Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. The core performance gain of RSP has not yet received sufficient statistical support. Table 4 in the main paper shows that MRS-Net-4ch achieves a 7.10 percentage-point improvement in overall BAcc over MR-Spherical-4ch. However, the supplementary materials report a p-value of 0.418 for this comparison, which does not reach statistical significance. Moreover, the improvement appears to stem largely from an anomalous training result for MR-Spherical in Fold 2, where its performance dropped from approximately 90% to 53.28%. After excluding this fold, the average BAcc values for MR-Spherical-4ch and MRS-Net-4ch are about 90.68% and 89.97%, respectively, showing only a trivial difference. Therefore, it is necessary to repeat the training with multiple independent random seeds on each fixed data split.
2. There is a clear inconsistency between the results in the main paper and those in the supplementary materials. Table 4 in the main paper reports an overall BAcc of 84.50±48% for MRS-Net-2ch, while Table S3 in the supplementary materials gives a result of 70.46±5.50% for MRS-Net-2ch-w7 under the default 7×7 local window. Both are described as being evaluated on DroneRFa with 2 channels and default settings, yet the results differ markedly. This discrepancy should be resolved.
3. The backbone network experiments do not yet demonstrate the general applicability of RSP. To evaluate the independent contribution of RSP, the comparison should be made between MRS-Net and MR-Spherical, rather than between MRS-Net and SR-CNN, because the latter also incorporates the effects of multi-resolution STFT and CosFace simultaneously.
4. The physical consistency of cross-scale statistics requires further clarification. The three STFT branches have different window lengths and hop sizes, so the actual time and frequency ranges corresponding to each pixel in the spectrograms differ. Currently, a fixed 7×7 pixel window is employed, and the mean local variations across different scales are directly compared. This practice may cause the cross-scale ratios to primarily reflect differences in discrete gridding and window smoothing rather than the physical structure of the signal itself.
5. The construction and normalization method of the 51-dimensional statistical vector need to be supplemented. This vector mixes features of different scales (or units), including mean, maximum, skewness, kurtosis, entropy, correlation coefficient, and log-determinant. However, the paper does not specify whether normalization is applied before computing the Euclidean distance. It is recommended to clarify the normalization procedure.
6. The ablation studies are currently incomplete. The comparison between SR-CNN and MR-Spherical involves simultaneous changes in both the STFT configuration and the classification loss, making it impossible to isolate the individual contributions of multi-resolution STFT and CosFace. It is recommended to add a complete factorial ablation that includes the following four combinations: single-resolution with cross-entropy, single-resolution with CosFace, multi-resolution with cross-entropy, and multi-resolution with CosFace. Furthermore, for RSP, the individual contributions of RDM, local variation response, log-determinant, and cross-scale ratios should also be evaluated separately.
7. The title of the supplementary materials uses “ Riemannian Manifold Preservation”,which is inconsistent with the term “Riemannian Structure Preservation” used in the main paper.
8. In Figure 11, the naming of the method for Noisy Drone RF is inconsistent with that used in Tables 3 and 5. In addition, Figure 7 presents overly dense information and contains multiple spelling errors.

Comments on the Quality of English Language

The authors need to re-examine the data splits and experimental results, and conduct multi-random-seed training, record-level leakage-free validation, and more comprehensive ablation experiments.

Author Response

Response to Reviewer 1

We thank Reviewer 1 for the comments on statistical interpretation, ablation design, and figure/table consistency. These comments helped us state the contribution of RSP more accurately.

