Joint Design of Transmitting Waveform and Receiving Filter via Novel Riemannian Idea for DFRC System
Abstract
:1. Introduction
2. System Model
2.1. Communication Model
2.2. Detection Model
3. Optimization Modeling of Radar and Communication Integrated System
4. Waveform Optimization Algorithm
- (1)
- Faster convergence speed: The second-order conjugate gradient algorithm, utilizing second-order derivative information, could more accurately determine the search direction and step size compared with the first-order conjugate gradient one, resulting in better results in the same number of iterations.
- (2)
- More effective optimization for high-dimensional data: The first-order conjugate gradient algorithm may have a slow convergence speed when optimizing high-dimensional data, while the second-order conjugate gradient algorithm can better overcome this problem.
- (3)
- Stronger numerical stability: The second-order conjugate gradient algorithm can better avoid numerical instability, which is particularly prominent in optimizing high-dimensional data.
- (4)
- Fewer iterations: Due to faster convergence, the second-order conjugate gradient algorithm typically requires fewer iterations to achieve the same optimization effect, which is particularly important for optimizing large-scale data.
Algorithm 1: The Manifold RIASCG for DFRC Waveform Design. |
Input: weight factor . Output: . |
While do |
1. Compute . 2. Compute the eigenvalue decomposition of , set the searching interval as [,], where is a searching upper-bound. 3. Find the optimal solution to (22) using golden-section search. 4. Compute . 5. Once the global minimizer is obtained, given its separability property, it can be employed as the reference waveform for the similarity constraint, denoted as . |
6. Compute according to (29). |
7. Compute according to (24). |
8. Compute the improved Armijo back-tracking line-search parameter , is the smallest non-negative integer satisfying |
9. Perform the projection step . 10. Obtain according to (25). 11. . |
End while Compute according to (26). |
5. Numerical Result
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Algorithm | ||||
---|---|---|---|---|
RIASCG | 0.6875 s | 2.7031 s | 14.1719 s | 100.0785 s |
RCG | 4.3751 s | 9.9843 s | 188.2811 s | 709.3284 s |
RCG-Armijo | 0.8281 s | 3.6718 s | 40.1406 s | 232.0167 s |
MM | 6.7968 s | 14.4375 s | 328.3755 s | 2562.1734 s |
MM-SQUAREM | 1.5937 s | 5.5156 s | 113.8751 s | 630.3911 s |
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Zhao, Y.; Zhao, Z.; Tong, F.; Sun, P.; Feng, X.; Zhao, Z. Joint Design of Transmitting Waveform and Receiving Filter via Novel Riemannian Idea for DFRC System. Remote Sens. 2023, 15, 3548. https://doi.org/10.3390/rs15143548
Zhao Y, Zhao Z, Tong F, Sun P, Feng X, Zhao Z. Joint Design of Transmitting Waveform and Receiving Filter via Novel Riemannian Idea for DFRC System. Remote Sensing. 2023; 15(14):3548. https://doi.org/10.3390/rs15143548
Chicago/Turabian StyleZhao, Yinan, Zhongqing Zhao, Fangqiu Tong, Ping Sun, Xiang Feng, and Zhanfeng Zhao. 2023. "Joint Design of Transmitting Waveform and Receiving Filter via Novel Riemannian Idea for DFRC System" Remote Sensing 15, no. 14: 3548. https://doi.org/10.3390/rs15143548
APA StyleZhao, Y., Zhao, Z., Tong, F., Sun, P., Feng, X., & Zhao, Z. (2023). Joint Design of Transmitting Waveform and Receiving Filter via Novel Riemannian Idea for DFRC System. Remote Sensing, 15(14), 3548. https://doi.org/10.3390/rs15143548