Simultaneous Source Number Detection and DOA Estimation Using Deep Neural Network and K2-Means Clustering with Prior Knowledge
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis paper presents a simultaneous source number detection and direction-of-arrival estimation scheme. The following concerns need to be addressed.
1. It would be good to summarize the organization of the paper at the end of Section 1.
2. It would be helpful to draw a figure corresponding to the model in Section 2.
3. After the description in Section 2, the prior arts can be reviewed in more detail so that they can be contrasted to the proposed scheme.
4. All the signal notations defined in Section 2 can be specified in Figure 1.
5. The detailed network structure including the layer information can be presented along with Figure 2.
6. The big-oh notation is usually expressed only in the highest-order term.
7. Some numerical examples can be presented for Table 1 with practical parameters.
8. Regarding Figure 6, the testing times need to be measured for various configurations.
9. It would be good to specify the reference numbers of the prior arts in the comparison figures and tables.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper develops and presents a new method, called the DNN-C (Deep Neural Network and Clustering) method, which is designed for simultaneously estimating the source number and DOAs (Direction-of-Arrivals). It consists of a simple fully-connected DNN and K2-means clustering, which involves only multiplications and additions, and avoid matrix decomposition. Simulation results show that the proposed method is computationally efficient than the conventional methods.
Overall, the proposed method look meaningful and interesting. Also, the paper is well organized. Therefore, I would recommend its publication in Electronics after a minor revision.
More Comments:
1. Lines 108-129: The matrix \widehat{R} is given by Equation (4), and its off-diagonal upper right triangular elements form the vector \mathbf{b}.
The matrix \widehat{R} is symmetric, so I understand that taking all M^2 entries of \widehat{R} is clearly redundant.
However, what about the diagonal entries of \widehat{R}?
When I first read the definition of \mathbf{b}, I thought the diagonal entries of \widehat{R} are all 1s.
But, according to Equation (4), the diagonal entries of \widehat{R} can be arbitrary number due to the noise term n(t) given in Equation (1).
Therefore, I think it is more reasonable to include the diagonal entries of \widehat{R} into the vector \mathbf{b}, thus forming an M(M+1)/2 dimensional vector rather than a M(M-1)/2 dimensional vector.
Please address this issue in detail.
Otherwise, please justify why the authors have neglected the diagonal entries from the vector \mathbf{b}.
2. Lines 345-349: The Probability of Detection (PD) is defined by Equation (38).
However, the authors multiplied the constant 100 in Equation, so that PD is between 0 and 100.
So, the units for PD is in percentage (from 0 to 100), rather than the standard probability (from 0 to 1).
Lines 352-355: Likewise, the Probability of Missed Detection (PMD) defined by Equation (42) has the constant factor 100, so the units for PMD is in percentage (from 0 to 100).
Therefore, I suggest the authors to include the units "percent" for PD and PMD in the text Lines 345-355, to avoid confusion.
Also, it would be nice if the authors could denote all the relevant units in Figures 7-14.
Currently, the units for the the vertical axis in Figures 7-14 are missing.
Please clarify the units for the the vertical axis in Figures 7-14
3. On page 12, Table 1: It is a bit confusing that the authors use the brackets "\mathcal{O} [.]" for the big-O notation and "\lfloor . \rfloor" for the rounding operation. I suggest that the authors to instead use the plain parentheses "\mathcal{O} (.)" for the big-O notation.
4. Line 580: "leverages"
These phrases often appear in sentences that are generated with AI tools such as ChatGPT.
Please remove these phrases and replace them with other wordings, such as "exploits".
5. Line 583-585: "DNN-C is immune to nonuniform noise" → "DNN-C is robust to nonuniform noise".
Author Response
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Reviewer 3 Report
Comments and Suggestions for AuthorsSource number detection/estimation and Direction-of-Arrival (DOA) estimation are two important topics in array signal processing. This paper presents This paper proposes a simple solution to efficiently estimate the source number and DOAs using deep neural network (DNN) and clustering, named DNN-C. I think this work is meaningful and innovative in practical. The main concerns are given as below,
(1) Is the source signal affect the performance? Since in real circumstance, the received signals are usually unknown and uncertain. My concern is about how to establish the training signals to overcome this problem?