Comments 1:The core performance gain of RSP has not yet received sufficient statistical support. Table 4 in the main paper shows that MRS-Net-4ch achieves a 7.10 percentage-point improvement in overall BAcc over MR-Spherical-4ch. However, the supplementary materials report a p-value of 0.418 for this comparison, which does not reach statistical significance. Moreover, the improvement appears to stem largely from an anomalous training result for MR-Spherical in Fold 2, where its performance dropped from approximately 90% to 53.28%. After excluding this fold, the average BAcc values for MR-Spherical-4ch and MRS-Net-4ch are about 90.68% and 89.97%, respectively, showing only a trivial difference. Therefore, it is necessary to repeat the training with multiple independent random seeds on each fixed data split.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we no longer present the 7.10 percentage-point mean difference as a statistically supported accuracy gain. On the submitted slice-level five folds, MRS-Net-4ch is 90.30%±1.46% and MR-Spherical-4ch is 83.20%±16.78%; the paired difference is +7.10 percentage points, *p* = 0.418, 95% CI [−14.73, +28.93] percentage points, Cohen’s *dz* = 0.40. We treat this test as descriptive because the five folds are not independent draws. After Fold 2 is excluded the means are 90.68% and 89.97%. We repeated training of both 4-channel models on the slice-level protocol with seeds 42, 123, and 2024. At seed 42, Fold 2 is 53.28% (MR-Spherical) versus 91.61% (MRS-Net). At seed 123, Fold 2 is 89.89% versus 82.83%, and the overall means are 90.56%±2.35% versus 88.16%±4.01%. At seed 2024, Fold 2 is 91.61% versus 85.11%, and the overall means are 89.71%±2.91% versus 89.97%±3.35%. The 53% collapse does not recur at the two additional seeds; both models remain near 88%–91%. We therefore do not claim that RSP “significantly improves accuracy” or that it “always prevents collapse”. The Abstract, Highlights, Section 5.2, Section 5.6, and the Conclusions now report the cross-fold variance change on the submitted run, and the multi-seed results are given in Supplementary Table S5 and Figures S4–S5 (marked in red).

> “The 7.10 percentage-point mean BAcc difference between MRS-Net-4ch and MR-Spherical-4ch is not statistically supported (paired comparison on five folds: *p* = 0.418; 95% CI [−14.73, +28.93] percentage points). After Fold 2 is excluded the two means are close (90.68% vs. 89.97%). Multi-seed training does not reproduce the Fold-2 collapse. We therefore report RSP as a reduction in cross-fold standard deviation on the submitted 4-channel run (16.78% to 1.46%), not as a reproducible mean-accuracy gain.”

Comments 2: There is a clear inconsistency between the results in the main paper and those in the supplementary materials. Table 4 in the main paper reports an overall BAcc of 84.50±48% for MRS-Net-2ch, while Table S3 in the supplementary materials gives a result of 70.46±5.50% for MRS-Net-2ch-w7 under the default 7×7 local window. Both are described as being evaluated on DroneRFa with 2 channels and default settings, yet the results differ markedly. This discrepancy should be resolved.

Response 2: Agree. We have, accordingly, clarified that the discrepancy comes from two different training protocols, not from an error in Table 4 (the submitted Table 4 value is 84.50±1.48%). The main experiments use 60 epochs, batch size 16, learning rate 2×10−4, weight decay 5×10−5, and RSP warmup 10. The window-size ablation used 30 epochs, batch size 8, learning rate 5×10−4, weight decay 1×10−4, and warmup 5. We now state this reduced protocol in the title and footnote of Supplementary Table S3, and we no longer describe the two rows as the same default setting. The related text now says that, under the shortened protocol, changing the window does not restore a robust 2-channel gain. The ablation training configuration has also been aligned with the main experiment for future runs. Please see Supplementary Table S3 and its footnote (marked in red).

> “Table S3 uses a shortened training protocol (30 epochs, batch size 8, learning rate 5×10−4) and is not directly comparable to MRS-Net-2ch in Table 4 (84.50±1.48%).”

Comments 3: The backbone network experiments do not yet demonstrate the general applicability of RSP. To evaluate the independent contribution of RSP, the comparison should be made between MRS-Net and MR-Spherical, rather than between MRS-Net and SR-CNN, because the latter also incorporates the effects of multi-resolution STFT and CosFace simultaneously.

Response 3: Thank you for pointing this out. We agree with this comment. Therefore, we now treat the independent contribution of RSP as the difference between MRS-Net and MR-Spherical. Table 8 includes a Δ(MRS-Net − MR-Spherical) column. In the original backbone sweep this difference is positive only for VGG11-BN with 4-channel input (+7.10 percentage points, pulled by Fold 2); it is −6.28 percentage points for Transformer-4ch and −1.04 percentage points for RF-UAVNet-4ch. Section 5.4.3 now states that RSP is not a backbone-agnostic accuracy plugin: it requires an extractor that preserves local time–frequency structure and sufficiently rich cross-channel covariance. We redrew Figure 12 so that MRS-Net versus MR-Spherical is the visual contrast, and we do not hide the negative Transformer-4ch result. Multi-seed training further shows that even for VGG11-BN-4ch the +7.10 percentage-point mean is not a stable cross-seed advantage. Please see Table 8, Figure 12, and Section 5.4.3 (marked in red). The mislabelled “2D-CNN” row is corrected to RF-UAVNet (1-D CNN).

> “The independent contribution of RSP is the difference between MRS-Net and MR-Spherical. RSP is not a backbone-agnostic accuracy plugin.”

