Optimization of RIS-Assisted 6G NTN Architectures for High-Mobility UAV Communication Scenarios

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors in this paper develop a framework for the optimization of RIS-assisted NTNs in a highly dynamic environment. The performance of the developed framework is analyzed via simulation. Overall, the topic is interesting. The reviewer has the following comments.

1. More explanations related to the challenges of joint optimization of RIS phase shifts need to be added.
2. The contribution of this paper seems to be unclear. The difference between this work and the existing one needs to be analyzed.
3. The validity that the RIS controller estimates the relative propagation delays of the direct and reflected paths based on real-time location and channel measurements needs to be clarified.
4. The number of equation (13) needs to be improved.
5. The modeling of small-scale fading components needs to be more specific.
6. There are many parameters to be determined in this paper. Some of them were discussed, while some of them were not discussed in the simulation. Please explain in detail how to determine these parameters to demonstrate the performance of the developed framework.
7. More explanations of “The balance between SINR, energy efficiency, and environmental constraints further underscores the need for adaptive RIS deployment strategies tailored to specific environments” need to be added.

Comments on the Quality of English Language

The quality of the English Language needs to be improved. There are some typos in the current version.

Author Response

Dear Reviewer,

We would like to sincerely thank you for your valuable time and constructive feedback on our manuscript titled "Optimization of RIS-Assisted 6G NTN Architectures for High-Mobility UAV Communication Scenarios." We carefully considered all your suggestions and made substantial revisions to improve the clarity, depth, and scientific rigor of our paper. Below, we provide a detailed point-by-point response to each of your comments.

Comment 1:  More explanations related to the challenges of joint optimization of RIS phase shifts need to be added.

Response: Thank you for this valuable suggestion. We have expanded our discussion on the challenges of joint optimization in the revised manuscript. Specifically, we now explain the computational complexity, the unit-modulus constraints, the sensitivity to rapidly varying CSI, and the scalability challenges when dealing with large RIS arrays. The discussion has been added and elaborated in Section 4 to emphasize the practical difficulties and the need for real-time, predictive optimization in the scenarios of high-mobility environments.

Comment 2: The contribution of this paper seems to be unclear. The difference between this work and the existing one needs to be analyzed.

Response: We appreciate this observation. We have now clearly outlined the key novel contributions of our work at the end of the Related Work section. Additionally, we provided a dedicated paragraph highlighting how our approach differs from existing studies by focusing on joint optimization under high-mobility constraints, introducing a Doppler-aware RIS reconfiguration strategy, and providing a scenario-based performance evaluation that was not addressed in prior works.

Comment 3: The validity that the RIS controller estimates the relative propagation delays of the direct and reflected paths based on real-time location and channel measurements needs to be clarified.

Response: Thank you for pointing this out. We have now provided a detailed explanation in Section 3.3 clarifying the feasibility of this assumption. We explained how the deterministic nature of NTN geometries, GPS-based localization, cooperative user feedback, and modern channel sounding techniques enable the RIS controller to estimate relative propagation delays with acceptable accuracy in real time. Supporting references and realistic estimation methods were also added.

Comment 4: The number of equation (13) needs to be improved.

Response: We appreciate this comment. We have now rewritten Equation (13) in a more formal mathematical format, properly using probability notation and including an optional extension using the cumulative distribution function (CDF) for further clarity. This change improves the mathematical soundness and readability of the expression.

Comment 5: The modeling of small-scale fading components needs to be more specific.

Response: Thank you for this insightful suggestion. We have revised Section 3.3 to explicitly specify the small-scale fading models used in our simulations. We clarified that Rayleigh fading is assumed for non-line-of-sight scenarios, while Rician fading is more appropriate for line-of-sight cases. We also provided the Rician fading expression and explained our decision to use Rayleigh fading as the baseline to ensure general applicability across scenarios.

Comment 6: There are many parameters to be determined in this paper. Some of them were discussed, while some of them were not discussed in the simulation. Please explain in detail how to determine these parameters to demonstrate the performance of the developed framework.

Response: Thank you for this important comment. We have now included a detailed explanation at the end of the Simulation Results Section 5, which explains the rationale and selection method for all simulation parameters in detail. We provided scenario-specific values, including shadowing standard deviations and interference power levels, and referenced prior studies to ensure reproducibility. We also clarified how each parameter aligns with realistic NTN deployment constraints.

Comment 7: More explanations of 'The balance between SINR, energy efficiency, and environmental constraints further underscores the need for adaptive RIS deployment strategies tailored to specific environments' need to be added.

