Variable-Step-Size Generalized Maximum Correntropy Affine Projection Algorithm with Sparse Regularization Term

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

 

This paper proposed a variable-step-size generalized maximum correntropy affine projection algorithm (C-APGMC) with a sparse regularization term. The algorithm takes full advantage of the sparsity of the system by incorporating a correlated entropy-inducing metric(CIM) that approximates the L0 norm of norms, assigning stronger zero-attraction to smaller coefficients at each iteration. The following aspects should be considered to improve the quality of this paper.

 

1.     This manuscript proposes a variable step-size generalized correntropy affine projection algorithm, abbreviated as C-APGMC. However, the aspects of variable step-size (VSS) and correntropy-induced metric (CIM) are not reflected in the abbreviation. Could the authors clarify what the first 'C' stands for? It is recommended to provide relevant explanations to enhance clarity.

2.     How does the selection of different kernel functions affect the correntropy-induced metric? What are the advantages of the Gaussian kernel function chosen in this study compared to other kernel functions? It is recommended that the authors provide further explanations to highlight the rationale behind this choice.

3.     The comparison algorithms used in the complexity analysis should be accompanied by references to clarify their origins. It is recommended that the authors provide appropriate citations to support the inclusion of these algorithms.

4.     There are some issues regarding the consistency and standardization of the mathematical notation, such as in the first sentence of the second paragraph on page 4, and in equations (14) and (15) on page 5. The authors should review and refine these notations to ensure clarity and uniformity.

5.     The formatting of the references is inconsistent. The authors are advised to revise the references to ensure compliance with the journal's guidelines.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In this research, a new variable-step-size generalized maximum correntropy affine projection algorithm (C-APGMC) with sparse regularization term is proposed. Overall, the authors’ objectives are to improve subsequent adaptive filtering applications and robustness especially when operating in high noise density areas and when engaged in sparse system identification. New components of the proposed algorithm are the correlation entropy-induced metric (CIM) and a mean square deviation (MSD)-based variable-step-size. Algorithms for simulating the cancellation of echoes are presented and the effectiveness is proven through further validation when compared to other existing algorithms. I have some recommendations as below.

 

The authors argue that this comes out to be faster with less computational complexity as compared to related algorithms. However, having a balance of computational costs of key operations such as diagonal matrix computation thrown in may help to determine the applicability of the algorithm.

The values of α, β, σ, and t have not been analyzed thoroughly to show the versatility for different kinds of data or indeed different conditions. To increase the sample study’s robustness, a sensitivity analysis of broader parameter changes is recommended.

The echo cancellation experiments are confined to certain situations. There are still aspects that would reveal more about the algorithm performance (Gaussian and impulse noise), specifically, the scenario that is with an extended echo path and with multi-talker noise interference.

A key aspect should be the inclusion of the systematic methods of adjusting the major important parameters, with the use of such techniques, as the grid search or adaptive approaches, to ensure environment adaptability.

Repeat tests on different noise types: colored noise, or even real-world recordings, to add further weight to the results.

Altogether, the paper presents many important contributions However, I think that specifying when the algorithm could not work effectively or might worsen the results (that has not been discussed in the paper or the introduction to the paper) would give a more complete point of view.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper presents a variable-step-size generalized maximum correntropy affine projection algorithm. The following concerns need to be addressed.

1.      It would be helpful to draw a graph corresponding to Table 2 that can visualize how they scale.

2.      It would be good to exemplify the complexities in Table 2 for practical parameters.

3.      The reference numbers of the algorithms can be specified within Table 2.

4.      The Vec method needs to be defined more clearly.

5.      Algorithm 1 would be better if properly indented.

6.      Unnecessary words such as “calculate” and “compute” can be omitted from Algorithm 1.

7.      It would be good to add an example for Algorithm 1.

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The paper introduces a novel adaptive filtering algorithm designed to enhance filtering performance in dynamic and complex environments. It incorporates a correlated entropy-inducing metric and a variable-step-size mechanism based on the mean square deviation criterion. The performance of the algorithm was assessed using computer simulations and for system identification and acoustic echo cancellation tasks under various noise/interference disturbances.

The paper is well structured, and the key contributions highlighted (integration of the correlated entropy-inducing metric to improve zero-attraction for smaller coefficients).

Comments:

Introduction

L46-48 "However, the development of modern technology has led to the increasing sparsity of echo paths, and the above traditional algorithms can lead to performance degradation in specific applications due to the difficulty of accurately capturing a small number of important parameters in the system [22]" - very general statement - what is the intended application area? What is the relation of technology development and sparsity of echo paths? The motivation is not clear. (Multipath signal propagation is related to the environment properties than just technolgy. However, indeed, we use more and more advanced systems that can exploit the multipath signal propagation. - Illustrative example would make it clearer for the readers.)

Simulation results

The selection of simulated examples has not been clearly justified and documented. While the paper demonstrates the algorithm’s effectiveness in echo cancellation and system identification scenarios, it could benefit from presentation of additional real-world application examples. This would provide a broader perspective on the algorithm’s versatility and practical impact, not just the results showing the performance for some examples (how can we assess the properties of the algorithm just on the simulated examples? How multipath was modelled in echo cancellation scenario? Was it just SNR or also a filter with multiple delay components? Was the response from Fig. 9 the only one used in the simulations? What about the influence of the delay spread?). Also, the explanation of the experimental setup in terms of the signal setup is not clear (some block diagrams illustrating the construction of signals for smooth and non-stationary environment models would make it clearer to understand the key assumptions made during the experiments).

Conclusion

This section would benefit form outlining potential future research directions and improvements (critical evaluation - is it better than existing algorithms in all aspects/application scenarios - are there any limitations?).

Minor comments:

outperforms the many existing -> outperforms many existing

Although the language does not limit the understanding of the paper, thorough proofreading is recommended.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The concerns have been addressed.

Author Response

Okay, thanks again for your advice and affirmation of the article.

Reviewer 4 Report

Comments and Suggestions for Authors

The Authors have addressed all the issues raised in the previous round of reviews, thank you.

Some additional minor recommendations for further paper improvement:

 Table 2. Computational complexity analysis of several algorithm.  -> algorithms (plural)

Also I would recommend to make this title more specific, i.e. Computational complexity analysis of the proposed and reference algorithms (or in a similar way).

 

Figure 1 and Figure 2 - "for increasing values of k. " -> for increasing number of filter taps k. (more specific and easier to follow, without the need to search in the text what k parameter dentoes)

Line 284 full stop instead of comma at the end of the line, Line 303 full stop missing - please check the punctuation in the entire manuscript.

 

Lines 295-296 "the convergence speed of the algorithm can be assessed by observing whether the curve representing the algorithm can drop to the lowest quickly"

not clear - to the lowest what?

 

Author Response

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Author Response File: Author Response.docx