Generalized Fractional Ambiguity Function and Its Applications

The ambiguity function (AF) is an essential time-frequency analysis tool to analyze the radar waveform properties in radar applications. It can be used effectively and reliably to analyze properties like the peak-to-side-lobe ratio, time delay resolution, Doppler resolution and tolerance characteristic. However, it fails to analyze higher-order chirp waveforms and is unable to estimate their parameters. To solve this problem, a generalized time-frequency transform-based generalized fractional AF (GFAF) and generalized fractional Wigner–Ville distribution (GFWVD) are proposed. GFAF is also a generalization of the Fourier transform-based ambiguity function and the fractional Fourier transform-based ambiguity function. The uncertainty principle for GFAF and GFWVD is derived. Examples are presented to demonstrate the effectiveness of GFAF in analyzing cubic chirp waveforms and estimating parameters of multicomponent cubic chirps. The superiority of GFAF is demonstrated by comparing the mean square error to Cramer–Rao lower bound and high-order ambiguity function under different input-signal-to-noise ratio conditions. The robustness is demonstrated by comparing the signal-to-noise ratio gain to that of the time domain-matched filtering and other ambiguity functions. Finally, fourth-order parameters of a real bat echolocation signal are estimated.