Response: We appreciate this request for further elaboration. At the end of Section 5.2, we have expanded our explanation to clarify how increasing the number of RIS elements improves SINR but increases power consumption and processing latency, which may not always be desirable. We explained how environmental factors such as interference, propagation conditions, and deployment constraints influence this balance and why adaptive, scenario-specific RIS configurations are necessary for optimal system performance.

We are grateful for your valuable feedback, which has significantly improved the quality and clarity of our manuscript. We hope that the revised version meets the expectations of the reviewers and the editorial board.

Sincerely,

Muhammad Shoaib Ayub (on the behalf of all co-authors)

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper has an interesting scope in the abstract level that unfortunately delivers less than promises. On the positive side, the number of cited references is sufficient and relevant to the topic. Also, the description of the related work in Section 2 is relatively fluent. Sections 3-5 raise quite a lot of technical questions (see more details below) and have also some organization/outlook issues to be resolved. Overall, the chosen research topic is timely and relevant as such but has limited novelty and contribution.

 

Main comments

Structure: On the surface the overall construction of the manuscript seems decent with respect to sections and their content and length. The abstract is formally OK but promises comprehensive analyses and simulation results whereas the paper covers these in quite generic and superficial manner. Introduction and Section 2 describe the background & scope, prior related work, and open research problems in a satisfactory way. Sections 3-5 provide the main technical content. Some of the sub-sections are very brief and lack explanations and references although there are plenty of examples of similar derivations in the literature. Simulation results in Section 5 would require more detailed discussion. It seems that the discussion of performance tradeoffs and trends in Sections 5.1. and 5.2.  goes beyond what is shown in Fig. 3. If so, such results should be added or communicated better within the text. The total length of the paper is reasonable but would be extended somewhat because of the modification requests.

Clarity: Graphical illustrations are readable. However, as stated above in ‘Structure’ and more under ‘Scientific soundness’, the general layout and storytelling are not clear enough in many places. In addition, there are some clarity-related remarks under the title ‘Minor comments’ below.

Scientific soundness: The overall research problem and associated system model is complex and mathematically challenging. The main complaint is that storytelling is cursory at places and does not disclose all required details of the models, parameters, and assumptions clearly enough. There are too many shortcuts taken in the derivations and sections feel disjointed. Authors’ own original ideas and theoretical contributions are modest. The type of the assumed RIS should be defined as it has direct implications to system model & requirements, assumptions, complexity, and performance. Table 2 includes some scenario/channel model-dependent parameters that should be specified or referenced (such as standard deviations). Generally, mathematical derivations and simulation assumptions should be detailed enough to allow the reader to replicate them. In Fig. 3 the general trend with all the metrics is such that the variation of RIS element volume is not much in any scenario at the average (almost flat lines). Outage probability seems to remain very high w.r.t. generally targeted values. At least if plotted as a function of SINR (with fixed M) the outage probability curve should go closer to zero. Many of the conclusions drawn in Section 5.2. deviate from the results shown in Fig. 3. This is confusing and should be carefully elaborated.

 

Minor comments

These are more detailed comments, remarks and examples. Many of these point out to structural/editorial revision needs to improve general outlook of the manuscript, such as typographical appearance, consistency and readability issues.

• Page 1, Abstract, line number 1: Using acronym RIS in plural form is a problem when also singular meaning is needed at places. Instead, defining RIS in singular would allow to use RISs in plural to make clear distinction between singular and plural use case.
• Page 2, Introduction, line number 33: … it … -> … they …
• Page 3, Introduction, line number 70: Avoid unnecessary capitalization of words within a sentence.
• Page 3, Introduction, line number 72: It is better to use consistent tense at least within parallel expressions (in this case bullet points, others are in present tense).
• Page 5, Section 3.1., line number 150 onwards: Formulate these definitions and other text as complete sentences and paragraphs with correct indentation if they are embedded within the regular text. This applies to equations as well. They are parts of the sentences and paragraphs around them and should have correct lead words, punctuation and ending. After (1), for example, the line beginning with the word ‘where’ should not have indentation and lines 170-171 should be within the same phrase as well without line breaks.
• Page 8, Section 4.1.1., equation between line numbers 224 and 225 (and onwards): Be consistent with equation numbering. It also helps to refer to them in the text.
• Page 8, Section 4.1.1., line number 225: Delete the full-stop.
• Pages 17-19, References: Be systematic and consistent with entry details according to the periodical guidelines. For example, now some authors have full last and first names presented but some have only initials of the first names presented.

