MAL-Net: Model-Adaptive Learned Network for Slow-Time Ambiguity Function Shaping
Designing waveforms with a Constant Modulus Constraint (CMC) to achieve desirable Slow-Time Ambiguity Function (STAF) characteristics is significantly important in radar technology. The problem is NP-hard, due to its non-convex quartic objective function and CMC constraint. Existing methods typicall...
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MDPI AG
2025-01-01
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| Series: | Remote Sensing |
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| Online Access: | https://www.mdpi.com/2072-4292/17/1/173 |
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| author | Jun Wang Xiangqing Xiao Jinfeng Hu Ziwei Zhao Kai Zhong Chaohai Li |
| author_facet | Jun Wang Xiangqing Xiao Jinfeng Hu Ziwei Zhao Kai Zhong Chaohai Li |
| author_sort | Jun Wang |
| collection | DOAJ |
| description | Designing waveforms with a Constant Modulus Constraint (CMC) to achieve desirable Slow-Time Ambiguity Function (STAF) characteristics is significantly important in radar technology. The problem is NP-hard, due to its non-convex quartic objective function and CMC constraint. Existing methods typically involve model-based approaches with relaxation and data-driven Deep Neural Networks (DNNs) methods, which face the challenge of dataimitation. We observe that the Complex Circle Manifold (CCM) naturally satisfies the CMC. By projecting onto the CCM, the problem is transformed into an unconstrained minimization problem that can be tackled using the CCM gradient descent model. Furthermore, we observe that the gradient descent model over the CCM can be unfolded as a Deep Learning (DL) network. Therefore, byeveraging the powerfulearning ability of DL and the CCM gradient descent model, we propose a Model-Adaptive Learned Network (MAL-Net) method without relaxation. Initially, we reformulate the problem as an Unconstrained Quartic Problem (UQP) on the CCM. Then, the MAL-Net is developed toearn the step sizes of allayers adaptively. This is accomplished by unrolling the CCM gradient descent model as the networkayer. Our simulation results demonstrate that the proposed MAL-Net achieves superior STAF performance compared to existing methods. |
| format | Article |
| id | doaj-art-6b7cbc08e1c2455d8f40c743d1e3e6fd |
| institution | Kabale University |
| issn | 2072-4292 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Remote Sensing |
| spelling | doaj-art-6b7cbc08e1c2455d8f40c743d1e3e6fd2025-01-10T13:20:29ZengMDPI AGRemote Sensing2072-42922025-01-0117117310.3390/rs17010173MAL-Net: Model-Adaptive Learned Network for Slow-Time Ambiguity Function ShapingJun Wang0Xiangqing Xiao1Jinfeng Hu2Ziwei Zhao3Kai Zhong4Chaohai Li5School of Mechanical and Electrical Engineering, Zhongshan Institute, University of Electronic Science and Technology of China, Zhongshan 528400, ChinaYangtze Delta Region Institute, University of Electronic Science and Technology of China, Quzhou 324000, ChinaYangtze Delta Region Institute, University of Electronic Science and Technology of China, Quzhou 324000, ChinaYangtze Delta Region Institute, University of Electronic Science and Technology of China, Quzhou 324000, ChinaYangtze Delta Region Institute, University of Electronic Science and Technology of China, Quzhou 324000, ChinaIntelligent Terminal Key Laboratory of Sichuan Province, Yibin Institute of UESTC, Yibin 644000, ChinaDesigning waveforms with a Constant Modulus Constraint (CMC) to achieve desirable Slow-Time Ambiguity Function (STAF) characteristics is significantly important in radar technology. The problem is NP-hard, due to its non-convex quartic objective function and CMC constraint. Existing methods typically involve model-based approaches with relaxation and data-driven Deep Neural Networks (DNNs) methods, which face the challenge of dataimitation. We observe that the Complex Circle Manifold (CCM) naturally satisfies the CMC. By projecting onto the CCM, the problem is transformed into an unconstrained minimization problem that can be tackled using the CCM gradient descent model. Furthermore, we observe that the gradient descent model over the CCM can be unfolded as a Deep Learning (DL) network. Therefore, byeveraging the powerfulearning ability of DL and the CCM gradient descent model, we propose a Model-Adaptive Learned Network (MAL-Net) method without relaxation. Initially, we reformulate the problem as an Unconstrained Quartic Problem (UQP) on the CCM. Then, the MAL-Net is developed toearn the step sizes of allayers adaptively. This is accomplished by unrolling the CCM gradient descent model as the networkayer. Our simulation results demonstrate that the proposed MAL-Net achieves superior STAF performance compared to existing methods.https://www.mdpi.com/2072-4292/17/1/173waveform designslow-time ambiguity functionconstant moduluscomplex circle manifoldMAL-Net methoddeepearning |
| spellingShingle | Jun Wang Xiangqing Xiao Jinfeng Hu Ziwei Zhao Kai Zhong Chaohai Li MAL-Net: Model-Adaptive Learned Network for Slow-Time Ambiguity Function Shaping Remote Sensing waveform design slow-time ambiguity function constant modulus complex circle manifold MAL-Net method deepearning |
| title | MAL-Net: Model-Adaptive Learned Network for Slow-Time Ambiguity Function Shaping |
| title_full | MAL-Net: Model-Adaptive Learned Network for Slow-Time Ambiguity Function Shaping |
| title_fullStr | MAL-Net: Model-Adaptive Learned Network for Slow-Time Ambiguity Function Shaping |
| title_full_unstemmed | MAL-Net: Model-Adaptive Learned Network for Slow-Time Ambiguity Function Shaping |
| title_short | MAL-Net: Model-Adaptive Learned Network for Slow-Time Ambiguity Function Shaping |
| title_sort | mal net model adaptive learned network for slow time ambiguity function shaping |
| topic | waveform design slow-time ambiguity function constant modulus complex circle manifold MAL-Net method deepearning |
| url | https://www.mdpi.com/2072-4292/17/1/173 |
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