Dear Reviewer zohP,

We sincerely appreciate your review and valuable feedback.

Based on the weaknesses you pointed out, we made changes to the manuscript to improve its overall quality. Specifically, to address the #1 major weakness you mentioned, we included a new Section 4.3 in the updated manuscript.

Here is a point-by-point response to the weaknesses you mentioned and the efforts we made to address them:

1. Dataset Applicability: The mmWave and SAR datasets we found are not applicable to this problem. For example, the commonly used mSTAR dataset (https://www.kaggle.com/datasets/atreyamajumdar/mstar-dataset-8-classes) contains SAR images but not the radar signals used to generate the images. In the meantime, we used commercial simulation software based on ray tracing, Ansys Electronics Desktop (referred to as “AEDT”), which has been used in many research studies as a benchmark (e.g., Phan et al., 2023; Ren et al., 2017). This is as close to real-world data as we can get with simulations.

We reconstructed a cube (provided the resolution is not high) using AEDT-generated data and provided the details in the newly added Section 4.3. We learned the AEDT-generated scene using GRT-based RIFT. Although the scene was not complex, this partially addresses your concerns about the gap between fully synthetic data and reality. We are working on reconstructing more complicated scenes and hope to provide an update early next week.

2. Accuracy of the GRT Model:

The accuracy of the GRT model is partially demonstrated in the case studies. For example, although the “true signal” in Section 4.2 was generated by our forward model, we tested two objects of the same shape with different reflectivities. RIFT was able to resolve the two objects, whereas the traditional method could not. The new Section 4.3 can serve, at least partially, as a validation tool for RIFT under real-world conditions.

3. Discussion of Related Work:

We updated the manuscript to address the lack of discussion you highlighted. We acknowledge that we were not aware of RadarField at the time of composing the first draft of this work.

4. Typographical and Notation Errors:

In the updated manuscript, we fixed all the typos and inconsistent notations you mentioned. We hope that our responses address your concerns and contribute to a potential improvement in your evaluation of our work.

Best regards, Authors of Submission 12994

References:

1. Tra Nguyen Phan, Bengt Oelmann, and Sebastian Bader. 2023. Towards Automated Design Optimization of Electromagnetic Energy Harvesting Transducers. In Proceedings of the 20th ACM Conference on Embedded Networked Sensor Systems (SenSys '22). Association for Computing Machinery, New York, NY, USA, 871–877. https://doi.org/10.1145/3560905.3568102

2. Ren, Q., Nagar, J., Kang, L., et al. Efficient Wideband Numerical Simulations for Nanostructures Employing a Drude-Critical Points (DCP) Dispersive Model. Scientific Reports, 7(2126), 2017. https://doi.org/10.1038/s41598-017-02194-1

Dear Reviewer zohP:

We appreciate your prompt response. While we agree that simulation is not a substitute for the real world, we believe that it is not fair to fully discount the successful reconstruction of scenes from commercial simulation softwares. To support our argument, we want to provide some information regarding the tool we use and the difference between scene reconstruction based on visual and radar signals.

1. The particular tool we used is widely accepted as an industry standard in antenna design and validation before manufacturing for at least a decade (Sun et al., 2014, Xu et al., 2019, Blair et al., 2019).

2. We are sorry that we did not directly mention this in the previous response, but we have provided in the general note that the tool we use does address multipath effect with ray tracing (please refer to this article for more information: https://www.ansys.com/blog/using-synthetic-data-for-radar-applications).

3. The most important noises to radar signals are thermal noise and clutter. Addition of Gaussian noise can correctly mimic behavior of thermal noise in radar (Rouphael, 2014). We will provide the result with thermal noise in the revision. There are other tools from the same company used in modeling for autonomous vehicles that address clutter and they use it with an automobile manufacturer (https://www.ansys.com/it-it/campaigns/bmw).

Given the usage of Ansys by both antenna designers and automotive companies, we are confident that it is suitable for this work. We would also like to argue in favor of our work in a more tangible way by illustrating the difference between 3D reconstruction with visual data and with radar signals.

