Hybrid FSK-PSK Waveform Optimization for Radar Based on Alternating Direction Method of Multiplier (ADMM)
Abstract
:1. Introduction
- (1)
- The low sidelobe waveform (LSW) optimization algorithm based on ADMM, i.e., LSW-ADMM, is proposed. Distinctive phase encoding sequences are used for different sub-pulses, which are optimized with the LSW-ADMM algorithm for sidelobe reduction. Compared with the conventional FSK-PSK signals modulated by the classical code sequences, a higher-order of randomness is achieved, which guarantees enhanced anti-jamming capability of the radar system.
- (2)
- To encounter the intra-pulse slice repeater jamming, the ASRJ-ADMM algorithm is proposed. Each sub-pulse of the FSK-PSK signal, which is coded with a distinctive set of phases, performs frequency hopping according to the optimized sequence. By ensuring the orthogonality of the sub-pulses of the FSK-PSK signal, the intra-pulse slice repeater jamming is effectively suppressed.
2. FSK-PSK Hybrid Modulated Signal Model
2.1. Ambiguity Function of the FSK-PSK Hybrid Modulated Signal
2.2. Autocorrelation Function of FSK-PSK Hybrid Modulated Signal
3. Low Sidelobe Waveform Optimization Algorithm Based on ADMM (LSW-ADMM)
3.1. ADMM Algorithm
3.2. LSW-ADMM Optimization Method
4. Anti-Slice-Repeater-Jamming Algorithm Based on ADMM (ASRJ-ADMM)
4.1. Intra-Pulse Slice Repeater Model
4.2. Intra-Pulse Slice Repeater Jamming Suppression Model
4.3. ASRJ-ADMM Optimization Method
5. Computational Complexity Analysis
6. Numerical Experiments
6.1. Optimization of the AF of the FSK-PSK Signal
6.2. Joint Optimization of Intra-Pulse Sub-Pulse Correlation Function
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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LSW-ADMM |
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ASRJ-ADMM |
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K = 2 | K = 4 | K = 8 | |
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FSK-PSK signal | −36.3435 | −35.4542 | −35.2794 |
PSK signal | −28.8652 | −29.2404 | −29.0089 |
K = 2 | K = 4 | K = 8 | |
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Not optimized | −36.3435 | −35.4542 | −35.2794 |
LSW-ADMM | −39.8323 | −39.2367 | −40.2767 |
GA | −36.9693 | −35.7298 | −35.8229 |
Discrete Phase | K = 2 AC-ASL CC-AL | K = 4 AC-ASL CC-AL | K = 8 AC-ASL CC-AL |
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Not optimized | −23.4898 −34.3268 | −23.5395 −33.2408 | −23.0620 −32.9777 |
LSW-ADMM | −27.6087 −37.5398 | −26.8966 −37.0582 | −28.5616 −37.6952 |
LSW-ADMM | 589 s | 647 s | 790 s |
ASRJ-ADMM | 623 s | 765 s | 810 s |
GA | 2305 s | 2465 s | 2725 s |
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Fei, Z.; Zhao, J.; Geng, Z.; Zhu, X.; Zhang, J. Hybrid FSK-PSK Waveform Optimization for Radar Based on Alternating Direction Method of Multiplier (ADMM). Sensors 2021, 21, 7915. https://doi.org/10.3390/s21237915
Fei Z, Zhao J, Geng Z, Zhu X, Zhang J. Hybrid FSK-PSK Waveform Optimization for Radar Based on Alternating Direction Method of Multiplier (ADMM). Sensors. 2021; 21(23):7915. https://doi.org/10.3390/s21237915
Chicago/Turabian StyleFei, Zhiting, Jiachen Zhao, Zhe Geng, Xiaohua Zhu, and Jindong Zhang. 2021. "Hybrid FSK-PSK Waveform Optimization for Radar Based on Alternating Direction Method of Multiplier (ADMM)" Sensors 21, no. 23: 7915. https://doi.org/10.3390/s21237915
APA StyleFei, Z., Zhao, J., Geng, Z., Zhu, X., & Zhang, J. (2021). Hybrid FSK-PSK Waveform Optimization for Radar Based on Alternating Direction Method of Multiplier (ADMM). Sensors, 21(23), 7915. https://doi.org/10.3390/s21237915