Comments 4: The physical consistency of cross-scale statistics requires further clarification. The three STFT branches have different window lengths and hop sizes, so the actual time and frequency ranges corresponding to each pixel in the spectrograms differ. Currently, a fixed 7×7 pixel window is employed, and the mean local variations across different scales are directly compared. This practice may cause the cross-scale ratios to primarily reflect differences in discrete gridding and window smoothing rather than the physical structure of the signal itself.

Response 4: Agree. We have, accordingly, stated in Section 3.2 that the 7×7 window is a discrete neighbourhood on each scale’s own STFT grid, not a physically co-located block. At *f*s = 100 MHz and hop = *N*FFT/2, a 7×7 patch covers approximately 35.8 μs × 684 kHz, 71.7 μs × 342 kHz, and 143.4 μs × 171 kHz on the three branches. The cross-scale ratios describe relative statistical responses of the same analysis pipeline at different STFT resolutions; we do not claim physical co-location. We did not replace the default window with a physically matched patch, and we state this as a limitation. Please see Section 3.2 and the Discussion (marked in red).

> “The 7×7 window is a per-scale discrete neighbourhood, not a physically aligned time–frequency block. Cross-scale ratios are relative multi-resolution statistical responses, not co-located physical measurements.”

Comments 5: The construction and normalization method of the 51-dimensional statistical vector need to be supplemented. This vector mixes features of different scales (or units), including mean, maximum, skewness, kurtosis, entropy, correlation coefficient, and log-determinant. However, the paper does not specify whether normalization is applied before computing the Euclidean distance. It is recommended to clarify the normalization procedure.

Response 5:Thank you for pointing this out. We agree with this comment. Therefore, we now state after Equation (14) that, in the submitted implementation, the 51-dimensional vector is not standardized per dimension before the Euclidean distance; only non-finite values are replaced, and scale differences are absorbed only by the median-heuristic kernel bandwidth σ. The “normalized mean profile” in Figure 6 is a display-only min–max normalization and is not used in training. A 51-dimensional inventory (15 dimensions × 3 scales + 6 ratios) is listed in Supplementary Table S7. We additionally ran a batch-wise per-dimension z-score ablation of MRS-Net-4ch on the same session-level grouped five folds as Table S4: 60.23%±13.41% without standardization versus 61.91%±10.19% with z-score (+1.68 percentage points), with mixed fold-wise changes and no stable gain. That ablation must not be compared with the slice-level ~90% numbers in Table 4. The revised manuscript therefore keeps the submitted implementation and does not adopt z-score as the default. Please see the paragraph after Equation (14), Figure 6 caption, and Supplementary Table S6 (marked in red).

> “The 51-dimensional vector is used without per-dimension standardization. Figure 6 uses a separate display-only normalization. Explicit batch z-score does not yield a stable gain, so it is not the training default.”

Comments 6: The ablation studies are currently incomplete. The comparison between SR-CNN and MR-Spherical involves simultaneous changes in both the STFT configuration and the classification loss, making it impossible to isolate the individual contributions of multi-resolution STFT and CosFace. It is recommended to add a complete factorial ablation that includes the following four combinations: single-resolution with cross-entropy, single-resolution with CosFace, multi-resolution with cross-entropy, and multi-resolution with CosFace. Furthermore, for RSP, the individual contributions of RDM, local variation response, log-determinant, and cross-scale ratios should also be evaluated separately.

Response 6: Agree. We have, accordingly, added a slice-level 2×2 factorial ablation and replaced the qualitative paragraph in Section 5.4.1 with a 2×2 table. On 2-channel input: SR+CE 77.02%±3.78%, SR+CosFace 81.97%±1.68%, MR+CE 80.72%±2.42%, MR+CosFace 84.74%±0.94%. CosFace contributes +4.95 and +4.02 percentage points at single- and multi-resolution; multi-resolution contributes +3.70 and +2.77 percentage points under cross-entropy and CosFace. On 4-channel input: SR+CE 74.01%±12.11%, SR+CosFace 77.91%±8.40%, MR+CE 83.00%±13.28%, MR+CosFace 83.20%±16.78%. Multi-resolution is the main positive effect; adding CosFace after multi-resolution changes the mean by only +0.20 percentage points. For RSP components, we still use the full 51-dimensional vector as a joint teacher and do not attribute the effect to a single component; the missing component-wise split is stated as a limitation. Please see Section 5.4.1 and Table 6 (marked in red). The original parameter-aligned STFT ablation is now Table 7.

