Design of Frequency-Hopping Sequence Based on Enhanced Runge Kutta Optimizer

doi:10.19678/j.issn.1000-3428.0067092

Abstract

Abstract:

Frequency-hopping technology has excellent anti-jamming and multiple access networks. Frequency-Hopping Sequence(FHS) is faced with the problems of poor performance index and difficulty in considering multiple indexes in design. Therefore, a design method of FHS based on an Enhanced Runge-Kutta optimizer(ERUN) is proposed. First, an objective function is constructed based on the Hamming correlation, complexity, uniformity, and average frequency-hopping interval of the FHS, and a design model of the FHS suitable for a heuristic optimization algorithm is established. Thereafter, aiming at the slow convergence speed and poor optimization accuracy of the Runge-Kutta optimizer(RUN) in complex optimization problems, the ERUN is proposed. The ERUN uses chaos opposition-based learning to improve the quality of the initial population, obtains a better individual update direction based on the quadratic interpolation method, and helps the population jump out of the local optimum through an adaptive t-distribution perturbation. The test results for the six benchmarks and objective functions demonstrate that ERUN has a faster convergence speed and higher solution accuracy than the three latest RUN variants. The obtained FHS is applied to a frequency-hopping system. The experimental results demonstrate that the Bit Error Rate(BER) of this method is approximately 4% in a fixed jamming environment and does not increase significantly in a changing jamming environment, demonstrating strong anti-jamming ability and complex environmental adaptability.

Key words: anti-jamming, Frequency-Hopping Sequence(FHS), Runge-Kutta optimizer(RUN), quadratic interpolation, adaptive t-distribution

摘要：

跳频技术具有优秀的抗干扰性能和多址组网性能, 跳频序列(FHS)作为其关键, 在设计时面临性能指标差、难以兼顾多指标的问题。提出一种基于增强型龙格库塔优化算法(ERUN)的跳频序列设计方法。利用跳频序列的汉明相关性、复杂度、均匀性和平均跳频间隔构建目标函数, 建立适用于启发式优化算法的跳频序列设计模型。针对龙格库塔优化算法(RUN)在复杂优化问题上收敛速度慢、寻优精度差的问题, 提出增强型龙格库塔优化算法。利用混沌反向学习机制提高初始种群质量, 基于二次插值法得到更好的个体更新方向, 并根据自适应t分布扰动帮助种群跳出局部最优。在6个基准测试函数和目标函数上的测试结果表明, 与RUN的3个最新变体相比, ERUN具有更快的收敛速度和更高的解精度。将得到的跳频序列应用于跳频系统中, 实验结果表明, 该方法在固定干扰环境下误码率为4%左右, 在变化干扰环境下误码率没有明显上升, 展现出了较强的抗干扰能力和复杂环境适应能力。

关键词: 抗干扰, 跳频序列, 龙格库塔优化算法, 二次插值, 自适应t分布

Yiheng ZHANG, Yian LIU, Hailing SONG. Design of Frequency-Hopping Sequence Based on Enhanced Runge Kutta Optimizer[J]. Computer Engineering, 2024, 50(4): 267-276.

张毅恒, 刘以安, 宋海凌. 基于增强型龙格库塔优化算法的跳频序列设计[J]. 计算机工程, 2024, 50(4): 267-276.

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Figures/Tables 19

Fig.1 Probability density curves of different distributions

Fig.2 Frequency-hopping sequence design process based on ERUN

Fig.3 Comparison of f₁ convergence curves

Fig.4 Comparison of f₃ convergence curves

Fig.5 Comparison of f₅ convergence curves

Fig.6 Comparison of f₁₀ convergence curves

Fig.7 Comparison of f₁₂ convergence curves

Fig.8 Comparison of f₁₃ convergence curves

Fig.9 Comparison of objective function convergence curves

Fig.10 Bipolar signal

Fig.11 Signal waveform after pulse-shaping

Fig.12 Signal waveform after frequency hopping

Fig.13 Received signal waveform

Fig.14 Signal waveform after de-hopping

Fig.15 Received signal after matched filtering

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