Inverse Design of Microstrip Antennas Based on Deep Learning

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper titled „Inverse Design of Microstrip Antennas Based on Deep Learning” presents a microstrip antenna optimization process using deep learning algorithm. The paper introduces and describes convolutional neural network, and binary particle swarm optimization applied for antenna design.

Overall, the paper is well-written and organized, but the results are difficult to evaluate, because lack of manufacturing and measuring the antenna.

My main observation and questions is the following:

1. The printed board thickness (2.5mm) of the antenna is too large compared to similar designs. What is the reason of choosing that dimension to 2.5mm.
2. The substrate loss has been neglected, or at least not reported, but that parameter is also important for calculating the antenna efficiency.
3. The antenna gain, directivity and efficiency is not evaluated.
4. It is not clear on Fig. 9.a that the antenna patch and feeding line are in the same plane.
5. You wrote: „The radiating patch and the feed line is printed on the top layer.”, which means for me that these are in the same plane.
6. You wrote: „The patch is divided into a 10×10 grid, where each pixel...”, „The pixel size is set to 32×32 mm”. What is the size of the patch? Based on the previous sentences the antenna patch size is 32x32cm, which would be unacceptable size for the working frequency range.

Without manufacturing and measuring the antenn, the article does not demonstrate applicability.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents an interesting and timely approach to automating microstrip antenna design using a combination of pixelated antenna modeling, a Convolutional Neural Network (CNN) as a surrogate for electromagnetic simulations, and Binary Particle Swarm Optimization (BPSO) for the inverse design process. The authors aim to generate antenna structures from specified performance targets, specifically focusing on S-parameters. The paper is generally well-structured, and the methodology is explained in a step-by-step manner. The results for the dual-band antenna design example are encouraging. However, some further clarification and revision are needed to strengthen the manuscript:

- The term "deep-CNN" is used without clear justification for its depth. A brief discussion on why this architecture was chosen over simpler CNNs would be helpful.

- The dataset contains only 12.6% resonant samples. The authors should discuss how this imbalance was addressed during training.

- The manuscript states that the radiating patch is discretized into a 10×10 binary matrix, and the pixel size is set to 32×32 mm. This would result in an overall radiating patch size of approximately 320×320 mm (excluding the 0.5 mm overlap effect for simplicity in this comment). For the targeted frequency range of 2-4 GHz (with a design example at 2.8 and 3.7 GHz ), an antenna of this physical size (roughly 32cm×32cm) seems unusually large. Microstrip antennas in this frequency band are typically much smaller to be "ideal for integration with modern portable devices" as mentioned in the introduction. Please clarify if this dimension is correct. If so, discuss the implications for practical applications. If incorrect, please provide the correct pixel dimensions and overall antenna size.

- There is a significant discrepancy between the textual description of the CNN architecture in Section 2.2.2 and the depiction in Figure 3.

• The text states: "Convolutional Layers: 10 blocks with kernel sizes decreasing from 5×5 to 2×2, (5→5→4→4→3→3→3→2→2→2, channel numbers varying from 32 to 128..." This description is unclear. Does "10 blocks" mean 10 convolutional layers? The sequence "(5 5 4→4→3 3→3→2→2 2)" is also confusing. Figure 3, however, only shows three convolutional layers with kernel sizes 5×5, 3×3, and 2×2, and channel numbers 32, 128, and 64 respectively.
• The text states: "Fully Connected Layers: 4 layers (500→200→50→50 neurons)". Figure 3 shows two fully connected layers, each with 512 neurons, followed by an output layer of 50 neurons.

These inconsistencies are critical and must be rectified. The exact architecture used needs to be clearly and consistently described in both the text and the figure to ensure the reader's understanding and the reproducibility of the work.

- In Section 2.2.1, it's mentioned that "A sample is labeled 'resonant' if it has at least two consecutive frequency points with S11​<−10dB". Figure 2 then shows "The distribution of the resonant frequency of the antenna in the dataset". How is a single "resonant frequency" determined for a sample that meets this criterion across two consecutive points? Is it the first point, the midpoint of the two, an average, or the point with the lowest S11​? This detail should be clarified.

- The CNN is trained on a very specific configuration (fixed feedline, 10×10 patch, 2–4 GHz). A discussion is needed on how well this method generalizes to:

• Different frequency bands.
• Different pixel resolutions (e.g., 20×20).
• Varying substrate properties.