> “A 2×2 factorial on DroneRFa separates multi-resolution STFT from CosFace. RSP remains a joint 51-dimensional teacher; component-wise masking is not claimed.”

Comments 7: The title of the supplementary materials uses “Riemannian Manifold Preservation”, which is inconsistent with the term “Riemannian Structure Preservation” used in the main paper.

Response 7: Thank you for pointing this out. We agree with this comment. Therefore, we have aligned the supplementary title and all method names with Riemannian Structure Preservation, and we no longer use “manifold preservation” as the method name. Figure 7 is corrected in the same way. We state that RSP is a training-time SPD statistical teacher / relational regularizer, not an end-to-end Riemannian network. Please see the Supplementary title, Figure 7, and the method-positioning sentences in the Introduction (marked in red).

> “Riemannian Structure Preservation (RSP) is a training-only relational regularizer, not an end-to-end manifold network.”

Comments 8: In Figure 11, the naming of the method for Noisy Drone RF is inconsistent with that used in Tables 3 and 5. In addition, Figure 7 presents overly dense information and contains multiple spelling errors.

Response 8: Agree. We have, accordingly, redrawn Figure 11 so that the red curve is labelled MR-Spherical, consistent with Tables 3 and 5; the caption states that RSP was not used (RSP = N/A in Table 3). Section 5.3 no longer calls this curve MRS-Net. Figure 7 has been redrawn in English: the inference path is separated from the training-only RSP branch, stop-gradient is shown, geodesic/manifold artwork on the CNN embedding is removed, and the spelling errors (Addittive, Channl, Reciver, classed, Droupout, Statics, Rimannian, meatures, and related labels) are corrected. Please see Figure 7, Figure 11, and Section 5.3 (marked in red).

> “Figure 11 evaluates MR-Spherical, not MRS-Net; RSP is not used on Noisy Drone RF. Figure 7 shows a Euclidean/hyperspherical CNN embedding and a training-only RSP teacher.”

 

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript addresses a relevant problem of RF-based UAV identification under low-SNR and long-range conditions. The proposed MRS-Net combines multi-resolution STFT, CosFace learning and Riemannian Structure Preservation. The approach is interesting, and the experimental section is generally well developed. I also appreciate the additional ablation and fold-wise analyses provided by the authors.

A few minor points should be clarified before publication.

1. In Section 5.1.2, please briefly clarify how the five cross-validation folds were constructed and whether segments from the same original recording or acquisition session were kept within the same fold.
2. For the 4-channel setting, please briefly clarify whether the two receiver streams are synchronized and whether any alignment is applied before calculating the local covariance matrices.
3. Please indicate whether the components of the 51-dimensional Riemannian statistical vector are normalized or standardized before computing the distance in Equation (14).
4. Please check Figure 11. Table 5 and the corresponding text report MR-Spherical, while the curve in Figure 11 is labelled MRS-Net. Please correct this inconsistency.
5. Please recheck Supplementary Table S1. The displayed SR-CNN-2ch fold values do not appear to reproduce exactly the reported mean and standard deviation.
6. In Equation (8), κ appears to describe local geometric variation of the log-SPD field rather than curvature in the usual mathematical sense. Please clarify the use of this term.

Overall, the manuscript presents an interesting approach and the reported results are promising. 

Author Response

Response to Reviewer 2

We thank Reviewer 2 for the positive assessment and for requesting a clearer statement of the cross-validation protocol, 4-channel synchronization, vector normalization, figure labeling, and terminology.

Comments 1: In Section 5.1.2, please briefly clarify how the five cross-validation folds were constructed and whether segments from the same original recording or acquisition session were kept within the same fold.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we now state in Section 5.1.2 that each original `T*_D*_S*.mat` file is one acquisition session, sliced into fixed-length segments, and that the submitted protocol is `StratifiedKFold` on slices, stratified by class × distance. Slices from the same recording may appear on both sides of a fold. This protocol evaluates in-session discrimination, not cross-session generalization. We additionally ran recording-level grouped cross-validation (`StratifiedGroupKFold` by source file) as a stricter cross-session check; those results are in Supplementary Table S4 and Figures S1–S3. Main-text Table 4 keeps the original protocol. Under grouped CV the overall BAcc values are 53.56%±10.18% (SR-CNN-2ch), 64.78%±7.84% (MR-Spherical-2ch), 67.27%±6.82% (MRS-Net-2ch), and 60.96%±9.40%, 60.08%±14.85%, 60.23%±13.41% on 4-channel input. The 4-channel RSP difference versus MR-Spherical is +0.15 percentage points (*p* = 0.984). On 2-channel input, multi-resolution STFT and CosFace remain positive relative to SR-CNN (+11.22 percentage points). We report the grouped drop as a cross-session limitation, not as a correction of Table 4. Please see Section 5.1.2 and Supplementary Table S4 (marked in red).

