Robust Adaptive Beamforming Algorithm Based on Complex Gauss–Legendre Integral

Round 1

Reviewer 1 Report

This paper reviewed the recent developments in robustness of beamforming algorithms improvement methods. In this paper, they proposed a new approach based on complex Gauss-Legendre integral. It presents the data model and simulation results in an organized way, verifying this new approach is effective to improve the robustness of the beamforming algorithm. 

Overall this is a good paper and I suggest to accept 

Author Response

We have made some editing changes to the English in the article. Thanks to the reviewers and editors for their help in revising and publishing the article.

Reviewer 2 Report

Recommendation: Accept with Minor Revisions.

 

Comments:

The manuscript titled “Robust Adaptive Beamforming Algorithm Based on Complex Gauss-Legendre Integral” introduces a novel beamforming algorithm, labeled as CGL-ISV. This approach aims to suppress external interferences and bolster the algorithm's robustness. A key distinction between the proposed CGL-ISV and its predecessors lies in its application of the Complex Gauss-Legendre Integral (CGL) to extract the interference noise covariance matrix, sans the desired signal components. This strategy appears to provide enhanced accuracy while curbing computational demands. Moreover, to counter the potential detriments posed by guidance vector mismatches, the algorithm employs an iterative search technique to refine the steering vector. Empirical evidence, provided through a series of simulation-based evaluations, further underscores the advantages of the CGL-ISV approach over existing methodologies, especially in terms of robustness and SINR performance. Notwithstanding the potential of the presented work, certain areas warrant attention and revision. I recommend publication, contingent on the following amendments:

 

1. Correction of Terminology: The term "Guass-Legendre Integral" is incorrect. This should be revised throughout the paper to "Gauss-Legendre Integral."

 

2. Typographical Error: The equations within the range of lines 90-99, particularly for Eq.1, suffer from missing symbols. A similar missing recurs at line 231. The textual coherence between lines 234-244 is compromised due to disjointed sentences. Furthermore, certain passages within the manuscript exhibit lapses in linguistic fluency.

 

3. Elaboration of Concepts: The exposition of several key terms and concepts remains cursory, potentially leading to reader confusion. In particular, foundational beamforming terminologies, such as LCMV, would benefit from a more detailed elucidation. The narrative transition observed on line 173, moving from the "3: The subspace of the interference signal" to "4: Construct the projection matrix," seems abrupt and warrants smoother integration. The experimental setup detailed between lines 230-244 could be rendered more intelligible through accompanying schematics that depict sensor placements, signal propagation, interference points and other setup.

 

4. Figures and Annotations: All figures should be accompanied by comprehensive captions to aid reader comprehension, irrespective of any textual references made within the manuscript. The caption for Figure 1, "This beam patterns," lacks professional polish and should be revised for clarity. Moreover, Figure 2 exhibits alignment issues which need rectification.

 

5. Clarification: The inferences drawn from Figure 4(d) suggest that LCMV & SVOA exhibit superior performance compared to GL & CGL-ISV under conditions of high interference numbers, in present of a 0.20λ perturbation. This observation necessitates a more thorough explanatory commentary.

 

 

I believe that once these revisions are addressed, the manuscript will be well-suited for publication.

Comments for author File: Comments.pdf

Certain passages within the manuscript exhibit lapses in linguistic fluency.

Author Response

Please see the attachment

Author Response File: Author Response.docx

Reviewer 3 Report

[1] Lines 92-93: Please check missing or mis-placed symbols.

[2] Line 115: Please elaborate how to specify the region $\Theta_i$.

[3] Eqn.(8): Please elaborate the reason and advantage of taking this integral.

[4] Eqn.(9): Please check missing index or subscript j.

[5] Line 127-171: The integral in eqn.(10) is well known and should be replaced by citing proper reference.

[6] Line 141: Please elaborate how to determine the neighborhood of interference.

[7] Line 173: Please elaborate matrix C.

[8] Eqn.(19): Please elaborate how the eigenvalues are computed.

[9] Figures 1-4: Please list key parameters in the caption as in conventional literature.

[10] Figure 1: value of -100 dB and below is not practical.

[11] Section 4.2: Please eleborate how to compute the SINR.

Grammar and writing style need to be improved.

Author Response

Please see the attachment

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

Previous comments have been addressed.

Minor grammar check will help.