周期分数阶傅里叶变换域多分量LFMCW信号间的分辨研究

Resolution on Multi Component LFMCW Signals in Periodic Fractional Fourier Transform Domain

周期分数阶傅里叶变换(Periodic Fractional Fourier Transform,PFRFT)是针对线性调频连续波(Linear Frequency Modulated Continuous Wave,LFMCW)信号的最佳检测方法,主要研究了PFRFT域中多分量LFMCW信号的分辨问题。通过对LFMCW信号在周期分数阶域的频谱特征,以及离散PFRFT计算条件下的频谱分布特征进行分析,推导了两个LFMCW信号在PFRFT域的临界分辨距离,得出临界分辨距离与量纲归一化因子有关的结论。针对PFRFT对多分量LFMCW信号的分辨问题,提出了一种综合优化的量纲归一化因子选择方法,仿真结果验证了该方法的有效性。

Periodic FRFT is the best detection method for linear frequency modulated continuous wave(LFMCW) signals. This paper mainly studies the resolution of multi-component LFMCW signals in periodic fractional domain. By analyzing the spectrum characteristics of LFMCW signals in the periodic fractional domain and the spectrum distribution characteristics of LFMCW signals in the discrete period FRFT calculation, the critical resolution distance of two LFMCW signals in the periodic FRFT domain is derived, and it is found that the critical resolution distance is related to the dimensional normalization factor. In order to improve the resolution of periodic FRFT to multi-component LFMCW signals, a comprehensive optimization method of dimension normalization factor selection is proposed. The simulation results verify the effectiveness of this method.