1. As it’s known to the ML community, hardware limitation is a concern for all works. What we try to achieve in this work is to emulate a synthetic aperture radar with implicit neural representation. The amount of data needed to achieve synthetic aperture radar imaging is significantly greater than that of optical imaging. To resolve 2 features spaced by 0.01m in a scene of dimension 10m with no aliasing, the number of "colors" or frequency samples required is 1000. The demand for data in radar imaging is significantly higher than that in optical imaging. The non-INR based reconstruction methods used significantly larger network while they are still using point clouds (Sun et al. 2021). We note that given the large amount of training data, our model achieves a large order of compression (>1000x)

2. The applicability of off-the-shelf dataset: While we appreciate the dataset you mentioned, it is not fully applicable to our problem. For the coloradar (Kramer et al. 2022), in particular, while the moving radar in a scene can be resolved with a change in the reference coordinate, the frame rate is 10Hz and 5Hz. We require both densely sampled viewpoints over a wide aperture, ideally with a stationary scene. While we do believe we could use this dataset eventually, it would require significant data cleaning and calibration which is not suitable for the revision. We hope our argument for the Ansys high-fidelity industry standard simulation will suffice.

Best Regards, Authors of Submission 12994

References:

1. C. Sun, H. Zheng, L. Zhang and Y. Liu, "Analysis and Design of a Novel Coupled Shorting Strip for Compact Patch Antenna With Bandwidth Enhancement," in IEEE Antennas and Wireless Propagation Letters, vol. 13, pp. 1477-1481, 2014, doi: 10.1109/LAWP.2014.2341596.
2. X. Xu et al., "Intelligent Design of Reconfigurable Microstrip Antenna Based on Adaptive Immune Annealing Algorithm," in IEEE Transactions on Instrumentation and Measurement, vol. 71, pp. 1-14, 2022, Art no. 8002714, doi: 10.1109/TIM.2022.3162281.
3. C. Blair, S. López Ruiz and M. Morales, "5G, A MultiPhysics Simulation Vision From Antenna Element Design to Systems Link Analysis," 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA), Granada, Spain, 2019, pp. 1420-1422, doi: 10.1109/ICEAA.2019.8879074.
4. Tony J. Rouphael, Chapter 3 - Noise in Wireless Receiver Systems, Wireless Receiver Architectures and Design, Academic Press, 2014, Pages 105-178, ISBN 9780123786401, https://doi.org/10.1016/B978-0-12-378640-1.00003-2.
5. Y. Sun, Z. Huang, H. Zhang, Z. Cao and D. Xu, "3DRIMR: 3D Reconstruction and Imaging via mmWave Radar based on Deep Learning," in 2021 IEEE International Performance, Computing, and Communications Conference (IPCCC), Austin, TX, USA, 2021, pp. 1-8, doi: 10.1109/IPCCC51483.2021.9679394.
6. Kramer, Andrew, Kyle Harlow, Christopher Williams, and Christoffer Heckman. “ColoRadar: The direct 3D millimeter wave radar dataset.” The International Journal of Robotics Research 41, no. 4 (2022): 351-360.

Edit: replaced an invalid link

References:

1. Xia, W., Zhou, Y., Jin, X., & Zhou, J. (2016). A Fast Algorithm of Generalized Radon-Fourier Transform for Weak Maneuvering Target Detection. International Journal of Antennas and Propagation, 2016(1), 4315616. https://doi.org/10.1155/2016/4315616

2. Z. Ding et al., "A Ship ISAR Imaging Algorithm Based on Generalized Radon-Fourier Transform With Low SNR," IEEE Transactions on Geoscience and Remote Sensing, vol. 57, no. 9, pp. 6385-6396, Sept. 2019, doi: 10.1109/TGRS.2019.2905863.

3. Biao Zhang and Yiming Pi. (2013). A 3D Imaging Technique for Circular Radar Sensor Networks Based on Radon Transform. International Journal of Sensor Networks, 13(4), 199–207. https://doi.org/10.1504/IJSNET.2013.055582

Dear Reviewer B7gc,

We sincerely appreciate your review and valuable feedback.

Based on the weaknesses you pointed out, we made changes to the manuscript to improve its overall quality and credibility.

Here are our efforts to address the weaknesses you mentioned:

1. We used commercial simulation software “Ansys Electronics Desktop 2023 R1” (referred to as “AEDT”), which is based on ray tracing and incorporates most of the effects encountered in real radar imaging tasks. In the updated manuscript, we provided details in the new Section 4.3. While this still does not fully address weakness #1 you pointed out, we are working on reconstructing more complex scenes using data from ray tracing simulations that are as close to real-world data as possible. We hope the reconstruction of scenes using commercial simulation software can enhance the credibility of our work, at least partially bridging the gap between synthetic and real-world data.

2. In the new manuscript, we further elaborated on the experimental setup in Appendices B.2, B.3, and B.7.

3. Several details addressing questions in weakness #2 appear in different sections. For example, the sampling of view angles is described in lines 299 to 304 of the previous submission.

