-->PONE-D-25-56680-->-->Scalable RIS-aided Hybrid Beamforming for mmWave Systems enables Multiple Sub-array Architectures: A Geometric Mean Approach-->-->PLOS One

Dear Dr. Nguyen Thanh,

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Academic Editor

PLOS One

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Additional Editor Comments:

Thank you for submitting your manuscript on RIS-aided mmWave hybrid beamforming with overlapped subarray architecture. The paper addresses a timely topic and proposes a technically sound optimization framework combining geometric mean rate maximization, block coordinate descent, and Riemannian manifold-based hybrid decomposition. The reviewers acknowledge the mathematical correctness of the approach and the promising numerical gains over existing methods.

However, reviewers have raised several substantial concerns regarding motivation, novelty clarification, contextualization with recent literature, fairness interpretation, algorithmic clarity, and experimental validation. These issues must be addressed thoroughly before the manuscript can be reconsidered for publication. A major revision is therefore required.

Below, we summarize the required revisions by theme. You are expected to respond point-by-point to all reviewer comments in a detailed rebuttal and revise the manuscript accordingly.

1. Motivation and Fairness Justification of the Geometric Mean Objective: A central concern raised by both reviewers is that the choice of geometric mean (GM) rate maximization is insufficiently motivated. You must clearly explain what specific fairness or reliability problem GM rate addresses in RIS-aided hybrid beamforming systems that conventional sum-rate or proportional-fair objectives do not.

2. Novelty Clarification and Contributions: While the contribution list is extensive, it lacks clarity regarding what is fundamentally new versus incremental. Please rewrite the contribution list so that each item reflects a distinct technical innovation, rather than a procedural step.

3. Related Work and Missing Literature (Including AI-Based Methods): The Introduction and related work sections are currently incomplete. Please include recent RIS literature, including but not limited to:

Basar et al., IEEE Access, 2019, Yildirim et al., IEEE TCOM, 2020, Ghavidel Aghdam et al., IEEEMECOM, 2024, Tang et al., IEEE TCOM, 2022, Recent RIS statistical and path-loss modeling works (e.g., indoor/outdoor, mmWave)

Expand the discussion on channel modeling and path-loss assumptions, which are critical in RIS systems. Clearly justify the adopted model and parameters with references.

Importantly, the manuscript must discuss AI-based and reinforcement-learning-based RIS and hybrid beamforming approaches, which are now major competing methodologies.

4. Computational Complexity and Convergence Claims: Claims of improved efficiency and convergence must be better substantiated. Provide a computational complexity analysis in Big- notation and/or in terms of dominant multiplications/additions.

5. Practical Relevance and Deployment Considerations: The manuscript motivates OSA and low-resolution RIS phases but lacks concrete system-level interpretation.

6. Notation, Organization, and English Quality

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Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. -->

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Partly

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-->2. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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-->3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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-->5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: The paper studies a reconfigurable intelligent surface aided downlink with hybrid beamforming under an overlapped sub array architecture, and it maximizes the geometric mean of user rates by alternating between a fully digital surrogate precoder and RIS phases, while enforcing unit modulus and OSA connectivity. The method uses a pseudoinverse based warm start for precoder, closed form RIS updates, and a normalized least squares update followed by Riemannian conjugate gradient steps. I have the following major comments:

1. The introduction lacks some coherence. Please solidify. Moreover, there are many previous related RIS works such as [REF01,REF02]. Kindly include.

2. Please discuss the novelty behind the optimization of the linear transmit beamformers and the RIS reflecting coefficients.

3. The choice of geometric mean of rates is not well motivated. In particular, the objective is to maximize $\left(\prod_{k=1}^K R_k\right) \quad$ with $R_k=\log _2\left(1+\mathrm{SINR}_k\right)$ in (12). Why is the geometric mean taken over the rates and not over $1+ \mathrm{SINR}_k$ ? The objective $\sum_k \log R_k$ weights users through $\log \log \left(1+\mathrm{SINR}_k\right)$, which compresses differences more than $\sum_k \log \left(1+\mathrm{SINR}_k\right)$. Explain this choice better aligns with your fairness target than the standard proportional fairness form or other types of fairness objectives.

4. Explain how discrete phases are enforced consistently across both blocks and how per iteration the discrete phases are activated.

5. In (14), please provide the exact inequality or tangent majorizer that turns $\sum_k \log R_k$ into this weighted sum at each step that can guarantee all regularity conditions.

6. Discuss the relation between the surrogate objective and fairness across users. In particular, Fig. 4 to Fig. 7 plot the GM Rate. Since GM can remain high even when one user is small, it would be useful to add a plot of the worst user rate and the median user rate for the same simulation to confirm that your GM design indeed lifts the weakest user relative to FC and NOSA.

