Research on resolution between multi-component LFM signals in the fractional Fourier domain

Abstract

When the initial frequencies and chirp rates of multi-component linear frequency modulation (LFM or chirp) signals are close, the signals may not be distinguished in the fractional Fourier domain (FRFD). Consequently, some signals cannot be detected. In this paper, first, the spectral distribution characteristics of a continuous LFM signal in the FRFD are analyzed, and then the spectral distribution characteristics of a LFM signal in the discrete FRFD are analyzed. Second, the critical resolution distance between the peaks of two LFM signals in the FRFD is deduced, and the relationship between the dimensional normalization parameter and the distance between two LFM signals in the FRFD is also deduced. It is discovered that selecting a proper dimensional normalization parameter can increase the distance. Finally, a method to select the parameter is proposed, which can improve the resolution ability of the fractional Fourier transform (FRFT). Its effectiveness is verified by simulation results.