Residual-aided CSI-free end-to-end learning for multiuser MIMO

Emmanuel Ampoma Affum; Osumanu Futa; Maxwell Afriyie Oppong; Daniel Owusu Biney

doi:10.1371/journal.pone.0344696

Peer Review History

Original SubmissionDecember 4, 2025
6 Jan 2026 Decision Letter - Daosen Zhai, Editor -->PONE-D-25-64863-->-->Residual-Aided CSI-free End-to-End Learning for Multiuser MIMO-->-->PLOS One Dear Dr. Biney, 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 Feb 20 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.. 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.. 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.. 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:--> A letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'. 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Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at . Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at . Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.... We look forward to receiving your revised manuscript. Kind regards, Daosen Zhai Academic Editor PLOS One Journal Requirements: When submitting your revision, we need you to address these additional requirements. 1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. 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There is no requirement to cite these works unless the editor has indicated otherwise. [Note: HTML markup is below. Please do not edit.] 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 ******** -->2. Has the statistical analysis been performed appropriately and rigorously? --> Reviewer #1: Yes Reviewer #2: Yes ****** -->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.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.-->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.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: Yes ****** -->4. 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: Yes Reviewer #2: Yes ****** -->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: 1. The novelty is not clearly established, as the proposed framework mainly combines existing techniques without clearly identifying a fundamentally new contribution. 2. Several key claims are overstated and insufficiently justified, especially the assertion that residual learning alone leads to a complexity reduction from O(K^3) to O(K log K). 3. The paper lacks theoretical support, with no convergence, stability, or performance analysis explaining why CSI-free detection can approach MMSE-genie bounds. 4. Important implementation details are unclear, particularly the graph construction, attention sparsification, and how the claimed complexity scaling is practically achieved. 5. The experimental evaluation is limited to simulations, with relatively weak baselines and insufficient justification for some reported metrics (e.g., energy and power results). Reviewer #2: This paper proposes a residual-aided CSI-free end-to-end learning framework, effectively addressing key issues in multiuser MIMO with outstanding performance and robustness, providing significant reference for related technical research. There are some issues that need to be addressed, as follows: 1. Supplement comparisons with similar Graph Transformer works post-2023 to strengthen advantages. 2. Experiments cover various simulated channel models but lack test data in real propagation environments. 3. Supplement hardware resource consumption data to support deployment evaluation. 4. Currently, only single-base-station uplink scenarios are verified. It is recommended to extend to typical scenarios to broaden the framework's application coverage. 5. Explore lightweight strategies to reduce resource thresholds for training and deployment. ****** -->6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. 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Revision 1
11 Jan 2026 Author Response Response to Reviewers Manuscript ID: PONE-D-25-64863 Title: Residual-Aided CSI-free End-to-End Learning for Multiuser MIMO Wesincerely thank the Academic Editor and Reviewers for their constructive feedback. We have carefully addressed each comment, and the manuscript has been substantially improved. Below we provide point-by-point responses. Reviewer #1 Reviewer Comment: 1. The novelty is not clearly established, as the proposed framework mainly combines existing techniques without clearly identifying a fundamentally new contribution. Response: Weagree that the novelty statement required clarification. The unique contribution lies in the synergistic integration of sparse graph transformers with iterative residual refinement for CSI-free detection—a combination not previously explored. Unlike OAMP-Net (requires CSI) or DeepRx (black-box CNN), our DU-SOR uses graph priors to condition blind residual updates. Change Made: Added explicit numbered contribution list in Introduction. Added “Dis tinction from Prior Work” paragraph clarifying differences from OAMP-Net, DeepRx, and recent GNNs. Renamed framework to “DU-SOR” throughout. Reviewer Comment: 2. Several key claims are overstated, especially the assertion that resid ual learning alone leads to a complexity reduction from O(Kˆ3) to O(K log K). Response: We have corrected this. The complexity reduction is attributed to the sparse attention mechanism, not