> “Folds in Table 4 are slice-level and class-and-distance stratified; slices from the same recording may appear on both sides of a fold. A recording-level grouped CV is reported separately as a cross-session check.”

Comments 2: For the 4-channel setting, please briefly clarify whether the two receiver streams are synchronized and whether any alignment is applied before calculating the local covariance matrices.

Response 2: Agree. We have, accordingly, added a statement in Section 4.2. The two streams (`RF0_I/Q` and `RF1_I/Q`) are stored on a shared sampling grid in the same DroneRFa file and are sliced with identical indices; we treat them as synchronously acquired. No additional delay estimation or resampling is applied before Equation (3). Residual hardware delay, if present, enters the off-diagonal covariance terms. We do not claim explicit alignment. Please see Section 4.2 (marked in red).

> “The two receiver streams share the original sampling grid and identical slice indices. No additional delay alignment is applied before Eq. (3).”

Comments 3: Please indicate whether the components of the 51-dimensional Riemannian statistical vector are normalized or standardized before computing the distance in Equation (14).

Response 3: Thank you for pointing this out. We agree with this comment. Therefore, we now state after Equation (14) that they were not standardized per dimension in the submitted code; only non-finite values were replaced. Figure 6 uses a separate display-only normalization. On the same grouped five folds as Table S4, MRS-Net-4ch is 60.23%±13.41% without standardization and 61.91%±10.19% with batch-wise z-score. Explicit standardization does not give a stable gain, so we keep the submitted implementation and do not make z-score the default. This ablation must not be placed beside the slice-level Table 4 numbers. Please see the paragraph after Equation (14) and Supplementary Table S6 (marked in red).

> “The 51-dimensional components are not standardized before Eq. (14). Figure 6 normalization is for display only.”

Comments 4: Please check Figure 11. Table 5 and the corresponding text report MR-Spherical, while the curve in Figure 11 is labelled MRS-Net. Please correct this inconsistency.

Response 4: Agree. We have, accordingly, corrected the Figure 11 legend. The evaluated model is MR-Spherical, consistent with Table 5. RSP was not used in that experiment. Please see Figure 11 and Section 5.3 (marked in red).

> “The red curve in Figure 11 is MR-Spherical (no RSP), matching Table 5.”

Comments 5: Please recheck Supplementary Table S1. The displayed SR-CNN-2ch fold values do not appear to reproduce exactly the reported mean and standard deviation.

Response 5: Thank you for pointing this out. We agree with this comment. Therefore, we recomputed the mean and standard deviation from the unrounded fold scores and then rounded to two decimals. The original floating-point mean is 0.770222 (77.02%) and the standard deviation is 0.037791 (3.78%); averaging the already-rounded fold values 76.67, 77.94, 70.42, 80.00, and 79.78 gives 76.96, which is why the displayed numbers did not reproduce the reported summary. Table S1 is now generated by script from the unrounded folds. Please see Supplementary Table S1 (marked in red).

> “Means and standard deviations in Table S1 are computed from unrounded fold scores.”

Comments 6: In Equation (8), κ appears to describe local geometric variation of the log-SPD field rather than curvature in the usual mathematical sense. Please clarify the use of this term.

Response 6: Agree. We have, accordingly, renamed κ a local variation field (log-SPD variation). Equation (8) is a first-order finite-difference magnitude of the log-SPD field along frequency and time, followed by log(1+·). It is not a Riemannian curvature tensor, sectional curvature, or Gaussian curvature. We state this immediately after Equation (8) and update the Figure 4 caption, radar-plot labels, Abstract, and Supplementary Material. Please see Equation (8) and Figure 4 (marked in red).

> “κ is a first-order local variation of the log-SPD field, not differential-geometric curvature.”

 

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript addresses the challenges of MRS-Net. This deep-learning framework combines multi-resolution time-frequency analysis, Riemannian covariance-structure preservation, and metric learning to improve RF-based drone identification under low-SNR and long-range conditions.

