Anti-Rain Clutter Interference Method for Millimeter-Wave Radar Based on Convolutional Neural Network

1. Summary

Thank you very much for the valuable comments provided by the reviewers. I believe these comments will make this article better. We will now respond to each reviewer's comments.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Can be improved

Are all the cited references relevant to the research?

Can be improved

Is the research design appropriate?

Can be improved

Are the methods adequately described?

Can be improved

Are the results clearly presented?

Can be improved

Are the conclusions supported by the results?

Can be improved

3. Point-by-point response to Comments and Suggestions for Authors

The manuscript studies the effect of rain clutter on millimeter-wave radar and provides an effective anti-rain clutter method for millimetre wave radar. However, I have the following concerns:

Comments 1: In the CST simulation the authors used a Gaussian signal, but this work focuses on the triangular wave linear FM signal, why not use the same signal in the simulation?

Response 1: Thank you for the reviewer's valuable comments, the use of CST electromagnetic simulation in this paper is to study the impact of rainfall environment on the signal propagation, the theoretical situation should be used in the linear FM signal, but the linear FM signal is a section of continuous output signal, there will be a probe to receive the signal at different moments of the situation, resulting in the inability to observe the signal propagation characteristics. The Gaussian signal, on the other hand, has a peak value based on which the propagation of the signal at different moments can be observed. Therefore, Gaussian signal is used in this paper for CST EM simulation.

Comments 2: The authors used spectrograms to create the data set, please add a description of the process of how the acquired signals were converted into the spectrograms used in the data set.

Response 2: Thank you for the valuable feedback provided by the reviewer. We have added the STFT algorithm conversion principle as follows:

To perform image recognition using CNN, it is essential to identify feature images that can easily distinguish between rain clutter and mixed signals. In this paper, the one-dimensional echo signal is converted into a two-dimensional spectrogram by short-time Fourier transform (STFT). This conversion not only provides richer feature information, but also effectively enhances the distinguishability of the signal, thus laying a solid foundation for the subsequent classification and identification work. By analysing the spectrogram, we can better understand the changing pattern of the signal in the rainfall environment, which provides support for improving the recognition accuracy. The mathematical expression of STFT is represented in Eq..:

In Eq., is the frequency, is the time, with the change of time , the window function will be shifted on the time axis to get the result of short time Fourier transform. From the above analysis, once the window function is selected, its shape will be fixed, and the corresponding frequency resolution will be determined. The short-time Fourier transform is equivalent to the projection of each segment of the function on the window function, which reduces the spectral leakage of each segment and improves the resolution of the spectral curve.

The spectrograms of the target signal in non-rain environment, the rain clutter signal in rain environment, and the mixed signal consisting of rain clutter and target signal are shown in Fig.10. These spectrograms illustrate the characteristics under different environmental and signal conditions, which facilitate the training and recognition tasks of the CNN.

Comments 3: The sample of the comparison network is not sufficient, please add the results of the comparison with other networks. The network in this paper is improved on the basis of VGGnet, and the comparison results are only with VGGnet, is it better to use other networks?

Response 3 Thank you for the reviewer's valuable comments, the author has added a comparison with the Resnet network, and the additions are listed below:

As can be seen in Fig.13, the model parameters have stabilised after more than 15 epochs. Therefore, recognition performance is subsequently validated on the test set using these stable parameters and the results are plotted as a confusion matrix. Further, these results are compared with the performance of the VGGNet model and the Resnet model. The results of the confusion matrix are shown in Fig.14.

(a)                                  (b)                                                       (c)

Figure 14. The results of the confusion matrix under different CNN model. (a) The confusion matrix under VGGnet model. (b) The confusion matrix under Resnet model. (c) The CNN confusion matrix under the model used in this paper

Table 4. The metrics of the model performance on the test set under different model

The recognition results of the test set are displayed in the confusion matrix in Fig. 14. As can be seen from the figure, the VGGNet model and the Resnet model have significantly more recognition error results than the CNN used in this paper. Despite the better performance of the CNN used in this paper, two mixed signals are still misidentified as rain clutter. The reason for this analysis may be due to the excessive energy of the rain clutter, which leads to recognition errors. By comparing the computational metrics in Table 4, the CNN model used in this paper outperforms the VGG network and the Resnet network in most of the metrics. Therefore, it can be concluded that the modified CNN is significantly better than the VGG network and the Resnet network in terms of recognition accuracy. Therefore, the modified CNN will be selected for subsequent practical applications.

Comments 4: The theoretical part of the theory on CNN network parameter selection is not detailed enough and lacks detailed descriptions of some key steps selected during the training process.

Response 4 Thank you for the valuable feedback provided by the reviewer. We have added some key steps as follows:

The complete steps for image recognition and classification using CNN are as follows:

1.         First, generate the spectrograms preprocessed with feature enhancement as shown in Fig.11 by using simulation. Then, normalize the image pixels to .

