多准则联合的频谱兼容波形快速优化方法

doi:10.12305/j.issn.1001-506X.2025.04.02

摘要/Abstract

摘要：

频谱兼容波形利用多段离散寂静带宽合成大带宽, 在满足带宽要求的同时有效对抗频域密集干扰。为了抑制频谱兼容波形的峰值旁瓣水平, 提出一种低峰值旁瓣频谱兼容波形设计方案。所提方案综合考虑波形的自相关峰值旁瓣性能和抗干扰性能, 构建加权目标函数。在波形恒模约束下, 该问题为非确定多项式难(non-deterministic polynomial-hard, NP-hard)问题。为此, 首先利用指数对数平滑技术逼近目标函数, 进而提出基于快速傅里叶变换的共轭梯度(conjugate gradient method based on fast Fourier transformation, CGFFT)法求解该问题。此外, 波形设计中需要根据性能指标要求选择合适的加权值, 为此提出一种加权值自适应确定方法, 最后通过数值仿真验证了所提方法的有效性。

关键词: 频谱兼容波形, 峰值旁瓣性能, 加权目标函数, 共轭梯度法

Abstract:

The spectrally compatible waveform uses multiple discrete silent bandwidths to synthesize a large bandwidth, which meets the bandwidth requirement and effectively combats dense interference in the frequency domain. In order to suppress the peak sidelobe level of the spectrally compatible waveform, a low peak sidelobe spectrally-compatible waveform design scheme is proposed. The proposed scheme comprehensively considers the autocorrelation peak sidelobe performance and anti-interference performance of the waveforms, and constructs a weighted objective function, which is an non-deterministic polynomial-hard (NP-hard) problem under the constant mode constraint of the waveforms. To this end, the objective function is first approximated using exponential logarithmic smoothing technique, and then the conjugate gradient method based on fast Fourier transformation (CGFFT) is proposed to solve the problem. In addition, the waveform design needs to select the appropriate weighting value according to the requirements of the performance index, and this paper proposes an adaptive determination method of the weighting value. Finally, the effectiveness of the proposed method is verified by numerical simulation.

Key words: spectrally compatible waveform, peak sidelobe level, weighted objective function, conjugate gradient method

中图分类号:

TN974

贾朝波, 于雷, 位寅生. 多准则联合的频谱兼容波形快速优化方法[J]. 系统工程与电子技术, 2025, 47(4): 1036-1047.

Zhaobo JIA, Lei YU, Yinsheng WEI. Fast optimization method for multi-criteria joint spectrally compatible waveform[J]. Systems Engineering and Electronics, 2025, 47(4): 1036-1047.

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p值	WPSL/dB
100	-20.089 7
1 000	-23.330 3
10 000	-24.186 0

算法	WPSL/dB	阻带能量P_out
CGFFT, λ=0.9	-23.669 0	3.939 0×10^－4
CGFFT, λ=0.99	-23.832 2	0.005 0
CGFFT, λ=0.999	-23.975 1	0.053 2
SCAN	-11.681 0	0.031 6
MM-WPSL	-22.508 1	0.006 0

算法	WPSL/dB	阻带能量
CGFFT, λ=0.9	-22.895 8	8.157 9×10^－4
CGFFT, λ=0.99	-23.047 4	0.007 9
CGFFT, λ=0.999	-23.200 1	0.073 8
SCAN	-12.235 8	0.078 9
MM-WPSL	-21.099 6	0.009 5

λ	WPSL/dB	P_out/10^-4
0.8	-23.576 2	1.521 7
0.9	-23.618 0	2.220 8
0.95	-23.628 0	5.586 0
0.99	-23.871 5	29
0.999	-24.150 3	363

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