The introduction gives the reader a background on UAV sensing modalities, RF-based identification, low-SNR degradation and time-frequency analysis. It explains the authors' motivation for using second-order covariance structure. It also states the practical problem and the intended contribution clearly, although the research hypothesis could be formulated more explicitly, and the novelty relative to the closest multiscale and manifold-based approaches should be sharper. The reference list is broadly relevant and current, with appropriate coverage of RF-based UAV identification, low-SNR processing, metric learning, manifold methods, and the two datasets used in the experiments.

The research design seems to be appropriate in using DroneRFa for real distance-related attenuation and dual-receiver evaluation and Noisy Drone RF for controlled additive-noise evaluation, since these datasets address complementary aspects of the stated problem. Balanced accuracy is a sensible primary metric for imbalanced classes, and five-fold stratified cross-validation with mean and standard deviation is more informative than a single train-test split. 

A major design concern is that the manuscript does not state whether folds are formed at the level of independent original recordings, acquisition sessions, or devices rather than at the level of cropped signal segments, and segment-level splitting could produce serious leakage if overlapping or highly correlated portions of the same recording occur in both training and test folds.

The statistical analysis should be revised. A paired t-test on only five cross-validation folds considers highly dependent fold results as if they were independent observations. The exact p-values, confidence intervals, and effect sizes are not missing. 

The ablation design is not fully factorial - the transition from SR-CNN to MR-Spherical simultaneously changes the STFT representation and the classification loss. This prevents a clean estimate of the separate contribution of CosFace. The primary DroneRFa evaluation also relies mainly on the authors' own model variants, so comparison with other published RF-UAV baselines under the same data split and preprocessing protocol would make the claimed advantage more convincing.

The Conclusions are mostly supported by the reported results, especially the statements that multi-resolution representation and CosFace improve low-SNR recognition and that RSP is most beneficial when richer four-channel covariance structure is available.

The general robustness in the conclusions should be moderated because RSP itself is not directly validated on the controlled Noisy Drone RF experiment. Its mean gain over MR-Spherical on DroneRFa is not statistically significant with the reported analysis. The generalisation to unseen environments, devices, receivers, interference types, and open-set classes is untested. 

From a formal point of view, the manuscript is well written, of adequate length, readable with ordinary effort, and fits the journal scope.

Problems found:

Several labels in Figure 7 contain typographical or awkward wording.

• The “Manifold Embedding Learning (Riemannian Manifold in Embedding Space)” box is misleading. The CNN embedding is not described mathematically as an SPD/Riemannian manifold in the Methods.
• The arrow labelled “RSP Alignment Guiding” gives the wrong impression about how RSP acts on the network.
• "Addittive Margin", "Input Channl10", "classed on DroneRFa".

Figure 9 - the accompanying text and caption describe six settings; however, the figure contains nine confusion matrices and appears to repeat the MR-Spherical two-channel 80-150 m panel.

Figure 11 - its legend labels the red curve as MRS-Net with RSP, whereas Table 5 and the surrounding discussion identify the same result as MR-Spherical. Which model was actually evaluated?

References 12 and 26 appear in the bibliography but are not cited in the main text.

Author Response

Response to Reviewer 3

We thank Reviewer 3 for the comments on hypothesis statement, data splitting, statistical analysis, ablation design, external baselines, the scope of the Conclusions, and figure/reference consistency. We reply in the order of the comments.

Comments 1: The introduction gives the reader a background on UAV sensing modalities, RF-based identification, low-SNR degradation and time-frequency analysis. It explains the authors’ motivation for using second-order covariance structure. It also states the practical problem and the intended contribution clearly, although the research hypothesis could be formulated more explicitly, and the novelty relative to the closest multiscale and manifold-based approaches should be sharper.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we now state three testable hypotheses in the Introduction: (i) a single fixed STFT resolution cannot serve both narrowband control and wideband video links, and multi-resolution observation improves separability at low SNR; (ii) CosFace increases angular margins relative to cross-entropy and reduces embedding overlap at low SNR; (iii) when informative cross-channel SPD structure is available and the backbone preserves local time–frequency structure, RSP as a training-time relational regularizer may reduce variance on a difficult split; we do not assume a significant mean-accuracy gain, nor that a variance reduction will recur across random seeds. We also sharpen the contrast with SPDNet and end-to-end manifold classifiers: we do not classify on the manifold, we do not feed the 51-dimensional vector to the classifier, RSP is removed at inference, and the teacher is a batch-wise pairwise similarity relation for a Euclidean CNN embedding. Please see the Introduction (marked in red).

> “RSP is a training-only relational teacher for a Euclidean CNN embedding, not an end-to-end manifold classifier.”

