基于自相关函数的SRSF信号感知矩阵优化方法

根据随机步进频率(random stepped-frequency, RSF)信号特征，结合感知矩阵优化理论，提出了一种基于自相关函数的稀疏RSF (sparse RSF，SRSF)信号感知矩阵优化方法. 首先，在构建稀疏重构模型的基础上，给出了SRSF信号波形参数与感知矩阵构造方式的内在联系；然后，研究了感知矩阵互相关系数矩阵与信号自相关函数（模糊函数的零多普勒切面）的关系，得出在特定条件下两者等价的结论，进而将二维感知矩阵优化问题转化为一维自相关函数的波形优化设计问题；最后，利用基于自相关函数最大旁瓣与均值旁瓣联合约束的波形优化方法对上述结论进行了验证. 仿真实验验证了感知矩阵互相关系数与信号自相关函数的关系，且通过对波形的设计，实现了优化感知矩阵、提升信号稀疏重构性能的目的.

A sensing matrix optimization method for sparse random stepped-frequency signal based on autocorrelation function

Based on the theory of sensing matrix optimization and the characteristics of step frequency waveform, this paper proposes a sensing matrix optimization method for sparse random step frequency signal based on autocorrelation function. Firstly, on the basis of constructing sparse reconstruction model, the internal relationship between the waveform parameters of sparse random step frequency signal and the construction mode of sensing matrix is given. Secondly, the relationship between the mutual coherence matrix and the autocorrelation function matrix of signal is analyzed, and the conclusion that under specific conditions, these two matrices are the same. Therefore, the optimal design of sensing matrix is transformed into the optimal design of sparse random stepped frequency signal based on autocorrelation function. Finally, a sparse waveform design method based on the joint constraint of the maximum and average sidelobes of the autocorrelation function is proposed. Simulation experiments verify the relationship between the mutual coherence matrix and the autocorrelation function matrix of signal, and through waveform design, the sensing matrix optimization and the improving performance of signal sparse recovery are realized.