Skip to main content
SpringerLink
Log in

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

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. A. Abdeldjalil, L. Nguyen, A. Karim et al., Underdetermined blind separation of nondisjoint sources in the time-frequency domain. IEEE Trans. Signal Process. 55(3), 897–907 (2007)

    Article  MathSciNet  Google Scholar 

  2. S. Assous, L. Linnett, Fourier extension and Hough transform for multiple component FM signal analysis. Digital Signal Process. 9(16), 115–127 (2014)

    MathSciNet  Google Scholar 

  3. J. Bobin, J. Rapin, A. Larue, J.L. Starck, Sparsity and adaptivity for the blind separation of partially correlated sources. IEEE Trans. Signal Process. 63(5), 1199–1213 (2015)

    Article  MathSciNet  Google Scholar 

  4. P. Bofill, M. Zibulevsky, Underdetermined blind source separation using sparse representations. Signal Process. 81(11), 2353–2362 (2001)

    Article  MATH  Google Scholar 

  5. Z. Chen, X. Geng, F. Yin, A harmonic suppression method based on fractional lower order statistics for power system. IEEE Trans. Ind. Electron. 63(6), 1–1 (2016)

    Google Scholar 

  6. L. Cirillo, A. Zoubir, M. Amin, Parameter estimation for locally linear FM signals using a time-frequency Hough transform. IEEE Trans. Signal Process. 56(9), 4162–4175 (2008)

    Article  MathSciNet  Google Scholar 

  7. CWRU Bearing Data Center. http://csegroups.case.edu/bearingdatacenter/pages/download-data-file

  8. A. Gualandi, E. Serpelloni, M.E. Belardinelli, Blind source separation problem in GPS time series. J. Geod. 90(4), 323–341 (2016)

    Article  Google Scholar 

  9. A. Guo, X. Li, C. Samson See, LFM signal detection using LPP-Hough transform. Signal Process. 91, 1432–1443 (2011)

    Article  MATH  Google Scholar 

  10. J. Han, Q. Wang, K. Qin, The non-stationary signal of time-frequency analysis based on fractional Fourier transform and Wigner–Hough transform. Lect. Notes Electrical Eng. 237(10), 1047–1054 (2014)

    Article  Google Scholar 

  11. R. Kulkarni, P. Rastogi, Simultaneous measurement of in-plane and out-of-plane displacements using pseudo Wigner–Hough transform. Opt. Express 22(7), 8703–8711 (2014)

    Article  Google Scholar 

  12. H. Li, Y. Zhao, Z. Cheng, D. Feng, Correlated LFM waveform set design for MIMO radar transmit beampattern. IEEE Geosci. Remote Sens. Lett. 14, 1–5 (2017)

    Article  Google Scholar 

  13. L. Li, T.S. Qiu, D.R. Song, Parameter estimation based on fractional power spectrum under alpha-stable distribution noise environment in wideband bistatic MIMO radar system. Int. J. Electron. Commun. 67(67), 947–954 (2013)

    Article  Google Scholar 

  14. L. Li, T. Qiu, X. Shi, Parameter estimation based on fractional power spectrum density in bistatic MIMO radar system under impulsive noise environment. Circuits Syst. Signal Process. 35(9), 3266–3283 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  15. L. Li, T. Qiu, Parameter estimation based on fractional lower order statistics and fractional correlation in wideband bistatic MIMO radar system. J. Syst. Palaeontol. 4(3), 269–278 (2014)

    Google Scholar 

  16. N. Li, C.W. Qu, F. Su, D.F. Ping, A new mixed LFM signal recognition method. J. Signal Process. 26(2), 286–290 (2010)

    Google Scholar 

  17. N. Linh-Trung, A. Belouchrani, K. Abed-Meraim, B. Boashash, Separating more sources than sensors using time-frequency distributions. J. Appl. Signal Process. 17, 2828–2847 (2005)

    MATH  Google Scholar 

  18. X. Liu, C. Sun, Y. Yang, J. Zhuo, High-range-resolution two-dimensional imaging using frequency diversity multiple-input-multiple-output sonar. Iet Radar Sonar Navig. 10(5), 983–991 (2016)

    Article  Google Scholar 

  19. F. Liu, H.F. Xu, D.P. Sun, Feature extraction of symmetrical triangular LFMCW signal using Wigner–Hough transform. J. Beijing Inst. Technol. 18(4), 478–483 (2009)

    Google Scholar 

  20. J. Long, H. Wang, Parameter estimation and time-frequency distribution of fractional lower order time-frequency auto-regressive moving average model algorithm based on \(S\alpha S\) process. J. Electron. Inf. Technol. 38(7), 1710–1716 (2016)

    Google Scholar 

  21. J. Long, H. Wang, D. Zha, Fractional low-order adaptive time-frequency distribution based on stable distribution noise. Comput. Eng. 18(9), 81–83 (2011)

    Google Scholar 

  22. J. Long, H. Wang, D. Zha, EEG-MUSIC source localization in \(\alpha \) stable noise environment. Comput. Eng. Appl. 49(2), 122–125 (2013)