residual learning alone. Residual connections improve convergence and gradient flow; the complexity gain comes from limiting attention to k ≈ logN neighbours. Change Made: Added Proposition 1 with formal proof attributing complexity to sparse adjacency matrix. Revised all claims to correctly credit sparse attention. Reviewer Comment: 3. The paper lacks theoretical support, with no convergence, stability, or performance analysis explaining why CSI-free detection can approach MMSE-genie bounds. Response: We have added rigorous theoretical analysis. Change Made: Added Theorem 1 (Convergence of Residual Refinement) based on Banach Fixed Point Theorem with complete proof. Added explanation of spectral normalisation for Lips chitz constraint enforcement. Reviewer Comment: 4. Important implementation details are unclear, particularly the graph construction, attention sparsification, and how the claimed complexity scaling is practically achieved. Response: We have significantly expanded implementation details. Change Made: Added Algorithm 1 with complete pseudocode. Added explicit description of k-NN graph construction. Clarified sparse mask A in attention equation (Eq. 5). Added proof showing how k ≈ logN leads to O(KlogK) complexity. Reviewer Comment: 5. The experimental evaluation is limited to simulations, with rela tively weak baselines and insufficient justification for some reported metrics (e.g., energy and power results). Response: We acknowledge the simulation limitation and have strengthened baselines and metrics. 1 Change Made: Added comparison with post-2023 GNN-Detector [39] in Table 2. Added OAMP-Net column. Specified that power was measured using NVML polling at 10ms intervals rather than TDP estimates. Added statement that all baselines were retrained on identical dataset. Added explicit Limitations subsection acknowledging simulation-only evaluation. Reviewer #2 Reviewer Comment: 1. Supplement comparisons with similar Graph Transformer works post 2023 to strengthen advantages. Response: Added comparisons with Lau et al. (Neurocomputing, 2024) and Wang et al. (IEEE TWC, 2023). Change Made: New citations [39], [40] added. Table 2 now includes GNN-Detector (2024) column showing 18.2ms latency, 4.5GB VRAM, 235W power vs. our 8.6ms, 2.1GB, 150W. Reviewer Comment: 2. Experiments cover various simulated channel models but lack test data in real propagation environments. Response: We acknowledge this limitation. Real-world validation with SDR testbeds is pro posed as future work. Change Made: Added explicit statement in Limitations subsection. Added “Field Trials” as Future Direction item 3. Reviewer Comment: 3. Supplement hardware resource consumption data to support deploy ment evaluation. Response: Hardware metrics are now comprehensively reported. Change Made: Added Table 2 with Inference Latency, VRAM Usage, Peak Power (NVML measured), and FLOPs for all methods. Added ablation showing VRAM increase to 4.2GB without sparse attention. Reviewer Comment: 4. Currently, only single-base-station uplink scenarios are verified. It is recommended to extend to typical scenarios to broaden the framework’s application coverage. Response: Multi-BS extension is proposed as future work. Change Made: Added “Distributed MIMO” as Future Direction item 2, proposing extension to CoMP and Cell-Free Massive MIMO where adjacency matrix represents inter-BS connectivity. Reviewer Comment: 5. Explore lightweight strategies to reduce resource thresholds for train ing and deployment. Response: Lightweight strategies are proposed as future work. Change Made: Added “Lightweight Strategies” as Future Direction item 1, proposing INT8 quantisation and structured pruning for edge deployment. Journal Requirements Reviewer Comment: 1. Please ensure that your manuscript meets PLOS ONE’s style require ments. Response: We have verified compliance with PLOS ONE formatting templates. Change Made: Verified title capitalisation, author affiliations format, figure caption format, and reference style against PLOS ONE templates. 2 Reviewer Comment: 2. PLOS ONE has specific guidelines on code sharing. Response: Code and data will be made fully available. Change Made: Added Data Availability Statement with GitHub repository URL and Zenodo DOI placeholder. Reviewer Comment: 3. When completing the data availability statement, you indicated you will make your data available on acceptance. Response: Data availability statement has been updated. Change Made: Statement now reads: “All data underlying the findings in this study, along with the source code required to reproduce the results, are fully available without restriction.” Repository links provided. Summary of Major Changes 1. Added formal theoretical analysis: Theorem 1 (convergence) and Proposition 1 (complexity) 2. Added Algorithm 1 with complete pseudocode 3. Added Table 2 with measured hardware metrics (NVML) 4. Added post-2023 GNN baseline comparisons [39], [40] 5. Added explicit Contributions list and “Distinction from Prior Work” paragraph 6. Added Limitations and Future Directions subsections 7. Added Data Availability Statement 8. Corrected complexity claims to attribute scaling to sparse attention Attachments Attachment Submitted filename: Response_to_Reviewers.pdf https://doi.org/10.1371/journal.pone.0344696.r002