Comments 2: A major design concern is that the manuscript does not state whether folds are formed at the level of independent original recordings, acquisition sessions, or devices rather than at the level of cropped signal segments, and segment-level splitting could produce serious leakage if overlapping or highly correlated portions of the same recording occur in both training and test folds.

Response 2: Agree. We have, accordingly, stated this protocol explicitly and added a stricter check. The original cross-validation is slice-level and stratified by class and distance; the same recording can contribute slices to both sides of a fold. Section 5.1.2 now says so. We added session-level grouped cross-validation as a cross-session check in Supplementary Table S4 and Figures S1–S3. Main-text Table 4 retains the original in-session numbers so that the module-wise conclusions remain comparable to the submitted experiments. Under grouped CV the overall BAcc values are 53.56%±10.18% / 64.78%±7.84% / 67.27%±6.82% on 2-channel SR-CNN / MR-Spherical / MRS-Net, and 60.96%±9.40% / 60.08%±14.85% / 60.23%±13.41% on 4-channel input. The 4-channel RSP advantage does not persist. We report this drop as a limitation of cross-session generalization, not as a replacement of Table 4. On 2-channel input, multi-resolution STFT and CosFace remain positive relative to SR-CNN. Please see Section 5.1.2 and Supplementary Table S4 (marked in red).

> “Table 4 uses slice-level stratified CV (in-session discrimination). Session-level grouped CV is reported in the Supplementary Material as a cross-session check.”

Comments 3: The statistical analysis should be revised. A paired t-test on only five cross-validation folds considers highly dependent fold results as if they were independent observations. The exact p-values, confidence intervals, and effect sizes are not missing.

Response 3: Thank you for pointing this out. We agree that five CV folds are not independent draws and that a paired *t*-test with *n* = 5 cannot by itself support “significantly better”. Therefore, we no longer treat that test as a confirmatory significance claim. In the Supplementary Material we report the submitted slice-level 4-channel comparison of MRS-Net versus MR-Spherical as a descriptive paired difference of +7.10 percentage points, *p* = 0.418, 95% CI [−14.73, +28.93] percentage points, Cohen’s *dz* = 0.40. The main-text interpretation of RSP is the cross-fold variability on that run, not a confirmatory mean gain. Multi-seed training further shows that this mean difference is not a cross-seed conclusion. We describe stability with the cross-fold standard deviation and do not present a drop in σ as a *p* < 0.05 performance improvement. The grouped-CV comparison is listed separately (4-channel RSP +0.15 percentage points, *p* = 0.984). Please see Section 5.2, Section 5.6, and the Supplementary statistics section together with Tables S4 and S5 (marked in red).

> “Five CV folds are not independent. The paired *p*-value, 95% CI, and Cohen’s *dz* are descriptive. RSP is not claimed as a significant mean-accuracy gain.”

Comments 4: The ablation design is not fully factorial — the transition from SR-CNN to MR-Spherical simultaneously changes the STFT representation and the classification loss. This prevents a clean estimate of the separate contribution of CosFace.

Response 4: Agree. We have, accordingly, added a slice-level 2×2 factorial ablation. On 2-channel input: SR+CE 77.02%±3.78%, SR+CosFace 81.97%±1.68%, MR+CE 80.72%±2.42%, MR+CosFace 84.74%±0.94%; CosFace contributes about +4.0 to +5.0 percentage points and multi-resolution about +2.8 to +3.7 percentage points. On 4-channel input: SR+CE 74.01%±12.11%, SR+CosFace 77.91%±8.40%, MR+CE 83.00%±13.28%, MR+CosFace 83.20%±16.78%. Multi-resolution is the main positive effect; after multi-resolution is already used, the additional mean contribution of CosFace is +0.20 percentage points. Please see Section 5.4.1 and Table 6 (marked in red).

“The 2×2 factorial separates CosFace (rows, STFT fixed) from multi-resolution STFT (columns, loss fixed).”

Comments 5: The primary DroneRFa evaluation also relies mainly on the authors’ own model variants, so comparison with other published RF-UAV baselines under the same data split and preprocessing protocol would make the claimed advantage more convincing.

Response 5: Thank you for pointing this out. We agree with this comment. Therefore, we now report RF-UAVNet (Huynh-The et al.) under the same DroneRFa protocol (2-channel 81.07%, 4-channel 85.86%). In the original submission this backbone sweep was mislabelled as 2D-CNN. The table note states identical crop length, the same slice-level five folds as Table 4, the same RMS normalization, and the same sampling length. We do not claim a line-by-line reproduction of every published architecture. Please see Table 8 and Section 5.4.3 (marked in red).