7. The computational complexity should be analyzed in terms of number of additions and multiplications or in terms of big-Oh notation.

8. Please explain whether the proposed algorithm gives the local or global optimum, even though there is a discussion on no guarantee of global optimality.

9. In Fig. 4(b), how can the GM rate of Q = 4 perform better than that of 16 and infinity ? Perhaps you may need to average over more Monte Carlo simulations.

10. The CSI error model and Fig. 7 are unclear. You define NCPE in (34) but the $x$ axis uses NMSE in dB and the caption says imperfect channel estimation, which is confusing.

References

[REF01] “Multi-Functional RIS for a Multi-Functional System: Integrating Sensing, Communication, and Wireless Power Transfer,” in IEEE Network, doi: 10.1109/MNET.2024.3482571

[REF02] “RIS-Enabled Integrated Sensing and Communication for 6G Systems,” 2024 IEEE Wireless Communications and Networking Conference (WCNC), Dubai, United Arab Emirates, 2024, pp. 1-6, doi: 10.1109/WCNC57260.2024.10571090

Reviewer #2: This manuscript studies an RIS-aided mmWave hybrid beamforming system that adopts an overlapped subarray architecture at the base station to improve spatial flexibility and hardware efficiency. The authors formulate a geometric mean rate maximization problem and develop a two-step BCD framework to optimize a fully digital equivalent precoder together with the RIS reflection phases. A Riemannian manifold-based factorization is applied to decompose the fully digital solution into realizable analog and digital parts under OSA constraints. The proposed initialization and optimization strategy improves convergence and achieves an 18.18 percent objective gain over previous methods. Simulation results show that 3-bit phase control is sufficient to approach continuous phase performance and that OSA can approach the performance of fully connected structures.

However, several issues still need to be resolved in the following:

1. The introduction explains the advantages of RIS and OSA architectures, but the manuscript does not clearly identify the specific fairness or reliability problem that geometric mean maximization uniquely addresses. Since GM rate optimization is the key point to your formulation, this manuscript needs a more concrete description of when and why the GM rate provides a necessary improvement over conventional sum rate objectives.

Please clarify the fairness-related performance gap observed in existing RIS hybrid beamforming methods and provide a concrete scenario, such as blockage-prone or cell-edge users, where GM rate offers distinct advantages.

2. The contribution list is long but does not clearly emphasize what is fundamentally new versus what is incremental. Some contributions are descriptive rather than conceptual.

(1) Please refine the contribution list so that each point states a unique technical advancement rather than a procedural step.

(2) Please explicitly identify what part of the algorithm or framework is new relative to the conference version referenced in the manuscript.

3. The Introduction section covers conventional optimization approaches but does not discuss AI-based precoding or reinforcement learning-based RIS control, which have become major competing directions in this field. Avoiding these methods creates a gap in the contextualization of your contribution, because AI techniques are often applied to the same type of non-convex joint beamforming problems.

(1) Please add a subsection in the introduction or related work that reviews AI-based hybrid beamforming and RIS optimization frameworks, including deep reinforcement learning approaches.

This discussion should highlight the advantages and disadvantages (or limitations) of AI methods relative to your fully model-based optimization framework.

(2) Please include a comparison table summarizing classical optimization, your proposed method, and AI-based methods, highlighting differences in complexity, interpretability, data requirements, and scalability.

(3) Please cite and compare with the following work in your Introduction and Performance Evaluation (experiments):

P. -H. Chou, B. -R. Zheng, W. -J. Huang, W. Saad, Y. Tsao, and R. Y. Chang, "Deep Reinforcement Learning-Based Precoding for Multi-RIS-Aided Multiuser Downlink Systems With Practical Phase Shift," in IEEE Wireless Communications Letters, vol. 14, no. 1, pp. 23-27, Jan. 2025, doi: 10.1109/LWC.2024.3482720.

Since your system involves a single RIS, it is a simpler configuration than a multi-RIS system in the above work. Therefore, it should be included a comparison of performances, algorithmic complexity, fairness behavior, and practicality.

4. The two-step BCD procedure, the RIS phase update, and the Riemannian manifold factorization are mathematically correct but difficult for readers to follow on first reading. Several steps involve complex transformations that would benefit from intuition and a structural overview.

(1) Please provide a high-level flow diagram summarizing the full optimization pipeline, showing the interaction between Q updates, RIS phase updates, and the hybrid decomposition stage.

(2) Please add brief intuitive explanations after major derivation steps to help us understand why each approximation or update rule is mathematically and conceptually reasonable.