Author Response

Dear Reviewer,

We sincerely thank you for your thorough review and valuable feedback on our manuscript. Your comments have greatly contributed to improving the clarity, depth, and scientific rigor of our work. We have carefully revised the manuscript to address each of your concerns in detail and the corresponding revisions highlighted in the re-submitted files. Below, we provide a consolidated response to your overall comments.

Commentà Structure: On the surface the overall construction of the manuscript seems decent with respect to sections and their content and length. The abstract is formally OK but promises comprehensive analyses and simulation results whereas the paper covers these in quite generic and superficial manner. Introduction and Section 2 describe the background & scope, prior related work, and open research problems in a satisfactory way. Sections 3-5 provide the main technical content. Some of the sub-sections are very brief and lack explanations and references although there are plenty of examples of similar derivations in the literature. Simulation results in Section 5 would require more detailed discussion. It seems that the discussion of performance tradeoffs and trends in Sections 5.1. and 5.2.  goes beyond what is shown in Fig. 3. If so, such results should be added or communicated better within the text. The total length of the paper is reasonable but would be extended somewhat because of the modification requests.

Response: We thank the reviewer for this comprehensive evaluation. In the revised manuscript, we have:

• Expanded the mathematical derivations with intermediate steps.
• Defined the RIS type (passive, reflective, narrowband, discrete phase shift) in Section 3.1.
• Added all system assumptions and deployment constraints.
• Improved the storytelling by making the sections more logically connected and ensuring the models, assumptions, and parameter choices are now fully transparent and reproducible.

Commentà Clarity: Graphical illustrations are readable. However, as stated above in ‘Structure’ and more under ‘Scientific soundness’, the general layout and storytelling are not clear enough in many places. In addition, there are some clarity-related remarks under the title ‘Minor comments’ below.

Response: We have carefully revised the manuscript to improve clarity and completeness. Specific improvements include:

• Clearer definitions, more comprehensive explanations, and explicit assumptions provided in the system model section.
• The type of RIS has now been explicitly defined as a passive, reflective, narrowband RIS with discrete phase shifts, which is essential for system complexity and performance evaluation.
• We have enhanced simulation setup details to ensure the results are fully traceable and reproducible.

Commentà Scientific soundness: The overall research problem and associated system model is complex and mathematically challenging. The main complaint is that storytelling is cursory at places and does not disclose all required details of the models, parameters, and assumptions clearly enough. There are too many shortcuts taken in the derivations and sections feel disjointed. Authors’ own original ideas and theoretical contributions are modest. The type of the assumed RIS should be defined as it has direct implications to system model & requirements, assumptions, complexity, and performance. Table 2 includes some scenario/channel model-dependent parameters that should be specified or referenced (such as standard deviations). Generally, mathematical derivations and simulation assumptions should be detailed enough to allow the reader to replicate them. In Fig. 3 the general trend with all the metrics is such that the variation of RIS element volume is not much in any scenario at the average (almost flat lines). Outage probability seems to remain very high w.r.t. generally targeted values. At least if plotted as a function of SINR (with fixed M) the outage probability curve should go closer to zero. Many of the conclusions drawn in Section 5.2. deviate from the results shown in Fig. 3. This is confusing and should be carefully elaborated.

Response: Thank you for raising this crucial point. In response:

• We added a detailed explanation in the Section 3.1 and 3.3 where all system assumptions, including synchronization, CSI acquisition, interference models, and mobility patterns, are clearly described.
• Detailed parameter selection and justification are now provided in the Section 5.
• Mathematical derivations, especially in the RIS phase shift optimization section, have been expanded with intermediate steps to ensure mathematical rigor and transparency.
• We clarified our original contributions and positioned our work within the existing literature more clearly by highlighting our Doppler-aware, predictive RIS configuration and joint optimization framework for high-mobility NTN scenarios areas that are underexplored in current research.
• We also emphasize that this work lays the foundation for more advanced real-time and machine learning-based RIS control strategies in future NTN systems.
• We provided a detailed discussion on the relatively flat trends in Fig. 3, (e.g., SINR and throughput) appear flat, especially beyond M=30, this is due to diminishing returns in beamforming gain when phase coherence is affected by Doppler-induced misalignment or environmental interference. Furthermore, latency and energy consumption increase with M, causing a trade-off even when SINR appears stable. These trade-offs explain why optimal performance is not always at the highest M and motivate the scenario-specific tuning discussed in Section 5.2.
• The relatively high outage probability values observed in some scenarios are due to a combination of aggressive interference modeling, short channel coherence time, and partial RIS alignment under Doppler effects. For example, in emergency and urban environments, we use high interference levels (mean: -80 dBm, standard deviation: 6–8 dB) to reflect dense spectrum usage, which degrades SINR despite RIS phase optimization. Additionally, mobility-induced Doppler shifts impact CSI accuracy, leading to sub-optimal phase configurations and less coherent signal combining. As a result, the effective SINR distributions remain wide, pushing outage probabilities above 10% in critical cases. These outcomes align with real-world conditions under imperfect control but can be improved with refined Doppler compensation and low-latency RIS updates.