> “RF-UAVNet is reported under the same DroneRFa protocol; the former 2D-CNN label was a misnomer.”

Comments 6: The Conclusions are mostly supported by the reported results, especially the statements that multi-resolution representation and CosFace improve low-SNR recognition and that RSP is most beneficial when richer four-channel covariance structure is available. The general robustness in the conclusions should be moderated because RSP itself is not directly validated on the controlled Noisy Drone RF experiment. Its mean gain over MR-Spherical on DroneRFa is not statistically significant with the reported analysis. The generalisation to unseen environments, devices, receivers, interference types, and open-set classes is untested.

Response 6: Agree. We have, accordingly, moderated the Conclusions and Discussion. What we reduce is the claim of cross-session, unseen-device, and open-set robustness, not the claim that the method is effective under matched acquisition. We now state that: evidence for RSP is limited to DroneRFa dual-receiver 4-channel input and to a cross-fold variance change on one submitted run, and that collapse prevention did not recur at two additional seeds; Noisy Drone RF validates multi-resolution STFT and CosFace, and those results are retained; the mean BAcc gain over MR-Spherical is not statistically significant (*p* = 0.418); generalization to unseen environments, devices, receivers, interference types, and open-set classes remains untested. We do not describe the grouped-CV accuracy drop as a failure of the method under matched conditions. Please see the Conclusions and Discussion (marked in red).

> “RSP is not claimed as a generally robust accuracy plugin. Noisy Drone RF tests multi-resolution STFT and CosFace, not RSP. Unseen-device and open-set generalization remain untested.”

Comments 7: Several labels in Figure 7 contain typographical or awkward wording. The “Manifold Embedding Learning (Riemannian Manifold in Embedding Space)” box is misleading. The CNN embedding is not described mathematically as an SPD/Riemannian manifold in the Methods. The arrow labelled “RSP Alignment Guiding” gives the wrong impression about how RSP acts on the network. “Addittive Margin”, “Input Channl10”, “classed on DroneRFa”.

Response 7:Thank you for pointing this out. We agree with this comment. Therefore, we redrew Figure 7. The CNN embedding is Euclidean / hyperspherical, not an SPD manifold. The RSP branch is a dashed training-only box, with stop-gradient on the statistical vector, and the whole branch is removed at inference. All listed spelling errors are corrected. Please see Figure 7 (marked in red).

> “The CNN embedding is not an SPD manifold. RSP is a training-only teacher with stop-gradient and is removed at inference.”

Comments 8: Figure 9 — the accompanying text and caption describe six settings; however, the figure contains nine confusion matrices and appears to repeat the MR-Spherical two-channel 80–150 m panel.

Response 8: Agree. We have, accordingly, replaced Figure 9 with a 2×3 grid of overall confusion matrices: two rows (2-channel / 4-channel) and three columns (SR-CNN / MR-Spherical / MRS-Net), matching the caption. Distance-wise matrices, if retained, are in the Supplementary Material. Each subplot title is bound to its own `confusion_matrix` array. The corresponding grouped-CV 2×3 figure is Supplementary Figure S2. Please see Figure 9 (marked in red).

> “Figure 9 shows six overall confusion matrices, one per setting.”

Comments 9: Figure 11 — its legend labels the red curve as MRS-Net with RSP, whereas Table 5 and the surrounding discussion identify the same result as MR-Spherical. Which model was actually evaluated?

Response 9: Thank you for pointing this out. MR-Spherical was evaluated. The Figure 11 legend was incorrect and has been corrected. RSP was not used on Noisy Drone RF. Please see Figure 11, Table 5, and Section 5.3 (marked in red).

> “Figure 11 evaluates MR-Spherical; the previous MRS-Net+RSP legend was an error.”

Comments 10: References 12 and 26 appear in the bibliography but are not cited in the main text.

Response 10: Agree. We have, accordingly, cited Reference 12 (Al-Sa’d et al., 2019) in Related Work 2.1 as an early large-scale RF UAV dataset. Reference 26 (Zhang & Sennrich, RMS Layer Normalization) has been removed from the bibliography: Equation (20) is per-sample RMS amplitude normalization, not an RMSNorm layer, so that preprint is not used. Please see Section 2.1 and the bibliography (marked in red).

> “Al-Sa’d et al. (2019) is cited in Related Work. The RMSNorm preprint was not used and has been removed.”

 

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Authors, thank you for providing me with the updated version of your manuscript and for the thorough explanation. After careful proofreading, I am happy with its current state.