HRRnet: A Parameter Estimation Method for Linear Frequency Modulation Signals Based on High-Resolution Spectral Line Representation
Abstract
:1. Introduction
2. Signal Denoising and High-Resolution Representation of the Time–Frequency Spectrum
3. Design and Parameter Optimization of HRRnet
3.1. Design of HRRnet
3.2. Parameter Optimization Algorithms for HRRnet
4. Simulation Verification and Analysis
4.1. Simulation Parameters
4.2. Analysis of Simulation Results
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Layer Name | Output Dimension | Convolution Kernel Size | Convolution Rate |
---|---|---|---|
Input | 2 × 512 | - | - |
Layer-0 | 32 × 32 | - | - |
Layer-1 | 32 × 32 × 32 | 3 × 3 | 1 |
Layer-2 | 32 × 32 × 32 | 3 × 3 | 2 |
Layer-3 | 64 × 32 × 32 | 3 × 3 | 5 |
MS-FE-3 | 64 × 32 × 32 | 1 × 1/3 × 3 | 1 |
MS-FE-4 | 64 × 32 × 32 | 1 × 1/3 × 3 | 1 |
Layer-4 | 2 × 512 | 1 × 1 | 1 |
Layer Name | Output Dimension | Convolution Kernel Size | Convolution Rate |
---|---|---|---|
Layer-9 | 32 × 32 × 32 | - | - |
Layer-5 | 32 × 32 × 32 | 3 × 3 | 1 |
Layer-6 | 32 × 32 × 32 | 3 × 3 | 2 |
Layer-7 | 64 × 32 × 32 | 3 × 3 | 5 |
MS-FE-3 | 64 × 32 × 32 | 1 × 1/3 × 3 | 1 |
MS-FE-4 | 64 × 32 × 32 | 1 × 1/3 × 3 | 1 |
Layer-8 | 1 × 5120 | 3 × 3 | 1 |
The Number of Training/ Testing Samples | Initial Frequency (Hz) | Frequency Modulation Coefficient (Hz) | Sampling Point Count | Sampling Frequency (Hz) |
---|---|---|---|---|
3000/500 | 15∼20 | 5∼10 | 256 |
Optimizer | Learning Rate | Number of Training Epochs | Validation Method | Learning Rate Decay Strategy |
---|---|---|---|---|
Adam | 0.001 | 100 | 10-fold cross-validation | 0.8 |
Network Name | NRM | DCNN | DnCNN |
---|---|---|---|
Number of Parameters | 4.21 M | 4.35 M | 4.37 M |
Computational Complexity | 122.66 M | 183.9 M | 198.97 M |
Network Name | HRRnet | NRM + CV-CNN | DCNN + CV-CNN |
---|---|---|---|
Number of Parameters | 56.81 M | 277.33 M | 277.47 M |
Computational Complexity | 246.05 M | 1146.11 M | 1207.35 M |
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Fei, S.; Yan, M.; Zhou, F.; Wang, Y.; Zhang, P.; Wang, J.; Wang, W. HRRnet: A Parameter Estimation Method for Linear Frequency Modulation Signals Based on High-Resolution Spectral Line Representation. Electronics 2025, 14, 1121. https://doi.org/10.3390/electronics14061121
Fei S, Yan M, Zhou F, Wang Y, Zhang P, Wang J, Wang W. HRRnet: A Parameter Estimation Method for Linear Frequency Modulation Signals Based on High-Resolution Spectral Line Representation. Electronics. 2025; 14(6):1121. https://doi.org/10.3390/electronics14061121
Chicago/Turabian StyleFei, Shunchao, Mengqing Yan, Fan Zhou, Yang Wang, Peiying Zhang, Jian Wang, and Wei Wang. 2025. "HRRnet: A Parameter Estimation Method for Linear Frequency Modulation Signals Based on High-Resolution Spectral Line Representation" Electronics 14, no. 6: 1121. https://doi.org/10.3390/electronics14061121
APA StyleFei, S., Yan, M., Zhou, F., Wang, Y., Zhang, P., Wang, J., & Wang, W. (2025). HRRnet: A Parameter Estimation Method for Linear Frequency Modulation Signals Based on High-Resolution Spectral Line Representation. Electronics, 14(6), 1121. https://doi.org/10.3390/electronics14061121