基于KKT最优性条件的频点可控FSK-PSK波形设计算法

doi:10.12305/j.issn.1001-506X.2025.05.12

摘要/Abstract

摘要：

针对频移键控-相移键控(frequency shift keying-phase shift keying, FSK-PSK)波形随机频点编码序列带来的相关性能下降问题, 构建频点可控FSK-PSK波形优化模型, 并从KKT(Karush-Kuhn-Tucker)最优性条件出发, 以最小化自相关积分旁瓣电平(integrated sidelobe level, ISL)为目标函数, 设计一种最优子问题迭代算法进行求解。最后, 通过仿真实验与多目标量子遗传算法(multi-objective quantum genetic algorithm, MoQGA)优化的FSK-PSK波形进行对比, 验证了设计的频点可控FSK-PSK波形在不同子脉冲频点数比下, 自相关旁瓣性能平均改善4.47 dB, 互相关旁瓣也进一步降低。

关键词: 低旁瓣波形, KKT条件, 频移键控-相移键控波形, 频点控制

Abstract:

In response to the degradation of correlation performance in frequency shift keying-phase shift keying (FSK-PSK) waveform due to random frequency point encoding sequences, a model for frequency controllable FSK-PSK waveform optimization is developed. Starting from the Karush-Kuhn-Tucker(KKT) optimality condition, an optimal subproblem iterative algorithm is designed to minimize the autocorrelation integrated sidelobe level(ISL) as the objective function. Finally, through simulation experiments and comparison with the FSK-PSK waveform optimized by multi-objective quantum genetic algorithm(MoQGA), it is verified that the designed frequency controllable FSK-PSK waveform improved the autocorrelation sidelobe performance by an average of 4.47 dB at different sub pulse frequency point ratios, and further reduced the cross-correlation sidelobes.

Key words: low-sidelobe waveform, KKT (Karush-Kuhn-Tucker) conditions, frequency shift keying-phase shift keying (FSK-PSK) waveform, frequency controllable

中图分类号:

TN911.7

吕树肜, 刘思琪, 施慧莉, 张劲东. 基于KKT最优性条件的频点可控FSK-PSK波形设计算法[J]. 系统工程与电子技术, 2025, 47(5): 1495-1506.

Shurong LYU, Siqi LIU, Huili SHI, Jindong ZHANG. Frequency-controllable FSK-PSK waveform design algorithm based on KKT optimality conditions[J]. Systems Engineering and Electronics, 2025, 47(5): 1495-1506.

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参数/优化算法	MoQGA	KKT	KKT-FAC
c_f=10, M=10	-30.224 8	-33.661 2	-33.558 3
c_f=10, M=20	-32.131 6	-35.454 8	-36.392 6
c_f=10, M=30	-33.497 6	-36.611 0	-37.633 9
c_f=20, M=20	-35.307 5	-38.459 6	-38.489 4
c_f=20, M=40	-38.575 8	-40.554 0	-41.456 0
c_f=20, M=60	-39.406 1	-42.089 9	-43.027 0
c_f=30, M=30	-39.622 1	-41.593 3	-41.738 4
c_f=30, M=60	-41.614 5	-43.827 9	-44.542 2
c_f=30, M=90	-43.242 1	-45.281 3	-46.016 3

参数/优化算法	MoQGA	KKT	KKT-FHC
c_f=10, M=10	-30.384 0	-33.623 2	-34.711 3
c_f=10, M=20	-31.824 1	-35.536 7	-36.457 2
c_f=10, M=30	-33.250 3	-36.209 5	-36.466 4
c_f=20, M=20	-35.923 4	-37.809 5	-39.228 1
c_f=20, M=40	-38.249 1	-40.823 7	-41.603 5
c_f=20, M=60	-39.738 0	-42.641 6	-43.132 6
c_f=30, M=30	-39.635 5	-41.744 4	-43.120 0
c_f=30, M=60	-41.774 7	-44.189 2	-45.246 2
c_f=30, M=90	-43.119 0	-45.447 6	-46.018 5

参数/优化算法	MoQGA	KKT	KKT-FAHC
c_f=10, M=10	-30.530 1	-33.676 5	-35.032 9
c_f=10, M=20	-31.787 5	-35.559 6	-37.235 1
c_f=10, M=30	-33.650 5	-36.700 6	-38.229 5
c_f=20, M=20	-35.647 9	-37.650 2	-39.751 3
c_f=20, M=40	-37.855 0	-40.619 7	-42.607 0
c_f=20, M=60	-39.356 6	-42.252 3	-43.735 4
c_f=30, M=30	-39.060 3	-42.002 4	-44.264 5
c_f=30, M=60	-41.835 6	-44.063 8	-45.938 0
c_f=30, M=90	-43.250 2	-45.194 2	-46.433 9