Minor comments: These are more detailed comments, remarks and examples. Many of these point out to structural/editorial revision needs to improve general outlook of the manuscript, such as typographical appearance, consistency and readability issues.

Comment 1: Page 1, Abstract, line number 1: Using acronym RIS in plural form is a problem when also singular meaning is needed at places. Instead, defining RIS in singular would allow using RISs in plural to make clear distinction between singular and plural use case.

Response: Thank you for this careful observation. We have revised the manuscript to define RIS in singular form at first introduction and consistently use “RISs” for the plural case throughout the paper to ensure grammatical clarity and distinction between singular and plural forms.

Comment 2: Page 2, Introduction, line number 33: “… it …” -> “… they …”

Response: This correction has been made as suggested. The pronoun has been updated from “it” to “they” to properly refer to the plural subject in the sentence.

Comment 3: Page 3, Introduction, line number 70: Avoid unnecessary capitalization of words within a sentence.

Response: We have carefully reviewed the entire manuscript and removed unnecessary capitalizations within sentences, including the correction at line 70 and other similar instances to ensure consistency and typographical accuracy.

Comment 4: Page 3, Introduction, line number 72: It is better to use consistent tense at least within parallel expressions (in this case bullet points, others are in present tense).

Response: Thank you for the helpful suggestion. We have revised the bullet points to ensure consistent use of present tense throughout all parallel expressions in the Introduction and other relevant sections.

Comment 5: Page 5, Section 3.1., line number 150 onwards: Formulate these definitions and other text as complete sentences and paragraphs with correct indentation if they are embedded within the regular text. This applies to equations as well. They are parts of the sentences and paragraphs around them and should have correct lead words, punctuation and ending. After (1), for example, the line beginning with the word ‘where’ should not have indentation and lines 170-171 should be within the same phrase as well without line breaks.

Response: We have thoroughly revised Section 3.1 and all subsequent sections to ensure:

• Definitions and explanations are now written as complete sentences and properly structured paragraphs.
• Equations are smoothly embedded within the text with appropriate lead-in phrases, punctuation, and grammatical flow.
• Instances such as the line beginning with "where" after Equation (1) have been corrected by removing unnecessary indentation and line breaks.
• Similar adjustments were made throughout the manuscript for consistency.

Comment 6: Page 8, Section 4.1.1., equation between line numbers 224 and 225 (and onwards): Be consistent with equation numbering. It also helps to refer to them in the text.

Response: We have carefully checked the entire manuscript for equation numbering consistency.
All equations are now:

• Properly numbered in sequential order.
• Consistently referred to within the text using their assigned equation numbers.

Comment 7: Page 8, Section 4.1.1., line number 225: Delete the full-stop.

Response: The unnecessary full-stop has been removed as suggested.

Comment 8: Pages 17-19, References: Be systematic and consistent with entry details according to the periodical guidelines. For example, now some authors have full last and first names presented but some have only initials of the first names presented.

Response: We have carefully revised the entire reference list to ensure:

• Consistent formatting in line with the journal’s guidelines.
• Uniform presentation of author names (initials of first names and full last names).
• Standardized formatting for journal titles, volume numbers, page ranges, and year of publication.

We trust that the revised manuscript now presents a comprehensive, scientifically sound, and reproducible study aligned with your expectations.

Thank you again for your constructive feedback.

Sincerely,

Muhammad Shoaib Ayub (on the behalf of all co-authors)

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In this paper, authors studied optimization of RIS-assisted 6G NTN architecture for high-mobility UAV communication. Basically, the motivation of the paper is good and the proposed scheme is novel. Also, authors evaluated the performance of the proposed scheme through extensive simulations with various settings and scenarios. Moreover, the organization of the paper is good.

To improve the paper, the below minor parts are recommended to be updated by authors.

• Authors can improve the visibility of some figure. For example, Figure 2 can be improved with more representations.
• Authors can check if there are minor typos and unclear sentences in the manuscript.