29 Jan 2026 Decision Letter - Daosen Zhai, Editor -->PONE-D-25-64863R1-->-->Residual-Aided CSI-free End-to-End Learning for Multiuser MIMO-->-->PLOS One Dear Dr. Biney, 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 Mar 15 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.. 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.. 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.. 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:--> A letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'. 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Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at . Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at . Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.... We look forward to receiving your revised manuscript. Kind regards, Daosen Zhai Academic Editor PLOS One Journal Requirements: 1. 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. [Note: HTML markup is below. Please do not edit.] 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: All comments have been addressed Reviewer #2: All comments have been addressed ******** -->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: Yes Reviewer #2: Yes ****** -->3. Has the statistical analysis been performed appropriately and rigorously? --> Reviewer #1: Yes Reviewer #2: Yes ****** -->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.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.-->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.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: Yes ****** -->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: Yes Reviewer #2: Yes ****** -->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: 1. The link between the proposed DU-SOR framework and classical Successive Over-Relaxation (SOR) is unclear. The update rules mainly resemble residual refinement, without an explicit relaxation factor or clear correspondence to standard SOR iterations. The authors should clarify this connection or reconsider the terminology. 2. The convergence analysis based on the Banach fixed-point theorem is not fully convincing. While spectral normalization is mentioned, it is not rigorously shown that the overall network mapping is strictly contractive, nor is it explained why convergence implies near-MMSE performance. 3. The claimed complexity reduction from O(K^3) to O(K log K) relies on strong assumptions that are insufficiently justified, particularly regarding the relationship between the number of graph nodes and the number of users in massive MIMO settings. 4. Important implementation details affecting reproducibility are missing, including the definition of features used for k-NN graph construction, the distance metric, and whether the graph is dynamically constructed per sample. 5. The “CSI-free” and end-to-end system assumptions require further discussion, especially regarding the practicality of deploying a learnable encoder at the user equipment and its compatibility with standard communication systems. Reviewer #2: I have no further comments on the methodology or results. I agree with acceptance of the manuscript. However, formatting issues still remain, particularly regarding punctuation around equations and the reference list. The journal name abbreviations are not consistently or correctly formatted. The authors should carefully revise the manuscript by thoroughly checking against recently published papers and applying the journal’s formatting rules throughout. ****** -->7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files.). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our For information about this choice, including consent withdrawal, please see our For information about this choice, including consent withdrawal, please see our For information about this choice, including consent withdrawal, please see our Privacy Policy..-->..--> Reviewer #1: No Reviewer #2: No ******** [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] To ensure your figures meet our technical requirements, please review our figure guidelines: https://journals.plos.org/plosone/s/figures You may also use PLOS’s free figure tool, NAAS, to help you prepare publication quality figures: https://journals.plos.org/plosone/s/figures#loc-tools-for-figure-preparation. NAAS will assess whether your figures meet our technical requirements by comparing each figure against our figure specifications. https://doi.org/10.1371/journal.pone.0344696.r003
Revision 2
4 Feb 2026 Author Response Response to Reviewers Manuscript ID: PONE-D-25-64863R1 Title: Residual-Aided CSI-free End-to-End Learning for Multiuser MIMO: A Deep Unfolding Approach We sincerely thank the Academic Editor and Reviewers for their constructive feedback. We have carefully addressed each comment, and the manuscript has been substantially improved. Below we provide point-by-point responses. Reviewer #1 Reviewer Comment: 1. The link between the proposed DU-SOR framework and classical Suc- cessive Over-Relaxation (SOR) is unclear. The update rules mainly resemble residual refinement, without an explicit relaxation factor or clear correspondence to standard SOR iterations. The au- thors should clarify this connection or reconsider the terminology. Response: We agree that the connection