Otherwise, the method may be seen as case-specific.

- Figure 9b appears to be a validation of the BPSO-derived design against full-wave simulation, not a comparison between different algorithms. Please correct the caption to accurately reflect the its content.

- The radiation patterns (Figure 10) are presented but not discussed in detail. How do they compare to conventional designs? Are there trade-offs in gain or efficiency?

- The manuscript clearly states the design objective was a dual-band antenna operating at 2.8 GHz and 3.7 GHz. However, the presented S11 results in Figure 9b for the BPSO-optimized antenna show resonant frequencies closer to 2.6 GHz and approximately 3.15-3.2 GHz. Consistently, the radiation patterns in Figure 10 are provided at 2.6 GHz and 3.15 GHz. While these results accurately characterize the performance of the antenna structure ultimately obtained through the inverse design, they indicate a notable deviation from the initial target operating frequencies. The authors should address this discrepancy, perhaps by discussing the reasons for the shift or the achieved performance in relation to the original goals. This clarification would strengthen the evaluation of the proposed inverse design framework's accuracy in meeting specific performance targets.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper proposes a deep learning-based inverse design framework for microstrip antennas, integrating pixelated modeling, CNN-based forward prediction, and the BPSO algorithm. However, several issues warrant attention:

1. ​The Abstract does not adequately detail the operational workflow or highlight the advantages of the proposed methodology. Clarifying these aspects is recommended.
2. ​The machine learning model in this study was trained on a substantial dataset of 150,000 simulation samples. While this large-scale dataset ensures model robustness, it raises an important question: If key design parameters (e.g., substrate dimensions, dielectric constant, or patch geometry) are modified, would retraining the model require an equally large dataset? If so, the authors should explicitly address the method's adaptability and scalability across different application scenarios, particularly regarding the trade-off between model accuracy and computational efficiency.
3. ​Figure 1 fails to provide a clear illustration of the antenna's ground plane structure.
4. ​Given the maturity of MATLAB-HFSS/CST co-simulation interfaces, the authors should evaluate whether the current workflow—requiring massive training data—could be streamlined. Specifically, could the simulation results be directly utilized as fitness values for structural optimization, bypassing the machine learning surrogate model? A detailed discussion on the necessity and advantages of the machine learning component in this optimization framework would strengthen the methodological contribution.
5. ​The description pertaining to Figure 3 (lines 116-119) appears inconsistent with the figure's content.
6. ​Section 3 necessitates a more detailed explanation of the BPSO-based inverse design workflow, explicitly illustrating how the CNN surrogate model proposed in Section 2 is integrated and utilized within this process.
7. ​The fitness function currently does not incorporate key radiation performance parameters. Although the final optimized design demonstrates good radiation patterns at both resonant frequencies (Fig. 10), the generalizability of this result requires further validation. The authors should provide additional discussion on how radiation performance is inherently guaranteed during the optimization process.
8. The impact of weight coefficients in the fitness function on convergence behavior and optimization accuracy needs further clarification. The authors are encouraged to analyze the relationship between weight selection and convergence speed/solution quality through parametric sensitivity studies.
9. Fabrication and measurement of the designed antenna prototype are highly recommended. Presenting these experimental results would provide crucial empirical validation for the effectiveness of the proposed methodology.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have modified the article in the light of these comments, so it is acceptable for publication.

Author Response

Dear  Reviewer,      

      We are extremely grateful for your thorough review and constructive feedback, which have been instrumental in enhancing the manuscript. Your confirmation that the revisions address the concerns is highly appreciated.   Thank you for your guidance throughout this process.

 Sincerely,

Guang-Hua Sun

Reviewer 3 Report

Comments and Suggestions for Authors I have one more small question. In Figure 1b, the feed line and the radiation patch are shown on the same plane, which is confusing. Please have the author check if there are any errors in the drawing of the picture.

Author Response

Dear Reviewer,  

    Thank you for pointing out the confusion in Figure 1b. We have re-evaluated the drawing and confirmed that the feed line and radiating patch are correctly depicted on the same plane. To enhance clarity, we have revised the sentence in Line 88: "The radiating patch and the feed line is printed on the top layer (the same plane).".  

     We appreciate your attention to detail, which helps improve the manuscript’s clarity.

Best regards,
Guang-Hua Sun