Author Response

Dear Reviewer,

We sincerely appreciate your positive evaluation of our manuscript and your recognition of the novelty, motivation, and organization of our work. We are grateful for your constructive suggestions, which have helped us further improve the clarity and presentation of the paper. Below are our detailed responses to your comments.

Comments: In this paper, authors studied optimization of RIS-assisted 6G NTN architecture for high-mobility UAV communication. Basically, the motivation of the paper is good and the proposed scheme is novel. Also, authors evaluated the performance of the proposed scheme through extensive simulations with various settings and scenarios. Moreover, the organization of the paper is good.

To improve the paper, the below minor parts are recommended to be updated by authors. Authors can improve the visibility of some figure. For example, Figure 2 can be improved with more representations. Authors can check if there are minor typos and unclear sentences in the manuscript.

Response: Thank you for this valuable suggestion. We have carefully revised Figure 2 to enhance its visual clarity and improve its representational detail. We also have carefully proofread the entire manuscript to correct minor typographical errors and improve sentence clarity throughout the text. Additionally, we aligned the tense, refined the language for consistency, and ensured that all technical descriptions are precise and unambiguous.

Once again, we thank you for your supportive and constructive review. Your suggestions have been instrumental in improving the final version of our manuscript.

Sincerely,

Muhammad Shoaib Ayub (on the behalf of all co-authors)

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

In the revised version, the authors have properly addressed most of my comments. The reviewer still has two minor comments.

1. The advantage of utilizing the RIS technology in UAV communications needs to be further highlighted to further demonstrate the motivation of this work.
2. In the future, intelligent multi-modal sensing-communication integration [R1, R2] seems to be a feasible path that can facilitate the development of aerial networks with RIS. The authors are recommended to discuss how to incorporate intelligent multi-modal sensing-communication integration into the development of aerial networks with RIS based on the proposed method.

[R1]  "Real-Time Digital Twins: Vision and Research Directions for 6G and Beyond," IEEE Communications Magazine, vol. 61, no. 11, pp. 128-134, Nov. 2023

[R2] “A LiDAR-aided channel model for vehicular intelligent sensing-communication integration,” IEEE Transactions on Intelligent Transportation Systems, vol. 25, no. 12, pp. 20105-20119, Dec. 2024.

Author Response

Dear Reviewer,

We sincerely appreciate your positive feedback on our revised manuscript and your acknowledgment that most of your previous comments have been properly addressed. We are grateful for your additional insightful suggestions, which have helped us further improve the quality and depth of the manuscript.

• We have now further emphasized the unique advantages of integrating RIS technology into UAV communications in the Introduction sections.
• We have now incorporated a new discussion in the Conclusion section regarding the integration of intelligent multi-modal sensing and communication, as suggested. We also referenced [R1] and [R2] to support the feasibility of this future path.

We believe this addition aligns well with the evolving trends in 6G and supports the future potential of our proposed methodology when combined with intelligent sensing-communication architectures.

Once again, we thank you for your constructive and insightful feedback, which has greatly enriched our work.

Sincerely,

Muhammad Shoaib Ayub (on behalf of all co-authors)

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

I would like to thank the authors for the detailed response and revision upon my first-round review comments. Most of the comments have been addressed adequately as requested. However, there are still some issues I would like to point out (either comments not completed properly/completely or not interpreted the way I meant).

 

Main comments

Scientific soundness: Table 2 includes some scenario/channel model-dependent parameters that should be specified or referenced (such as standard deviations). Generally, mathematical derivations and simulation assumptions should be detailed enough to allow the reader to replicate them. In Fig. 3 the general trend with all the metrics is such that the variation of RIS element volume is not much in any scenario at the average (almost flat lines). Outage probability seems to remain very high w.r.t. generally targeted values. At least if plotted as a function of SINR (with fixed M) the outage probability curve should go closer to zero. Many of the conclusions drawn in Section 5.2. deviate from the results shown in Fig. 3. This is confusing and should be carefully elaborated. [Original comment]

The original comment is not completely addressed in the revision. Regarding scenarios, there should be clear parameter sets for urban, rural, highway, indoor, and emergency cases to see how they are different from each other. Parameters could, e.g., be tabulated for easy comparison (or at least referenced to see where they have been taken). Regarding the outage probability I would like to remind that 10% rules out many of the practical use cases and all true reliability-requiring applications. [New comment]

 

Minor comments

Most of the original comments have been addressed. I would like to point out some minor issues that should be taken care latest in the final editing phase. Many of these are outlook and typographical in nature.

