Model-Driven Deep-Learning-Based Underwater Acoustic OTFS Channel Estimation

Round 1

Reviewer 1 Report

I reviewed the manuscript, JMSE-2503698, “Model-driven deep learning-based underwater acousticOTFS channel estimation”.  Authors employed a residual neural network to estimate the underwater acoustic channel in the detection of orthogonal time-frequency signals. Authors claim that the proposed method outperforms the treshold based and othogonal matching pursuit channel estimation techniques. Authors base this conclusion on comparison by simulation and tests using WATERMARK field dataset. Manuscript is well written. Reading the abstract will be easier if authors avoid using abreviations (UWA, OTFS, etc.) in the abstract.

Author Response

We greatly appreciate your comments on our submitted manuscript. We have revised our manuscript according to your suggestion. We revised UWA to underwater acoustic, OMP to orthogonal matching pursuit, BER to bit error rate. We keep the abbreviation OTFS as it appears in the title of the paper. We keep the abbreviation DnCNN, as the full name is too long. And from the abbreviation DnCNN, the readers can see it is a variation version of CNN.

Reviewer 2 Report

jmse-2503698

 

In this article, the authors propose an approach for OTFS channel estimation in UWA environments, utilizing a model-driven deep learning technique. The method incorporates a residual neural network into the OTFS channel estimation process. Specifically, the OMP algorithm and denoising convolutional neural network collaborate to perform channel estimation. The cascaded DnCNN denoises the preliminary channel estimation results generated by the OMP algorithm for more accurate OTFS channel estimation results. The author’s work is timely new and interesting, but the current work possesses some limitations. In this regard, some of the suggestions are listed below:

 

1.     There are many grammatical mistakes and typos that need to be corrected with detailed proofreading.

2.     Figure 7 is not cited in the text. Also, check use Fig. or Figure throughout the paper, keep consistency in the paper.

3.     The key contribution should be added highlighted further. I suggest to add the key contribution in the last second paragraph of the introduction section in bullet form for better understanding.

4.     To know more about underwater communication and detection, the author can also refer to “Localization and Detection of Targets in Underwater Wireless Sensor Using Distance and Angle Based Algorithms,” IEEE ACCESS.”

5.     Please add some discussion after “2.1. UWA OTFS system model” and then add figure 1. Never add a figure at the beginning of a section.

6.     All the convolutional kernel size in DnCNN is set to 3 × 3, is this size is fixed? Or can be varied? If we change it, then what will be the outcomes? Please explain in detail.

7.     Moreover, is the number of multi-paths 8 is fixed? And what will be affect if we choose a higher number or a smaller number of paths?

8.     References seem very limited; more recent references should be cited in comparison and literature review.

 

 

Extensive editing of English language required

Author Response

We greatly appreciate your valuable comments on our submitted manuscript. We have revised the manuscript according to your comments and suggestions. We next address your concerns and suggestions in the order you posed them.

 

Point 1: There are many grammatical mistakes and typos that need to be corrected with detailed proofreading.

Reply: We checked the writing of the article sentence by sentence, corrected grammatical errors, and revised the expression. These changes are marked up in the manuscript.

 

Point 2: Figure 7 is not cited in the text. Also, check use Fig. or Figure throughout the paper, keep consistency in the paper.

Reply: Thank you for the reminder. Figure 7 is cited in Section 4.2 of the paper. Meanwhile, we use “Figure” in the paper to keep consistency.

 

Point 3: The key contribution should be added highlighted further. I suggest to add the key contribution in the last second paragraph of the introduction section in bullet form for better understanding.

Reply: Thank you for the advice. We have added the key contribution in the last second paragraph of the introduction section. Our main contributions are:

(1) We address the design of system parameters for enabling effective UWA OTFS communication, considering the specific characteristics of the UWA channel. We discuss the configuration of subcarrier spacing, the number of subcarriers per symbol, and the number of symbols per frame in the delay-Doppler domain, taking into account the influence of multi-path and Doppler effects.

(2) We propose a model-driven deep learning technique for UWA OTFS channel estimation. Considering the more pronounced Doppler effect in the UWA channel compared to the radio channel, the channel information often deviates from the compressed sensing sparsity assumption typically assumed in the classical OMP estimation algorithm. To address this issue, our method incorporates the OMP algorithm and denoising convolutional neural network (DnCNN) collaboration for channel estimation. The use of a lightweight DnCNN network with a single residual block reduces computational complexity while still preserving the accuracy of the neural network.  The proposed method can obtain better channel estimation results by denoising the preliminary channel estimation.

 

Point 4: To know more about underwater communication and detection, the author can also refer to “Localization and Detection of Targets in Underwater Wireless Sensor Using Distance and Angle Based Algorithms,” IEEE ACCESS.”

Reply: Thank you for the advice. We've added the relevant underwater communication and detection papers in the introduction and added the recommended article.

 

Point 5: Please add some discussion after “2.1. UWA OTFS system model” and then add Figure 1. Never add a figure at the beginning of a section.

Reply: Thank you for the advice. We've added some advantages of the OTFS system compared with the OFDM system in underwater acoustic channels.

 

Point 6: All the convolutional kernel size in DnCNN is set to 3 × 3, is this size fixed? Or can be varied? If we change it, then what will be the outcomes? Please explain in detail.