5. Since the manuscript claims improved efficiency and faster convergence, such evidence should be quantified.

(1) Please include a runtime or algorithmic complexity comparison to support the claims of computational efficiency.

(2) Please add two additional baselines, including WMMSE-based hybrid beamforming and a DDPG-based RIS control method, to contextualize the performance gains of your method.

6. The manuscript motivates OSA hardware feasibility and low phase resolution, but the practical context of these choices is not illustrated. Since RIS and hybrid architectures face real-world constraints, the relevance of the proposed method would be clearer with concrete examples.

(1) Please describe one or two realistic deployment scenarios where OSA-based RIS hybrid beamforming is beneficial, such as indoor hotspot expansion, factory automation, or blockage mitigation.

(2) Please briefly discuss control overhead, calibration, or signaling requirements for RIS phase updates and OSA analog precoding.

7. Several notation-related issues in the manuscript affect readability.

(1) Please prepare a notation table placed either at the end of the Introduction or at the beginning of the System Model.

The table should include:

(a) All variables, vectors, matrices, and sets

(b) A concise description of their roles

(c) Dimensions where appropriate

(d) Constraints (unit modulus, discrete phase set, manifold space, etc.)

(e) Iteration indices with a clear explanation of which algorithmic stage they belong to

(2) Please unify the superscript and subscript conventions so that iteration indices, user indices, antenna indices, and RIS indices follow a consistent ordering and formatting.

(3) Please ensure each symbol is explicitly defined at its first occurrence and that symbols reused for different purposes (such as μ variations) are renamed or clarified to avoid ambiguity.

8. Comments on the Quality of English.

(1) Sentences are often too long and contain multiple nested clauses, which makes several technical descriptions difficult to follow.

Please break long sentences into shorter units and simplify clause structure to improve clarity, especially in Sections 2 and 3.

(2) Some symbols and technical terms appear before being clearly defined, and several pronouns (“this,” “that,” “these”) refer to ambiguous antecedents.

Please ensure that each variable is explicitly defined at first use and replace vague pronouns with specific referents to reduce ambiguity.

(3) Minor grammatical inconsistencies appear throughout the manuscript, including article usage, subject-verb agreement, and inconsistent compound noun formatting (e.g., “fully digital” vs “fully-digital,” “phase shifter” vs “phase-shifter”).

Please perform a careful language pass to correct these recurring issues and maintain consistent technical terminology.

Reviewer #3: This paper investigated a RIS-aided hybrid beamforming system designed for scalable operation in the millimeter wave channel. The authors proposed a framework that jointly optimizes the linear transmit beamformers and the programmable reflecting coefficients of the RIS elements. Generally, the authors have done an interesting work, however, some parts need to be further improved.

Please see the detailed comments in the attached file.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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Attachments

Attachment

Submitted filename: Comments to PONE-D-25-56680.pdf

-->PONE-D-25-56680R1-->-->Scalable RIS-aided Hybrid Beamforming for mmWave Systems enables Multiple Sub-array Architectures: A Geometric Mean Approach-->-->PLOS One

Dear Dr. Nguyen Thanh,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Jun 29 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:-->

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• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

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As the corresponding author, your ORCID iD is verified in the submission system and will appear in the published article. PLOS supports the use of ORCID, and we encourage all coauthors to register for an ORCID iD and use it as well. Please encourage your coauthors to verify their ORCID iD within the submission system before final acceptance, as unverified ORCID iDs will not appear in the published article. Only  the individual author can complete the verification step; PLOS staff cannot  verify ORCID iDs on behalf of authors.

We look forward to receiving your revised manuscript.

Kind regards,

Trong-Minh Hoang

Academic Editor

PLOS One

Journal Requirements:

If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise.

Additional Editor Comments :

Decision: Major revision

The authors should provide more explicit technical explanations in the rebuttal, strengthen the quantitative justification for the geometric mean objective, and clarify the manuscript’s main novelty relative to existing RIS-aided hybrid beamforming methods.

The reviewer also requests broader or better-scoped experimental evaluation, clearer discussion of assumptions and limitations, stronger comparison with analytical and learning-based methods, more rigorous statistical analysis, and full compliance with PLOS data availability requirements.

See the full detailed comments from reviewers.

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Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.-->

Reviewer #1: (No Response)

Reviewer #2: (No Response)

Reviewer #3: All comments have been addressed

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-->2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. -->

Reviewer #1: (No Response)

Reviewer #2: Partly

Reviewer #3: Yes

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-->3. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #1: (No Response)

Reviewer #2: No

Reviewer #3: Yes

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-->4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: (No Response)

Reviewer #2: No

Reviewer #3: No

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-->5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #1: (No Response)

Reviewer #2: Yes

Reviewer #3: Yes

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-->6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: The reviewer has no further comments on the manuscript.