• Page 3, Introduction, line number 72: It is better to use consistent tense at least within parallel expressions (in this case bullet points, others are in present tense). [Original comment]

Second bullet point is still in past tense: evaluated -> evaluate [New comment]

• Page 5, Section 3.1., line number 150 onwards: Formulate these definitions and other text as complete sentences and paragraphs with correct indentation if they are embedded within the regular text. This applies to equations as well. They are parts of the sentences and paragraphs around them and should have correct lead words, punctuation and ending. After (1), for example, the line beginning with the word ‘where’ should not have indentation and lines 170-171 should be within the same phrase as well without line breaks. [Original comment]

This applies to revised/added text as well. See indentation on lines 210, 221 and 387. [New comment]

• Pages 17-19, References: Be systematic and consistent with entry details according to the periodical guidelines. For example, now some authors have full last and first names presented but some have only initials of the first names presented. [Original comment]

Deviation in author notification seems to remain in the revised manuscript although claimed to be addressed. [New comment]

• Section 5, line numbers 410-427: Separate bolded words in the bulleted parameter list. [New comment]

Author Response

Dear Reviewer,

We would like to sincerely thank you for your continued thorough review and for carefully assessing the revisions. Your detailed feedback has been extremely helpful in improving the scientific consistency, presentation quality, and completeness of our manuscript. We have carefully addressed each of your major and minor comments, as detailed below.

Major Comment:

Comment:         

The original comment is not completely addressed in the revision. Regarding scenarios, there should be clear parameter sets for urban, rural, highway, indoor, and emergency cases to see how they are different from each other. Parameters could, e.g., be tabulated for easy comparison (or at least referenced to see where they have been taken). Regarding the outage probability I would like to remind that 10% rules out many of the practical use cases and all true reliability-requiring applications.

Response:

• Thank you for emphasizing the importance of clearly specifying the scenario-specific parameter sets. In the revised manuscript, we have clarified that all scenario-specific parameters were selected in a manner consistent with the principles outlined in 3GPP TR 38.821, ensuring that our simulation assumptions remain traceable to industry standards.
• Regarding the outage probability concern, we have now explicitly addressed the outage probability issue in the Simulation Results section particularly in outage probability part. The revised manuscript acknowledges that the observed outage probability levels in all evaluated scenarios remain above 10%, which is not sufficient for ultra-reliable low-latency communication (URLLC) or other mission-critical applications.

We believe these revisions directly and transparently address your concerns while maintaining scientific integrity.

Minor Comments:

1. Comment:

Page 3, Introduction, line number 72: Consistent tense in bullet points. Second bullet point is still in past tense: evaluated → evaluate.

Response:

Thank you for carefully checking this detail. We have now corrected the tense in the second bullet point. All bullet points now consistently use present tense.

2. Comment:

Page 5, Section 3.1., line number 150 onwards: Definitions and equations should be integrated as complete sentences with correct indentation and flow. This also applies to revised/added text. See indentation on lines 210, 221, and 387.

Response:

We appreciate this correction. We have carefully reviewed the entire manuscript, indentation errors on lines 210, 221, and 387 have been corrected, and all subsequent equation environments have been consistently formatted with appropriate punctuation.

3. 3. Comment: Pages 17–19, References: Be systematic and consistent with entry details. Deviation in author name formatting remains.

Response:

Thank you for your careful observation. We have now systematically reviewed and corrected all references to ensure full consistency in formatting. Specifically, author names are now presented uniformly using initials for first names and full last names throughout the entire reference list, in accordance with the journal’s style guidelines.

4. Comment:

Section 5, lines 410–427: Separate bolded words in the bulleted parameter list.

Response:

Thank you for this observation. We have now separated the bolded parameter names in the bulleted list in Section 5 as recommended.

We are grateful for your detailed and constructive feedback throughout this process. We believe the manuscript has been significantly improved as a result of your valuable insights, and we hope the current version meets your expectations.

Thank you once again for your time and thoughtful review.

Sincerely,

Muhammad Shoaib Ayub (on behalf of all co-authors)

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

I reviewed the revised manuscript. All my requests have been addressed by authors carefully. I appreciate the valuble efforts of author to improve the paper. 

Author Response

Dear Reviewer,

Thank you for your valuable time and suggestions for our manuscript. We appreciate you accepted all our previous revisions as per your guidance. 

Best regards,

Muhammad Shoaib Ayub (On the behalf of all authors)