In this paper, a novel method, that employs a fractional Fourier transform and a tuneable Sigmoid transform, is proposed, in order to estimate the Doppler stretch and time delay of wideband echoes for a linear frequency modulation (LFM) pulse radar in an alpha-stable distribution noise environment. Two novel functions, a tuneable Sigmoid fractional correlation function (TS-FC) and a tuneable Sigmoid fractional power spectrum density (TS-FPSD), are presented in this paper. The novel algorithm based on the TS-FPSD is then proposed to estimate the Doppler stretch and the time delay. Then, the derivation of unbiasedness and consistency is presented. Furthermore, the boundness of the TS-FPSD to the symmetric alpha stable ( S α S ) noise, the parameter selection of the TS-FPSD, and the feasibility analysis of the TS-FPSD, are presented to evaluate the performance of the proposed method. In addition, the Cramér⁻Rao bound for parameter estimation is derived and computed in closed form, which shows that better performance has been achieved. Simulation results and theoretical analysis are presented, to demonstrate the applicability of the forgoing method. It is shown that the proposed method can not only effectively suppress impulsive noise interference, but it also does not need a priori knowledge of the noise with higher estimation accuracy in alpha-stable distribution noise environments.
Keywords: LFM pulse radar; alpha stable distribution noise; fractional power spectrum density; parameter estimation; tuneable Sigmoid transform.