and micro-motion signal spectral aliasing, which refers to the spectrum aliasing of signals whose frequency components change over time. The proposed method relies on model training, and for unknown signals, spectral de-aliasing could be challenging.
Comment 10: In your opinion, what potential areas of improvement or research directions exist in the spectral de-aliasing method based on the complex-valued U-Net network?
Answer: In my opinion, this method is widely used. In the military, for targets such as missiles and helicopters, this method can be used to solve the possible spectrum aliasing problem of these targets, providing reliable data for the next step of feature extraction and target recognition. In civilian use, targets such as wind turbines that generate micro-motion signals can also use this method to solve the problem of spectrum aliasing. I have modified the manuscript in 5. Conclusion. ‘For the network, the next step can be to further optimize the network structure, improve the model training dataset, and improve the model's robustness and usage range.’.
Comment 11: With the increasing advancements in big data and AI technologies, what future research trends or challenges do you foresee in the realm of radar signal processing?
Answer: With the increasing advancements in big data and AI technologies, deep learning has been widely used in radar signal processing. I believe that currently, the biggest trend is to combine deep learning with radar signal processing based on the updates and upgrades of radar. At first the challenge is the high cost and usage cost of radar, making it difficult to collect a sufficient amount of high-quality data; Secondly, the current radar performance varies, and even two radars of the same model may have differences in performance, which makes algorithm design difficult; Thirdly, radar collects a large amount of data and contains a relatively small percentage of effective data, which urgently needs to be addressed for effective data extraction.
Author Response File: 
Author Response.docx
Reviewer 2 Report
This paper presents spectral de-aliasing of Micromotion signals using complex valued U-Net. Comments to Authors are the following:
1. What are signals representing in Figs 2. It looks that they are frequency modulated signals. Are they representing Doppler signals of rotating motions?
2. You are using a radar with sampling rate of 400kHz? In Figs2 , Fs/2 are 1 -4k Hz. There is no motivation of reasons for aliasing. Modern microcontrollers can easily sample signal up to 5MHz.
3. Again, it is not clear, why you use zero padding to your received signal.
4. What kind of signal is radar emitting?
5. s(t) is receiving signal, correct the notation in sec. 2.3
6. What X(z) represents. Z transform of received signal?
7. MTI represents gradient operation. Within noisy environments it is not desired to use gradient methods.
8. You obtain spectrogram of the received signal, transform 1d signal to 2D and consider 2D signal as image and then you apply image processing technique to remove undesired signal. Is it necessary to increase the dimensionality of the signal? Usually, we would like to have as small as possible dimensions of processed signal.
9. Input images are complex valued or just operations of convolution are complex valued?
1 What do the variables x and y represent in (5)?
1 Line 217. How you compute convolutions using real and imaginary parts?
1 Test signals are presented only for one target with one kind of motion. Rotation vibrations can be different. Discussion is missing.
Author Response
Dear Reviewer:
Thank you for your insightful comments and constructive suggestions for our manuscript entitled “Spectral De-aliasing Method of Micro-motion Signals Based on a Complex-valued U-Net Network” Those comments are valuable and very helpful for revising and improving our paper. We have studied them carefully and have made corresponding corrections and modifications which we hope meet with approval.
A point-by-point reply to each comment is given in the following. For ease of reference, we use an independent reference set in each reply.
General Comment: This paper presents spectral de-aliasing of Micromotion signals using complex valued U-Net. Comments to Authors are the following.
Answer: Thanks for your comments and valuable suggestions. I have modified the paper accordingly.
Comment 1: What are signals representing in Figs 2. It looks that they are frequency modulated signals. Are they representing Doppler signals of rotating motions?
Answer: Thank you for pointing this out. The signal in Figure 2 is the micro-Doppler signal of the rotating target, and I have added explanations to explain the signal in Figure 2 in paper. ‘Figure 2 are time-frequency results of a rotating target.’.
Comment 2: You are using a radar with sampling rate of 400kHz? In Figs2, Fs/2 are 1 -4k Hz. There is no motivation of reasons for aliasing. Modern microcontrollers can easily sample signal up to 5MHz.
Answer: We were really sorry for our careless mistakes. Thank you for the reminder. Fs is pulse repetition frequency and sampling rate is AD sampling rate. In paper sampling frequency is pulse repetition frequency. Spectrum aliasing occurs in the pulse dimension. Our parameter description is not rigorous enough and has been modified in paper. ‘Figure 3a displays the radar. Its carrier frequency is 24 GHz, bandwidth is 20 MHz, AD sampling rate is 400 kHz, and pulse repetition frequency is 4000 Hz.’