4. There are indeed some questions you mentioned in weakness #2 that we did not address well. Below, we provide point-by-point answers to these questions so you don’t have to search the updated manuscript for the answers.

We also hope the updated manuscript addresses your concerns more comprehensively.

We conducted further investigation into related work and improved the writing. We hope the rewritten sections, which are described in the general response to all reviewers, address this concern.

Point-by-Point Answers to Questions in Weakness #2:

1. Sampling of View Angles: The sampling of view angles is described in lines 299 to 304 of the previous submission. We acknowledge that these details could have been placed differently. The problem setups corresponding to Sections 4.1, 4.2, and the newly added Section 4.3 are distinct, so they were not included in Section 3. Accordingly, we renamed Section 4 to “Experimental Setups, Results, and Discussions.”

2. Matrix A: We acknowledge that we did not include a link to Appendix B.3 at its first mention. Matrix A is defined in B.3, and the link to B.3 previously appeared at the end of Section 3.1 (lines 192–193).

3. Noise in Radar Data: We did not add any noise to the radar data. The GRT itself is a first-order approximation (under the Born approximation, which simplifies interactions between the scene and the wave to interactions between each voxel and the wave) and inherently contains inaccuracies, such as not accounting for the multipath effect mentioned by reviewer zohP. We updated the manuscript accordingly. However, we acknowledge that the absence of noise could impact your evaluation of our work's robustness. We are running experiments with Gaussian noise and will update the manuscript next week.

4. Choice of Forward Model: We chose the GRT as the forward model of radar, which is not directly related to radar calibration. The ability to normalize the radar signal's amplitude in our problem setting is explained in Appendix B.3.

5. GRT Model: The GRT model operates under the Born approximation, as stated in Section 3. Other approximations, such as the Kirchhoff approximation, also simplify Maxwell’s equations, which are the accepted "adequate" model for electromagnetic waves. The imperfections in reconstructions from AEDT simulations can partially be attributed to these approximations. However, GRT and its variants are widely used in modeling wave propagation, especially in radar signal processing (e.g., Xia et al., 2016; Ding et al., 2019; Zhang and Pi, 2013).

6. Voxel and Radar Position Tracking: The positions of voxels and the radar can be tracked because they share a unified coordinate system.

7. Granularity: Granularity refers to the resolution used to discretize the scene and prepare the data. It works the same way for SIREN and the normalized version of RIFT. We clarified this point in the updated manuscript in the second paragraph of Section 3.1.

8. Details of Lines 188–193 in the Previous Submission: The details corresponding to lines 188–193 in the previous submission are in Appendix B.3. Due to the 10-page limit, we were unable to include this explanation in the body of the paper.

We hope our responses address your concerns and contribute to a potential improvement in your evaluation of our work.

Best regards, Authors of Submission 12994 (Removed the reference for character limit, will provide in the next reply.)

Dear Reviewer dWXL,

We sincerely appreciate your review and valuable feedback.

Based on the weaknesses you pointed out, we made changes to the manuscript to improve the overall quality and credibility of the work.

Here are the measures we took to address the weaknesses you mentioned:

1. Although we did not have access to a real-world radar dataset, we used commercial simulation software “Ansys Electronics Desktop 2023 R1” (referred to as “AEDT”), which is based on ray tracing and incorporates most of the effects encountered in real radar imaging tasks. Provided the reconstruction was not performed at very high resolution, our method outperformed the traditional least-squares-based radar imaging algorithm. Using scene rendering from the AEDT-generated data, we are confident in stating that we provided a first-order emulator of a scene with a significantly smaller data footprint.

2. We provided a code example (please refer to the general reply) and further elaboration in Appendix B.6 on the choice and structure of the metrics.

3. Indeed, hyperparameter tuning is challenging, especially when reconstructing scenes generated by AEDT. To address this, we added Appendix B.7 to discuss the thought process for tuning the hyperparameters.

Here are the point-by-point answers to your questions:

1. Generating data from our forward models takes little time, as the GRT is a first-order estimation of the mapping from a scene to radar signals with no occlusion considered. Despite its simplicity, GRT is still widely used in radar imaging. For example, generating a scene with extents of 10m by 10m by 10m, a granularity of 0.2m, and 100 frequency points in the frequency band takes 7 minutes and 37 seconds on a graphics card, while commercial simulation takes 4 to 8 hours (depending on the ray tracing complexity). The difference in data generation speed primarily stems from the complexity of the forward model.