to classical SOR required clarification. The classical SOR method for solving linear systems Ax = b has the form x(t+1) = x(t) + ω(D + ωL)−1r(t) where ω ∈ (0, 2) is the relaxation parameter. Our framework generalises this by: (i) replacing the fixed linear operator (D + ωL)−1 with a learned nonlinear mapping G(t) θ , and (ii) making the relaxation factor data-adaptive via ω(t) = σ(M LP ω(Z(t))) where σ(·) is a sigmoid scaled to (0, 2). Change Made: Added dedicated “Connection to Classical SOR” paragraph in Section “Ma- terials and Methods” (page 7). Added Equation 7 showing classical SOR form and Equation 8 showing our learned generalisation. Explicitly stated how the sigmoid scaling to (0, 2) matches the classical SOR convergence range. Reviewer Comment: 2. The convergence analysis based on the Banach fixed-point theorem is not fully convincing. While spectral normalization is mentioned, it is not rigorously shown that the overall network mapping is strictly contractive, nor is it explained why convergence implies near-MMSE performance. Response: We have completely revised the convergence analysis with a mathematically rigor- ous proof. The previous proof incorrectly used the triangle inequality, yielding a factor (1+ωLG) > 1 which cannot establish contraction. The corrected proof uses squared-norm expansion and explic- itly requires two conditions: (1) Lipschitz continuity with constant LG, and (2) strong monotonicity with constant γ > 0, such that ⟨Gθ(u, y) − Gθ(v, y), u − v⟩ ≤ −γ∥u − v∥2. Under these conditions and ω < 2γ/L2 G, we derive the contraction factor q2 = 1 − 2ωγ + (ωLG)2 < 1. Change Made: Completely rewrote Theorem 1 (Convergence of Residual Refinement) with corrected proof using squared-norm expansion. Added explicit assumptions (Lipschitz continu- ity and strong monotonicity) in the theorem statement. Added Remark explaining that strong monotonicity reflects training to approximate a descent direction, and that Lipschitz continuity is enforced via spectral normalisation. Added reference to S3 Fig showing empirical verification that Lipschitz constant remains below 1 throughout training. Reviewer Comment: 3. The claimed complexity reduction from O(K3) to O(K log K) relies on strong assumptions that are insufficiently justified, particularly regarding the relationship between the number of graph nodes and the number of users in massive MIMO settings. Response: We have added detailed justification for the complexity claims. The graph G = (V, E) is constructed with \|V\| = N nodes corresponding to BS antenna elements. In massive MIMO 1 systems with loading ratio β = K/N (typically β ∈ [0.1, 0.5]), both K and N scale together. The sparse k-NN attention with k = c log N neighbours yields O(N log N ) complexity per iteration, which translates to O(K log K) under fixed β. Change Made: Added “Graph-System Mapping” paragraph explicitly clarifying the relation- ship between graph nodes (N ) and users (K). Added three-step proof in Proposition 1 showing: (Step 1) sparse attention complexity, (Step 2) justification for k = c log N based on spectral prop- erties of random geometric graphs and antenna coupling decay, (Step 3) complexity derivation. Added “Conditions and Limitations” paragraph stating when the bound holds and acknowledging worst-case O(K2) for highly correlated channels. Reviewer Comment: 4. Important implementation details affecting reproducibility are miss- ing, including the definition of features used for k-NN graph construction, the distance metric, and whether the graph is dynamically constructed per sample. Response: We have significantly expanded the implementation details to ensure full repro- ducibility. Change Made: Added complete “Graph construction details” subsection specifying: • Node Features: fn = [\|yn\|,/ yn, px n, py n] ∈ R4 where \|yn\| and/ yn are magnitude and phase of received signal, and (px n, py n) are normalised antenna coordinates (Equation 9). • Distance Metric: Euclidean distance d(vi, vj ) = ∥fi − fj ∥2 (Equation 10). • Graph Sparsity: k = 8 nearest neighbours based on sensitivity analysis reported in Ablation Studies. • Static vs. Dynamic: Hybrid approach where base topology is precomputed from antenna geometry (static) while edge weights are dynamically updated each forward pass. Formal adjacency matrix definition with learnable temperature parameter τ (Equation 11). Reviewer Comment: 5. The “CSI-free” and end-to-end system assumptions require fur- ther discussion, especially regarding the practicality of deploying a learnable encoder at the user equipment and its compatibility with standard communication systems. Response: We have added a comprehensive discussion of practical deployment considerations addressing encoder complexity, standards compatibility, model distribution, and fallback modes. Change Made: Added “Practical deployment considerations” subsection in Discussion cover- ing: • Encoder Complexity: ∼47,000 parameters, <200 KB storage, <0.5 ms latency on Snap- dragon 888. • Compatibility with Standards: Power normalisation layer ensures outputs lie within standard QAM constellation regions, enabling graceful fallback for legacy receivers. • Model Distribution: Three mechanisms—factory provisioning, System Information Block (SIB) broadcast, and federated