基于改进的模拟退火算法的频谱受限序列设计

Spectrum Constrained Sequence Design Based on Modified Simulated Annealing Algorithm

电磁频谱的广泛应用和有限的频谱资源决定了频谱受限序列设计在军事和通信领域的重要地位。本文在低相关要求的基础上引入了频谱约束和能量约束,提出基于改进的模拟退火算法的全局算法,用于联合优化频谱受限序列的非周期自相关和峰均功率比,首先利用凸优化算法搜索任意单个频谱受限序列的最优功率谱,即最优频域幅度,再设计合适的目标函数,固定频域幅度,以频域序列的相位为自变量,利用提出的算法搜索最优相位。并进一步搜索了具有良好非周期相关特性的频谱受限序列集,数值实验表明,该算法是快速收敛且有效的,设计的频谱受限序列具有近似期望低、非周期自相关特性和低峰均功率比特性,设计的频谱受限序列集具有良好非周期自相关和互相关特性,对任意频谱约束都具有普适性。

The wide application of electromagnetic spectrum and the limited spectrum resources contribute to the important position of spectrum constrained sequence design in military and communication fields.This paper introduces spectrum and energy constraints on the basis of low correlation requirements and proposes a global algorithm based on a modified simulated annealing algorithm to jointly optimize the aperiodic autocorrelation and the peak-to-average power ratio of spectrum constrained sequence.First of all,the convex optimization algorithm is adopted to search the optimal power spectrum of any single spectrum constrained sequence,namely the optimal frequency domain.Then,the optimal phase is searched with the aid of the proposed algorithm after designing appropriate objective function,fixing the frequency domain amplitude and employing the frequency domain sequence as the independent variable.In addition,the spectrum constrained sequence with good aperiodic correlation characteristics is searched.The numerical experiments show that the algorithm is rapidly converged and efficient;the designed spectrum constrained sequence is characterized by low approximate expectation,aperiodic autocorrelation and low peak-to-average power ratio;the designed spectrum constrained sequences are universal to arbitrary spectrum constraints for its good aperiodic autocorrelation and crosscorrelation.