A WHT Signal Detection-Based FLO-TF-UBSS Algorithm Under Impulsive Noise Environment

Abstract

Linear frequency modulated (LFM) signal is used to describe radar echo signal, and Wigner–Hough transform (WHT) is a useful detection tool for LMF signals. The noise in radar echo signal has strong pulse under complex environment, which belongs to $$\alpha $$ stable distribution process. The WHT method degenerates under $$\alpha $$ stable distribution environment. Hence, fractional lower-order pseudo-Wigner–Ville distribution (FLO-PWVD) time–frequency method is introduced, and fractional lower-order pseudo-Wigner–Hough transform (FLO-PWHT) method based on the FLO-PWVD method and Hough transform is proposed for the detection of LFM signals. When the LFM signals are overlapped in time domain and generalized signal-to-noise ratio (GSNR) is relatively low, the FLO-PWHT method degenerate, even which cannot work. Therefore, fractional lower-order spacial time–frequency matrix is applied to substitute spacial time–frequency distribution matrix, and a new fractional lower-order spacial time–frequency underdetermined blind source separation (FLO-TF-UBSS) algorithm employing the time–frequency underdetermined blind source separation algorithm (TF-UBSS) is proposed in this paper. Also, we combine the FLO-PWHT method with the FLO-TF-UBSS algorithm and propose a fractional lower-order spatial time–frequency underdetermined blind source separation pseudo-Wigner–Hough transform (FLO-TF-UBSS-PWHT) method. The simulation results show that the FLO-PWHT method is obviously better than the existing PWHT algorithm under $$\alpha $$ stable distribution noise or Gaussian noise environment, which is robust. The FLO-TF-UBSS algorithm can effectively downgrade mean square error of the reconstructed LFM signals, and its performance is better than the existing TF-UBSS and minimum dispersion BSS algorithms. The FLO-TF-UBSS-PWHT algorithm can work well in the cases of time domain overlapping and relatively low GSNR; its performance is better than the FLO-PWHT algorithm, which has certain toughness. Finally, we apply the FLO-PWVD, FLO-TF-UBSS, and FLO-PWHT methods to analyze and extract fault features of the bearing outer race fault signal in DE; the experimental results illustrate their performance superiority.