2. Typically, scene reconstruction from radar signals is achieved using ordinary least squares (OLS) methods. Without delving too deeply into least squares methods, the simplest explanation for RIFT’s superior performance is that the representation power of neural networks (NN) is significantly better than that of linear models. Additionally, least squares require considerable time due to the scale of the problem. The matrix we effectively invert is a 2D matrix with dimensions equal to (number of frequency samples × number of T/R pairs × number of viewpoints) by (number of voxels used to discretize the scene). This matrix can easily reach hundreds of GB in size, whereas the RIFT model checkpoint never exceeds 2MB. Thus, in addition to requiring less data to reconstruct the scene, RIFT also has smaller RAM requirements compared to the OLS baseline we used (though we did not experiment with other OLS solvers and cannot generalize this claim to all OLS solvers).

3. The analogy we would like to draw is as follows: m-SSIM and t-IoU are similar to metrics used in image segmentation. For example, if the segmentation is perfect, the inferred bounding box exactly aligns with the ground truth. m-SSIM measures how closely the reconstructed shape resembles the actual object, while t-IoU represents the IoU of the bounding boxes. Meanwhile, the p-RMSE of the radar signal is analogous to the loss function in NeRF (Mildenhall et al., 2020), which measures the error in the perceived signal (radar signal for RIFT and images for NeRF). The radar signal can be visualized as images of the scene using the signal processing techniques mentioned in this work (Na et al., 2006).

We hope that our responses address your concerns and contribute to a potential improvement in your evaluation of our work.

Best regards, Authors of Submission 12994

References:

1. Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. NeRF: Representing scenes as neural radiance fields for view synthesis. CoRR, abs/2003.08934, 2020. URL https://arxiv.org/abs/2003.08934.
2. Yibo Na, Yilong Lu, and Hongbo Sun, "A Comparison of Back-Projection and Range Migration Algorithms for Ultra-Wideband SAR Imaging," Fourth IEEE Workshop on Sensor Array and Multichannel Processing, 2006., Waltham, MA, USA, 2006, pp. 320-324, doi: 10.1109/SAM.2006.1706146.

I am very grateful for your detailed reply and the efforts you have made in revising the manuscript. I have carefully considered your responses to the concerns I raised. It is evident that you have taken the review process seriously and have made reasonable attempts to address the identified weaknesses. After reviewing your responses, I find that they have enhanced my understanding of the work. Overall, my original assessment of the paper persists.

Dear Reviewer cpE5,

We sincerely appreciate your review and valuable feedback.

Based on the weaknesses you pointed out, we have made changes to the manuscript to address the presentation issues you mentioned and to improve the overall quality of the work. In the supplemental materials, we have provided the code example used to generate the benchmarks, along with detailed comments.

Here are the measures we took to address the weaknesses you mentioned:

1. Please refer to the overall comment for the changes made to improve the presentation of the paper (including the correction of typos). Additionally, in the supplemental materials, we included all vector graphics used in generating the figures. We hope these supplemental materials further enhance the readability of our work.

2. We used the commercial simulation software "Ansys Electronics Desktop 2023 R1" (referred to as “AEDT”), which is based on ray tracing and incorporates most of the effects encountered in real radar imaging tasks. In Section 4.3, we included a case study of reconstruction using AEDT data. Although the scene remains simplistic, the ray tracing forward generation can be considered as close to real radar data as possible, and we hope this supplemental section further strengthens the soundness of our work.

Here are point-by-point answers to your questions (if applicable):

1. In the update, a paragraph was omitted because the statement does not apply to reproducing the scene generated by the AEDT proxy of a real-world scene. Please let us know if you are still interested in the details of accumulating gradient descent, and we would be happy to provide further explanation.

2. We relocated Figure 1. It was originally intended to serve as a teaser figure, but multiple reviewers expressed dissatisfaction with its placement.

3. We only mentioned the result of Figure 3 corresponding to Table 1. We added a brief discussion of it.

4. We corrected the typos you mentioned.

We hope that our responses address your concerns and contribute to a potential improvement in your evaluation of our work.

Best regards, Authors of Submission 12994

Dear Reviewer cpE5,

We appreciate your response.

In a new comment to reviewer zohP, we have provided some details about 1. The implementation and the difference between radar imaging and optical imaging, and 2. Our justification on the reliability of the simulation tool we use. in the second reply to reviewer zohP. We believe this additional information can provide a different perspective on our work.

We hope our comment can provide more useful information.

Best, Authors of Submission 12994