2.         Secondly, classify the simulated dataset, using 80% for the training set and 20% for the test set.

3.         Thirdly, construct a CNN model as shown in Fig. 12, choose the cross-entropy loss function, and select the stochastic gradient descent optimisation algorithm

4.         Fourth，train the model and optimize it with gradient descent, setting the learning rate to 0.00001 and the batchsize to 3. Stop training when the loss function stabilizes.

5.         Finally, evaluate the model performance on the test set by calculating metrics such as accuracy, precision, recall and so on.

1. Summary

Thank you very much for the valuable comments provided by the reviewers. I believe these comments will make this article better. We will now respond to each reviewer's comments.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Yes

Is the research design appropriate?

Yes

Are the methods adequately described?

Yes

Are the results clearly presented?

Yes

Are the conclusions supported by the results?

Can be improved

3. Point-by-point response to Comments and Suggestions for Authors

This paper summarizes the classification and recognition method of rain clutter scene based on convolutional neural network. The research problem is reasonable, the research method is appropriate, and the numerical verification can support the hypothesis. Minor repairs are recommended, but the following issues must  be discussed in detail:

Comments 1: Why does the distance measurement noise decrease after model movement in Figure 9?

Response 1: Thank you for the reviewer's valuable comments, Figure 9 shows the ranging results of the triangular wave LFM detector, in the first ten metres of clutter is more obvious because the detector's detection distance is only 20 metres, in the first 10 metres of the echo signal does not contain target information, while the echo signal behind contains target information, due to the target's energy is concentrated in a frequency band, so in the process of ranging through the frequency of the target is more prominent, the ranging results will be accurate.

Comments 2: How does the complexity of the proposed model compare with the comparison algorithm? The performance of the paper should be compared with the models reviewed in the Introduction section, such as ResNet, EfficientNet, etc.

Response 2: Thank you for the reviewer's valuable comments, the author has added a comparison with the Resnet network, and the additions are listed below:

As can be seen in Fig.13, the model parameters have stabilised after more than 15 epochs. Therefore, recognition performance is subsequently validated on the test set using these stable parameters and the results are plotted as a confusion matrix. Further, these results are compared with the performance of the VGGNet model and the Resnet model. The results of the confusion matrix are shown in Fig.14.

(a)                                  (b)                                                       (c)

Figure 14. The results of the confusion matrix under different CNN model. (a) The confusion matrix under VGGnet model. (b) The confusion matrix under Resnet model. (c) The CNN confusion matrix under the model used in this paper

Table 4. The metrics of the model performance on the test set under different model

The recognition results of the test set are displayed in the confusion matrix in Fig. 14. As can be seen from the figure, the VGGNet model and the Resnet model have significantly more recognition error results than the CNN used in this paper. Despite the better performance of the CNN used in this paper, two mixed signals are still misidentified as rain clutter. The reason for this analysis may be due to the excessive energy of the rain clutter, which leads to recognition errors. By comparing the computational metrics in Table 4, the CNN model used in this paper outperforms the VGG network and the Resnet network in most of the metrics. Therefore, it can be concluded that the modified CNN is significantly better than the VGG network and the Resnet network in terms of recognition accuracy. Therefore, the modified CNN will be selected for subsequent practical applications.

Comments 3: Is the sample shown in Figure 14 from the simulation? If derived from simulation, more samples may need to be generated to test whether the inference performance is truly 100%.

Response 3 Thank you for the reviewer's valuable comments, the author has added the spectrograms from 2400 to 3600.

Batch-generated spectrograms, as shown in Fig.11, were used to create a dataset for subsequent image recognition. This dataset consists of a total of about 3600 spectrograms, including 1200 target signals, 1200 rain clutter signals, and 1200 mixed signals. For each type of signal, 960 images are designated for the training set and 240 images for the test set.

After increasing the number of training and test sets, the results of the comparison of the network models used in this paper are as follows：

(a)                                     (b)

Figure. The results of the confusion matrix under different number of spectrograms. (a) The confusion matrix under 2400 spectrograms. (b) The CNN confusion matrix under 3600 spectrograms.

Table. The metrics of the model performance on the test set under number of spectrograms.

It can be seen from the results in the above graph that the accuracy decreases as the number of samples increases, but it still remains above 99%, so the inference performance of the model used in this paper can be guaranteed

Comments 4: Need to analyze the real-time detection and deployment of the application, including the sample sampling time used by the model, model inference time. Is it possible for a sample to have rain in the first half and no rain in the second half?

Response 4 Thank you for the reviewer's valuable comments, I think the reviewer has this question should be related to comment 1, the reviewer think that it is due to the lack of subsequent rain that the subsequent ranging results are free of clutter, but the ranging results are due to the limited detector detection results, and I can assure you that the data used in this paper are all in a rainfall environment. We collecting signals in rainfall environments and then subsequently processed use a computer for measure ranging