refinement. • Hybrid Deployment Mode: Decoder-only mode where UEs use standard 64-QAM and only BS employs neural decoder, achieving 70% of full E2E gains with no UE modification. Reviewer #2 Reviewer Comment: I have no further comments on the methodology or results. I agree with acceptance of the manuscript. However, formatting issues still remain, particularly regarding punc- tuation around equations and the reference list. The journal name abbreviations are not consistently 2 or correctly formatted. The authors should carefully revise the manuscript by thoroughly checking against recently published papers and applying the journal’s formatting rules throughout. Response: We thank the reviewer for their positive assessment. We have carefully revised all formatting issues throughout the manuscript. Change Made: Made the following formatting corrections: • Equation Punctuation: Reviewed all 16 equations and ensured proper punctuation (com- mas when followed by “where” clauses, periods at end of sentences). Fixed adjacency matrix equation (Eq. 11) to include period. • Bibliography Format: Reformatted all 55 references to Vancouver/ICMJE style as required by PLOS ONE: – Standardised journal abbreviations (e.g., “IEEE Trans Wirel Commun” consistently) – Corrected page number truncation (e.g., 134-42 instead of 134-142) – Ensured “et al.” used after 6 authors – Corrected conference proceedings format with location, date, and publisher • Figure References: Standardised to “Fig” without period throughout. • Figure Numbering: Changed to consecutive numbering (Fig 1, Fig 2, Fig 3). • Terminology: Changed “huge MIMO” to “massive MIMO” (standard terminology). Summary of Major Changes 1. Added “Connection to Classical SOR” paragraph with explicit equations showing relationship to classical method (Eqs. 7–8) 2. Completely revised Theorem 1 with mathematically rigorous convergence proof using squared- norm expansion and explicit assumptions 3. Added “Graph-System Mapping” paragraph and three-step proof in Proposition 1 justifying O(K log K) complexity 4. Added complete “Graph construction details” subsection with node features, distance metric, sparsity, and static/dynamic construction (Eqs. 9–11) 5. Added “Practical deployment considerations” subsection addressing encoder complexity, stan- dards compatibility, model distribution, and hybrid mode 6. Corrected all equation punctuation throughout manuscript 7. Reformatted entire bibliography to Vancouver/ICMJE style 8. Standardised figure references and numbering We believe these revisions fully address all reviewer concerns and significantly strengthen the manuscript. We thank the reviewers for their valuable feedback that has improved the quality of this work. Sincerely, Emmanuel Ampoma Affum (on behalf of all authors) Attachments Attachment Submitted filename: Response_to_Reviewers_auresp_2.pdf https://doi.org/10.1371/journal.pone.0344696.r004
24 Feb 2026 Decision Letter - Daosen Zhai, Editor Residual-Aided CSI-free End-to-End Learning for Multiuser MIMO PONE-D-25-64863R2 Dear Dr. Daniel, 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. Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication. An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager® and clicking the ‘Update My Information' link at the top of the page. 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If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.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.-->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.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. 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Formally Accepted
Acceptance Letter - Daosen Zhai, Editor PONE-D-25-64863R2 PLOS One Dear Dr. Biney, I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS One. Congratulations! Your manuscript is now being handed over to our production team. At this stage, our production department will prepare your paper for publication. This includes ensuring the following: * All references, tables, and figures are properly cited * All relevant supporting information is included in the manuscript submission, * There are no issues that prevent the paper from being properly typeset You will receive further instructions from the production team, including instructions on how to review your proof when it is ready. Please keep in mind that we are working through a large volume of accepted articles, so please give us a few days to review your paper and let you know the next and final steps. Lastly, if your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. You will receive an invoice from PLOS for your publication fee after your manuscript has reached the completed accept phase. If you receive an email requesting payment before acceptance or for any other service, this may be a phishing scheme. Learn how to identify phishing emails and protect your accounts at https://explore.plos.org/phishing. If we can help with anything else, please email us at customercare@plos.org. Thank you for submitting your work to PLOS ONE and supporting open access. Kind regards, PLOS ONE Editorial Office Staff on behalf of Dr. Daosen Zhai Academic Editor PLOS One https://doi.org/10.1371/journal.pone.0344696.r006

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