Broadband DOA Estimation by Exploiting DFT Extrapolation
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
Round 1
Reviewer 1 Report
The paper discusses increasing the DOA estimation using DFT extrapolation in a broadband context.
The paper is fine and besides a few correction, I would add that, given the fact that the DFT (periodogram) is used for DOA, which is a notoriously bad spectral estimator in the presence of noise, I would suggest to add the variance of the DOA in the graphs as in practical applications, one will typically not be able to take the mean of several signals. And if one is able to have several signals, better methods (than the periodogram) do exist.
Also the conclusions need to be nuanced as the paper only reports on a few simulations using a small number of sources. How about more sources?
Regarding minor corrections:
- line 60: it should be Q_kk
- eq (5): there is a ^(mu-1) missing on the Q
- line 71, I guess former and latter should be reversed
- line 72: "number samples series" should be "number of samples in the series"
- line 80: "and its number was set to" should be "and the number of sources was"
- line 83: if the standard deviation of the noise is the average of the absolute value of the samples signal, it is not clear how the SNR is varied. Please clarify.
- a general remark: virtual arrays are typically something else than an extrapolated array. For instance line 93, I'd rather suggest using "a 12-element array extrapolated to 36 elements".
- line 114: where the ESTIMATED number of peaks
- line 129: the conclusion is the same as for the case of 3 sources. It should however be nuanced as the improvement requires more bandwidth. How about 5 sources? Is there a case where no improvement at all would be observed?
- line 149: sentence is not clear. I'd suggest "...a array with a relatively small number of elements can accuratly estimate the DOA of a small number of sources."
Author Response
COMMENT: The paper discusses increasing the DOA estimation using DFT extrapolation in a broadband context.
The paper is fine and besides a few correction, I would add that, given the fact that the DFT (periodogram) is used for DOA, which is a notoriously bad spectral estimator in the presence of noise, I would suggest to add the variance of the DOA in the graphs as in practical applications, one will typically not be able to take the mean of several signals. And if one is able to have several signals, better methods (than the periodogram) do exist.
RESPONSE: Thanks for the detailed comment. As many performance comparisons are made only with the averaged error alone in existing DOA studies such as the reference below, RMSE alone is sufficient for the performance evaluation of the proposed algorithm.
Reference: R. Shafin, L. Liu and J. Zhang, "DoA Estimation and RMSE Characterization for 3D Massive-MIMO/FD-MIMO OFDM System," 2015 IEEE Global Communications Conference (GLOBECOM), 2015, pp. 1-6, doi: 10.1109/GLOCOM.2015.7417413.
COMMENT: Also the conclusions need to be nuanced as the paper only reports on a few simulations using a small number of sources. How about more sources?
RESPONSE: Thank you for the detailed comment. We added the result to the paper by simulating the case where there are five sources in Fig. 3.
COMMENT: Regarding minor corrections:
- line 60: it should be Q_kk
- eq (5): there is a ^(mu-1) missing on the Q
- line 71, I guess former and latter should be reversed
- line 72: "number samples series" should be "number of samples in the series"
- line 80: "and its number was set to" should be "and the number of sources was"
- line 83: if the standard deviation of the noise is the average of the absolute value of the samples signal, it is not clear how the SNR is varied. Please clarify.
- a general remark: virtual arrays are typically something else than an extrapolated array. For instance line 93, I'd rather suggest using "a 12-element array extrapolated to 36 elements".
- line 114: where the ESTIMATED number of peaks
- line 129: the conclusion is the same as for the case of 3 sources. It should however be nuanced as the improvement requires more bandwidth. How about 5 sources? Is there a case where no improvement at all would be observed?
- line 149: sentence is not clear. I'd suggest "...a array with a relatively small number of elements can accuratly estimate the DOA of a small number of sources."
REPONSE: Thank you for the detailed comments. We corrected the manuscript based on the comments about minor corrections. Followings are the response needed.
line 83: We added that SNR was calculated based on the average of the absolute values.
a general remark: We revised the manuscript based on the suggestion.
line 129: We paraphrased the conclusion and rewritten it. it doesn’t mean that more bandwidth is required for DFT extrapolation but means that the bandwidth where DOA estimation is possible is extended. We also added simulation results for the case of 5 sources. Improvements are seen in the five signals as well.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The article may be of interest to the scientific community of researchers.
For a better perception of a scientific text, it is advisable to present the material in simpler phrases.
Mathematical proofs are at the proper level.
The bibliography contains an insufficient number of modern references reflecting the current state of affairs.
It is necessary to reduce the paper to a full the last page.
Author Response
COMMENT: The article may be of interest to the scientific community of researchers.
For a better perception of a scientific text, it is advisable to present the material in simpler phrases.
RESPONSE: Thanks for the detailed comment. We added a detailed description to help understand.
COMMENT: Mathematical proofs are at the proper level.
The bibliography contains an insufficient number of modern references reflecting the current state of affairs.
RESPONSE: Thanks for the detailed comment. We added recent study [7-8].
COMMENT: It is necessary to reduce the paper to a full the last page.
RESPONSE: Thanks for the detailed comment. We added more sentence while responding to other comments and last page has become full.
Author Response File: Author Response.docx
Reviewer 3 Report
1. In the line 19 of the page one, "SOIs" , please give its full name.
2. In the lines 116, 123, and 126 of the page 3, "100 MHz", "200 MHz", which may seem confusing.
3. The hyperparameter $\lambda$ is heuristic. And this is what the authors claim to be an innovation relative to [9]. There is almost no easy way to determine $\lambda$ in practice. Please try to give theoretical guidance on hyperparameter selection. Otherwise, the innovation of this paper is too weak.
Author Response
COMMENT: 1. In the line 19 of the page one, "SOIs" , please give its full name.
RESPONSE: Thanks for the detailed comment. We added its full name.
COMMENT: 2. In the lines 116, 123, and 126 of the page 3, "100 MHz", "200 MHz", which may seem confusing.
RESPONSE: Thanks for the detailed comment. We corrected the frequencies.
COMMENT: 3. The hyperparameter $\lambda$ is heuristic. And this is what the authors claim to be an innovation relative to [9]. There is almost no easy way to determine $\lambda$ in practice. Please try to give theoretical guidance on hyperparameter selection. Otherwise, the innovation of this paper is too weak.
RESPONSE: Thanks for the detailed comment. If the lambda is too large or the tolerance is too small in the iterative process using the Cauchy regularizer, the extracted signal becomes zero because of the excessive iteration and excessive increment of sparsity. we set the hyperparameters heuristically to prevent this from happening. We added this to the paper.
Author Response File: Author Response.docx
Round 2
Reviewer 3 Report
(1) In the line 141 of the page 4, "In Figure 2(b)" should be replaced with "In Figure 3(b)".
(2) In the page 1, "To verify the validity of the proposed algorithm, we estimated the broadband DOAs for multiple signals of interest(SOIs), and the RMSE was reduced in the extended antenna array. " Please polish this sentence.
Author Response
(1) In the line 141 of the page 4, "In Figure 2(b)" should be replaced with "In Figure 3(b)".
response: Thanks for the detailed observation. We corrected the figure number.
(2) In the page 1, "To verify the validity of the proposed algorithm, we estimated the broadband DOAs for multiple signals of interest(SOIs), and the RMSE was reduced in the extended antenna array. " Please polish this sentence.
response: Thanks for the detailed comment. We revised the sentence to make it clear.