(2) In subsection 3.6, Evaluation Criterion. The authors defined PD, FAR and PMD that are generally utilized in detection theory. I think the authors should give a detailed description to these criterions, especially to let readers know why you want to use these. Besides, these results corresponding to Figure 7 to Figure 14 seems not efficient to verify the performance. We can see a lot of time, the PD is 100 or 0, especially in different SNRs. I suggest the authors think about this and make it more clearly.
(3) In subsection 4.2, absence of sources. This part is not suitable here. And the comparison is meaningless.
(4) In Figure 8(d), the legends make the figure not clear? And I don’t known the meaningful of PD, FAR and PMD to your performance.
(5) To check the font of Figures. And make the axis range of Figures suitable. I can’t evaluate your performance as you choose a very large axis range.
(6) How you get the CRB. I think the authors should give some descriptions.
(7) In Figure 15 and 17. The results are similar. I am wondering if these results can give a positive conclusion. I don’t know if your method may have a problem or my concern in problem (1) “How to establish the training signals to overcome this problem? ”
Author Response
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Reviewer 4 Report
Comments and Suggestions for AuthorsThe authors propose a technique for DoA estimation and source number determination based on a regression model developed through a DNN. The DNN is trained through numerically generated samples and real-world data taken from a Uniform Circular Array of antennas, thus comparing the proposed technique to classic algorithms from the array signal processing scientific literature. The paper is well written and rigorous in the mathematical description, but there are some details that require attention before I can recommend the paper for publication.
l.1: DOA: Always declare acronyms before using them.
l.23-25: The authors should extend the context and the reason why DoA estimation is important, along with possible applications, a little more.
l.27-29: These are not the only possible techniques for DoA estimation.
l.32: This problem should be better discussed
l.45: The authors previously published several articles addressing the DoA estimation through the DNN. I think it would be better to understand the novelty with respect to previously published and referenced articles, in particular 19,21,27.
l.48: The authors should also indicate possible research works in which not only simulations are involved, but also experiments in a real propagation scenario.
l.90-94: This part would be better collocated in the conclusions, while it would be better to close the introduction by inserting a summary of the paper's organization.
l.94: The introduction can be further expanded and included in the literature other works that propose the experimental validation of the DoA estimation technique in the presence of multiple sources which are not based on ML approaches but on lightweight and real-time-enabled techniques like phase interferometry (e.g. multiple source AoA estimation through phase interferometry).
l.524-526: More details about the experimental setup must be given. Those details should include: the propagation environment, the signal frequency, the RF front-end details such as ADC sampling rate and bit depth, etc. All those parameters strongly affect the DoA Estimation, maybe more of the DNN performance itself.
Author Response
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Author Response File: Author Response.pdf
Reviewer 5 Report
Comments and Suggestions for AuthorsThe paper proposes a method that integrates a fully-connected DNN to generate a spatial spectrum and a specially designed K2-means clustering algorithm to extract source information from this spectrum. The method leverages prior knowledge of array signal processing to transform source detection into a binary clustering problem, making it more efficient and robust against nonuniform noise. The Authors highlight the effectiveness of the method through numerous and extensive computer simulations, demonstrating that it significantly reduces testing time compared to classical methods like MDL/NUMDL/SSM-MUSIC.
The paper can be improved in the following aspects:
Section 5. Experimental Results based on Real Data
Although, the key contribution of the paper is related to the development of data processing models, the description of the experimental setup should provide more details on the radio part of the setup (i.e. devices used, their configuration, antenna system setup, propagation environment).
Method description/discussion of the results:
Simulations - what assumptions concerning the propagation environment were used in the experimental part? What may be the influence of multipath propagation/reflections on the method's performance?
The paper does not discuss the practical challenges of implementing the proposed method in a real-time environment. As the Authors noticed in the 6. Conclusion section, the method has some limitations. These should further addressed in the paper:
- the proposed DNN-C method requires extensive training data, this can be a challenge in terms of data collection and processing. The method's scalability and applicability for real-world scenarios should be discussed.
- how can the method be adpated for different array geometries/configurations?
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe concerns have been addressed.
Reviewer 3 Report
Comments and Suggestions for AuthorsNo more comments.
Reviewer 4 Report
Comments and Suggestions for AuthorsThe authors addressed my previous concerns, therefore now I can recommend the paper for publication. Good luck with the rest of the review process.