Reply: The size of convolutional kernel in DnCNN is fixed. In the original paper that first proposes DnCNN [1], it has been verified that the convolution kernel size of 3 × 3 is effective, based on the theory in Ref. [2]. Therefore, we set the size of convolutional kernel to be 3 × 3.

[1] Zhang K, Zuo W, Chen Y, et al. Beyond a Gaussian denoiser: Residual learning of deep cnn for image denoising. IEEE transactions on image processing, 2017, 26(7): 3142-3155.

[2] Simonyan K, Zisserman A. Very deep convolutional networks for large-scale image recognition. 3rd International Conference on Learning Representations (ICLR 2015), San Diego, CA, USA, 2015, 1-14.

 

Point 7: Moreover, is the number of multi-paths 8 is fixed? And what will be affect if we choose a higher number or a smaller number of paths?

Reply: The number of multi-paths can be varying. The number of multi-paths 8 is large enough, so we’ve added the simulation results of multi-paths 4 in the paper.

• The number of multi-paths 4: Compared with OMP channel estimation, the proposed DnCNN-based channel estimation has about 0.9 dB gain at 4 Hz Doppler shift and 1.7 dB gain at 6 Hz Doppler shift at an MSE of 0.8 × 10^-3. Comparing the performance of different scales of Doppler shifts for OMP channel estimation, at an MSE of 0.8 × 10^-3, the SNR required for 2 Hz Doppler shift is about 1.4 dB and 2.8 dB lower than that for 4 Hz and 6Hz Doppler shift, respectively. At the same MSE, for the proposed DnCNN-based OTFS channel estimation, the required SNR for 2 Hz Doppler shift is about 1.3 dB and 1.9 dB lower than that for 4Hz and 6Hz.
• The number of multi-paths 8: Compared with OMP channel estimation, the proposed DnCNN-based channel estimation has about 1.1 dB gain at 4 Hz Doppler shift and 3.5 dB gain at 6 Hz Doppler shift at an MSE of 0.8 × 10^-3. Comparing the performance of different scales of Doppler shifts for OMP channel estimation, at an MSE of 0.8 × 10^-3, the SNR required for 2 Hz Doppler shift is about 1.8 dB and 4.8 dB lower than that for 4 Hz and 6Hz Doppler shift, respectively. At the same MSE, for the proposed DnCNN-based OTFS channel estimation, the DnCNN-based channel estimation requires SNR for 2 Hz Doppler shift is about 1 dB and 1.7 dB lower than that for 4Hz and 6Hz.

From the performance analysis of the multi-paths 4 and multi-paths 8, the DnCNN-based channel estimation method shows good performance under different numbers of channel paths. So the proposed method has good robustness to various channel conditions.

 

Point 8: References seem very limited; more recent references should be cited in comparison and literature review.

Reply: Thank you for the advice. We have added 9 recent references to our manuscript, which include UWA communication and detection, the pilot design in OTFS channel estimation, and the design of convolutional kernel size in DnCNN.

Reviewer 3 Report

The paper presents an innovative solution to the complex problem of accurate channel estimation in underwater acoustic (UWA) OTFS systems operating in challenging conditions, such as severe Doppler and multi-path effects. The authors' approach to developing a deep learning (DL) -based UWA OTFS channel estimation method is both novel and seems highly practical. Combining the DnCNN-based approach with the OMP algorithm authors made channel estimation more precise and robust to Doppler shifts.

To further improve the quality of the paper I propose to the authors the following minor changes:

1. Correct the statement in line 204 “The residual block learns to minimize the difference

between the input n and the output H^OMP.” It seems incorrect based on the previous explanations and figures.

2. Explain how the threshold-based method is implemented (which parameters are used) in performance analysis

Author Response

We greatly appreciate your valuable comments on our submitted manuscript. We have revised the manuscript according to your comments and suggestions. We next address your concerns and suggestions in the order you posed them.

 

Point 1: Correct the statement in line 204 “The residual block learns to minimize the difference between the input n and the output H^OMP.” It seems incorrect based on the previous explanations and figures.

Reply: Thank you for the advice. The expression is corrected to “The residual block learns to minimize the difference between the input n and the output H^DL”.

 

Point 2: Explain how the threshold-based method is implemented (which parameters are used) in performance analysis

Reply: The threshold-based channel estimation method sets a threshold of the pilot symbol for channel estimation. Reference [1] proposed a pilot-aided channel estimation scheme for OTFS for the first time and also proposed the threshold-based method. The threshold is set to 3*sqrt(\sigma_p^2), where \sigma_p^2 is the effective noise power of the pilot signal. The later papers, such as reference [2], also employ the same threshold setting for further design. In this paper, we also use the same setting. The setting is illustrated in the revised manuscript.

 

[1] Raviteja P, Phan K T, Hong Y. Embedded pilot-aided channel estimation for OTFS in delay–Doppler channels. IEEE transactions on vehicular technology, 2019, 68(5): 4906-4917.

[2] Liu W, Zou L, Bai B, et al. Low PAPR channel estimation for OTFS with scattered superimposed pilots. China Communications, 2023, 20(1): 79-87.

Round 2

Reviewer 2 Report

NA

 

Minor editing of English language required