    Google Scholar 

  23. J. Long, H. Wang, D. Zha, Evoked potential blind extraction based on fractional lower order spatial time-frequency matrix. J. Biomed. Eng. 32(2), 269–274 (2015)

    Google Scholar 

  24. F. Lu, Z. Huang et al., Underdetermined blind source separation (BSS): a time-frequency approach. Chin. J. Electron. 9(39), 2068–2072 (2011)

    Google Scholar 

  25. X. Ma, C. Nikias, Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics. IEEE Trans. Signal Process. 44(11), 2669–2687 (1996)

    Article  Google Scholar 

  26. M. Ma, Y. Shen, Z. Kong, A detection method for LFM signals based on blind source separation and Wigner–Hough transform. J. Proj. Rocket. Misseles Guidance 27(4), 251–253 (2007)

    Google Scholar 

  27. S. Mohamed, A.M. Karim, B. Messaoud, Blind separation of impulsive alpha-stable sources using minimum dispersion criterion. IEEE Signal Process. Lett. 12(4), 281–284 (2005)

    Article  Google Scholar 

  28. S. Mohamed, A.M. Karim, B. Messaoud, Blind separation of impulsive alpha-stable sources using minimum dispersion criterion. IEEE Signal Proc. Lett. 12(4), 281–284 (2005)

    Article  Google Scholar 

  29. G. Qian, P. Wei, H. Liao, Efficient variant of noncircular complex FastICA algorithm for the blind source separation of digital communication signals. Circuits Syst. Signal Process. 35(2), 705–717 (2016)

    Article  MATH  Google Scholar 

  30. S. Redif, S. Weiss, J. Mcwhirter, Relevance of polynomial matrix decompositions to broadband blind signal separation. Signal Process. 134, 76–86 (2017)

    Article  Google Scholar 

  31. X.S. Ren, Y.H. Shen et al., Algorithm for mixing matrix estimation based on time-frequency analysis. J. Signal Process. 4(28), 545–553 (2012)

    Google Scholar 

  32. M. Shao, C. Nikias, Signal processing with fractional lower order moments instable processed and their applications. Proc. IEEE 81(7), 986–1010 (1993)

    Article  Google Scholar 

  33. J. Su, H. Tao, X. Rao et al., Robust multicomponent LFM signals synthesis algorithm based on masked ambiguity function. Digital Signal Process. 44(9), 102–109 (2015)

    Article  Google Scholar 

  34. B. Tang, Parameters estimation and detection of MIMO-LFM signals using MWHT. Int. J. Electron. 103(3), 439–454 (2016)

    Article  Google Scholar 

  35. H. Wang, J. Long, D. Zha, Frequency spectrum estimate based on decomposed FLOC matrix under stable distribution noise. Appl. Mech. Mater. (556–562), 4563–4567 (2014)

    Article  Google Scholar 

  36. H. Wang, J. Long, D. Zha, Pseudo Cohen time-frequency distributions in infinite variance noise environment. Appl. Mech. Mater. (475–476), 253–258 (2014)

    Google Scholar 

  37. H. Wang, J. Long, D. Zha, Modeling and parameter estimation based on FLO-TFMA. Comput. Eng. Appl. 51(20), 178–182 (2015)

    Google Scholar 

  38. Y. Zhang, P. Wang, S. Feng, P. Zhang, Design of adaptive millimeter-wave MIMO systems in rain scattering. IEEE Trans. Veh. Technol. 65(7), 5317–5326 (2016)

    Article  Google Scholar 

  39. H. Zhang, G. Hua, L. Yu, Y. Cai, G. Bi, Underdetermined blind separation of overlapped speech mixtures in time-frequency domain with estimated number of sources. Speech Commun. 89, 1–16 (2017)

    Article  Google Scholar 

  40. A. Zhang, T. Qiu, X. Zhang, Blind signals separation method based on fractional lower order moments. J. Commun. 27(3), 32–35 (2006)

    Google Scholar 

  41. X. Zhu, W. Zhu, B. Champagne, Spectrum sensing based on fractional lower order moments for cognitive radios in \(\alpha \) stable distributed noise. Signal Process. 111, 94–105 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

This work is financially supported by Natural Science Foundation of China (61261046, 61362038), the Natural Science Foundation of Jiangxi Province China (20151BAB207013), the Research Foundation of health department of Jiangxi Province China (20175561), science and technology project of provincial education department of jiangxi (GJJ161083), and science and technology project of Jiujiang university China (2016KJ001, 2016KJ002).

Author information

Authors and Affiliations

  1. College of Electronic and Engineering, Jiujiang University, Jiujiang, 332005, China

    Junbo Long, Peng Li & Huicheng Xie

  2. College of Information Science and Technology, Jiujiang University, Jiujiang, 332005, China

    Haibin Wang

Authors
  1. Junbo Long
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haibin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Huicheng Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Junbo Long.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Long, J., Wang, H., Li, P. et al. A WHT Signal Detection-Based FLO-TF-UBSS Algorithm Under Impulsive Noise Environment. Circuits Syst Signal Process 37, 2997–3022 (2018). https://doi.org/10.1007/s00034-017-0703-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-017-0703-6

Keywords

Search

Navigation