Comment 3: Again, it is not clear, why you use zero padding to your received signal.
Answer: Thank you for this helpful comment. Spectrum aliasing occurs in the pulse dimension. In radar, the pulse repetition frequency is 50-8000Hz. Therefore, it is easy to occurs spectral aliasing for micro-motion signals. The zero interpolation is the foundation for Complex-valued UNet networks to eliminate excess frequency components and achieve spectrum aliasing resolution. The paper uses the zero interpolation to increase the sampling frequency, resulting in the appearance of aliased frequency components, but also generating other frequency components. The Figure 1(a) shows the time-frequency results of spectrum aliasing. The time-frequency results of the signal after interpolating once of zeros in Figure 1(b).
(a) (b)
Figure 1. Time-frequency results of micro-motion signal after using zero interpolation. (a) the Result when the sampling frequency does not meet the Nyquist Sampling Theorem. (b) the Result after interpolating once of zeros.
Comment 4: What kind of signal is radar emitting?
Answer: We use a specific narrow-band continuous wave micro radar in paper. Radar emits sawtooth and triangular waves. We have added explanations in the paper. ‘Radar emits sawtooth and triangular waves.’.
Comment 5: s(t) is receiving signal, correct the notation in sec. 2.3.
Answer: Thank you for this helpful comment. We have revised the manuscript. ‘s(t) represents the receiving signal’
Comment 6: What X(z) represents. Z transform of received signal?
Answer: Thank you for pointing this out. X(z) represents the result of z transformation of the receiving signal. The principle of MTI is illustrated through the schematic diagram after Z transformation, Figure 4 in paper. We have added explanations in the paper. ‘X(z) represents the result of z transformation of the receiving signal.’.
Comment 7: MTI represents gradient operation. Within noisy environments it is not desired to use gradient methods.
Answer: Thank you for pointing this out. Yes, the reviewer was absolutely correct. We are targeting our experimental environment with a high signal-to-noise ratio and the presence of strong clutter in the zero-frequency attachment, hence using MTI to remove clutter. Figure 2 presents the time-frequency result after MTI processing. The time-frequency results indicate that MTI processing can suppress environmental clutter.
(a) (b)
Figure 2. Time-frequency results (a)the Raw signal. (b) the Result after the MTI processing.
Comment 8: You obtain spectrogram of the received signal, transform 1d signal to 2D and consider 2D signal as image and then you apply image processing technique to remove undesired signal. Is it necessary to increase the dimensionality of the signal? Usually, we would like to have as small as possible dimensions of processed signal.
Answer: Thank you for your comments. The frequency contained in the micro-motion signal changes over time, and there is spectral aliasing in the micro-motion signal, which exists at a certain period of time within a cycle. If the micro-motion signal is one-dimensional, FFT cannot reflect the relationship between frequency components and time, and cannot solve spectral aliasing. By using STFT to convert the micro-motion signal into 2D, the relationship between the frequency components of the micro motion signal and time can be observed in the time-frequency domain. At the same time, UNet networks can be used to solve the problem of spectrum aliasing.
Comment 9: Input images are complex valued or just operations of convolution are complex valued?
Answer: In paper, the input is the micro-motion signal after STFT. The network inputs are the time-frequency results in complex field. So, the input images are is a complex-valued matrix.
Comment 10: What do the variables x and y represent in (5)?
Answer: We feel sorry for our carelessness. We have added explanations in the paper. ‘In Equation (5), represents the real part value of the complex values in the row and the column of the matrix, and represents the imaginary part value of the complex values in the row and the column, .
’
Comment 11: Line 217. How you compute convolutions using real and imaginary parts?
Answer: In Equation (7), we normalize the matrix. We have added explanations in the paper. ‘Then normalize the matrix. The real part and the imaginary part are separated, resulting in the real part matrix as follows:’.
Comment 12: Test signals are presented only for one target with one kind of motion. Rotation vibrations can be different. Discussion is missing.
Answer: Whether it is rotation or vibration, the frequency components of the generated micro-motion signals have the characteristic of changing over time. Compared to rotation, according to Equation (1), the frequency range of the micro-motion signal generated by vibration is relatively small and generally does not produce spectral aliasing, so it is not discussed in the paper. We have added discussion in the paper in Line 163. ‘Compared to rotation, according to Equation (1), the frequency range of the vibration generally does not produce spectral aliasing.’.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
Dear Authors,
you answered to all of my questions.
In my opinion paper is ready for publication.
