线性调频连续波信号的周期分数阶Fourier变换检测与估计

摘要

分数阶Fourier变换(FRFT)对LFM信号具有最优检测能力，但对线性调频连续波(LFMCW)信号的检测与估计是次优的。由于LFMCW信号可视为LFM信号的周期拓展，基于FRFT对LFM信号的能量聚集和相干累积思想，该文提出一种新的信号处理方法周期分数阶Fourier变换，以实现对LFMCW信号的检测和估计。周期分数阶 Fourier 变换的核函数可以与 LFMCW 信号实现最佳匹配，理论分析和仿真实验表明，随着观测时间的增加，可以实现对LFMCW信号的渐进最优估计，具有比FRFT更优的检测性能。%The FRaction Fourier Transform (FRFT) is optimal in the detection and parameter estimation of Linear Frequency Modulation (LFM) signal, but it is suboptimal for Linear Frequency Modulation Continuous Wave (LFMCW). LFMCW signal is a periodic extension of an LFM signal. In virtue of the energy congregation of FRFT for LFM signal and the coherent integrator in signal processing, this paper formulates a new detection and parameter algorithm for LFMCW signal, called the periodic FRFT. The theory analysis and simulation results show the proposed algorithm is asymptotically optimal in the detection and parameter estimation of LFMCW signal along with increasing observation time, and better than traditional FRFT algorithm.