Thank for you addressing my previous comments.

Reviewer #2: Several important issues remain only partially addressed:

1. While the authors have provided responses to most reviewer comments, many replies rely on referencing revised sections (e.g., “added in Section X”) without directly explaining the key technical rationale in the rebuttal.

Please provide concise but explicit explanations in the response letter for the core design choices and technical reasoning, rather than relying solely on manuscript revisions.

2. The motivation for adopting the geometric mean (GM) objective has been improved, but remains primarily qualitative without sufficient quantitative validation.

Please further strengthen the motivation by providing quantitative evidence (e.g., fairness metrics, rate distribution comparisons, or performance gaps) to clearly demonstrate the necessity of GM compared to sum-rate or proportional fairness approaches.

3. Although the contribution list has been rewritten, the distinction between fundamental novelty and incremental improvement is still not sufficiently distinguished from existing methods.

Please explicitly clarify:

(1) What is the primary technical novelty

(2) How it differs from existing RIS-aided hybrid beamforming methods at a methodological level

(3) What unique advantage is achieved beyond standard BCD or manifold-based approaches

4. Several reviewer concerns are addressed by stating that they are “outside the scope” (e.g., dynamic environments, robustness, extended performance metrics), without sufficient supporting discussion.

Please provide at least a brief analytical or conceptual discussion to justify these assumptions and clarify how they impact the applicability and generalizability of the proposed method.

5. The experimental evaluation remains limited, focusing primarily on geometric mean rate and convergence behavior, despite the added discussion.

Please either include additional performance evaluations or clearly limit the scope of the conclusions.

6. The positioning of the proposed method with respect to existing literature can be further strengthened, particularly in terms of deeper comparative analysis with both analytical and learning-based approaches.

Please enhance the discussion to more clearly highlight the advantages and limitations of the proposed framework.

Reviewer #3: The authors have addressed my concerns, please finally check the repeated references, such as [11]-[13] and [15], before uploading the final files.

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If you choose “no”, your identity will remain anonymous but your review may still be made public.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

**********

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-->PONE-D-25-56680R2-->-->Scalable RIS-aided Hybrid Beamforming for mmWave Systems enables Multiple Sub-array Architectures: A Geometric Mean Approach-->-->PLOS One

Dear Dr. Nguyen Thanh,

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The authors are required to strengthen the response letter by providing explicit technical explanations rather than only referring to revised sections; provide stronger quantitative justification for the geometric mean objective; clarify the primary methodological contribution relative to existing RIS-aided hybrid beamforming approaches, including BCD-based, manifold-based, analytical, and learning-based methods; discuss the assumptions and limitations related to dynamic environments, robustness, and extended performance metrics; strengthen the experimental evaluation or narrow the conclusions accordingly; improve the comparative positioning within the literature; and address data availability and reproducibility in accordance with PLOS ONE policy. The authors should also correct repeated references and provide a detailed point-by-point response, a tracked-changes manuscript, and a clean manuscript.

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Scalable RIS-aided Hybrid Beamforming for mmWave Systems enables Multiple Sub-array Architectures: A Geometric Mean Approach

PONE-D-25-56680R3

Dear Dr. Nguyen Thanh,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Trong-Minh Hoang

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PLOS One

Additional Editor Comments (optional):

Date: July 15, 2026

Manuscript ID: PONE-D-25-56680R2

Title: Scalable RIS-aided Hybrid Beamforming for mmWave Systems enables Multiple Sub-array Architectures: A Geometric Mean Approach

Authors: Hoang M. Tran, Tung V. Dinh, Hoa T. Nguyen, Huy T. Nguyen

Dear Dr. Nguyen Thanh and Co-authors,

On behalf of the Editorial Board of PLOS ONE, I am pleased to inform you that your manuscript has been accepted for publication, subject to the submission of final production files as described below.

After careful consideration of your revised manuscript (R2) and your detailed point-by-point response to all reviewer and editor comments, I am satisfied that the raised concerns have been adequately addressed. The revisions demonstrate a meaningful improvement in technical clarity, methodological justification, experimental evaluation, and compliance with PLOS ONE's publication criteria.

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Final clean manuscript (labeled "Manuscript") — no tracked changes, no highlighted text, fully proofread.

Final figure files — high-resolution, meeting PLOS ONE figure specifications (https://journals.plos.org/plosone/s/figures).

Data availability statement — confirming that all simulation parameters, datasets, and/or code sufficient to reproduce the reported results are publicly available or accessible upon reasonable request, in accordance with PLOS ONE data policy.

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Trong-Minh Hoang

Academic Editor

PLOS ONE