Detection and parameter estimation of multicomponent LFM signal based on the fractional fourier transform



This paper presents a new method for the detection and parameter estimation of multicomponent LFM signals based on the fractional Fourier transform. For the optimization in the fractional Fourier domain, an algorithm based on Quasi-Newton method is proposed which consists of two steps of searching, leading to a reduction in computation without loss of accuracy. And for multicomponent signals, we further propose a signal separation technique in the fractional Fourier domain which can effectively suppress the interferences on the detection of the weak components brought by the stronger components. The statistical analysis of the estimate errors is also performed which perfects the method theoretically, and finally, simulation results are provided to show the validity of our method.


LFM signal parameter estimation fractional Fourier transform 


  1. 1.
    Boashash, B., Estimating and interpreting the instantaneous frequency of a signal, Proc. IEEE, 1992, 80(4): 519–569.Google Scholar
  2. 2.
    Djuric, P. M., Kay, S. M., Parameter estimation of chirp signal, IEEE Trans on ASSP, 1990, 38(12): 2118–2126.CrossRefGoogle Scholar
  3. 3.
    Barbarossa, S., Petrone, V., Analysis of polynomial-phase signals by the integrated generalized ambiguity function, IEEE Trans on SP, 1997, 45(2): 316–327.CrossRefGoogle Scholar
  4. 4.
    Abatzoglou, T. J., Fast maximum likelihood joint estimation of frequency and frequency rate, IEEE Trans. on AES, 1986, 22 (6): 708–715.Google Scholar
  5. 5.
    Peleg, S., Porat, B., Linear FM signal parameter estimation from discrete-time observations, IEEE Trans. on AES, 1991, 27(4): 607–615.Google Scholar
  6. 6.
    Liu Yu, Fast dechirp algorithm, Journal of Data Acquisition and Processing (in Chinese), 1999, 14(2): 175–178.Google Scholar
  7. 7.
    Mao Yongcai, Bao Zheng, Parameter estimation of chirp signals with time varying amplitudes using cyclostationary approach, Chinese Journal of Electronics (in Chinese), 1999, 27(4): 135–136.Google Scholar
  8. 8.
    Li Yingxiang, Xiao Xianci, Linear frequency-modulated signal detection and parameter estimation in low signal-to-noise ratio condition, Systems Engineering and electronics (in Chinese), 2002, 24(8): 44–45.MATHGoogle Scholar
  9. 9.
    Haimovich, A. M., Pekham, C. D., Teti, J. G. et al., SAR imagery of moving targets: Application of time-frequency distributions for estimating motion parameters, Proc. 1994 SPIE’s International Symposium on Aerospace and Sensing, 1994, 2238: 238–247.Google Scholar
  10. 10.
    Rao, P., Taylor, F. J., Estimation of instantaneous frequency using the discrete Wigner distribution, Electronics Letters, 1990, 26(4): 246–248.CrossRefGoogle Scholar
  11. 11.
    Choi, H., Williams, W. J., Improved time-frequency representation of multicomponent signals using exponential kernels, IEEE trans. on SP, 1988, 37(6): 862–871.Google Scholar
  12. 12.
    Barbarossa, S., Analysis of multicomponent LFM signals by a combined Wigner-Hough transform, IEEE Trans. On SP, 1995, 43(6): 1511–1515.CrossRefGoogle Scholar
  13. 13.
    Tian Xiaohua, Liao Guisheng, Wu Yuntao, Joint estimation of Doppler and multipath time delay of overlapping echoes for LFM pulse radar, Chinese Journal of Electronics (in Chinese), 2002, 30(6): 857–860.Google Scholar
  14. 14.
    Namias, V., The fractional Fourier transform and its application in quantum mechanics, J. Inst. Appl. Math, 1980, 25: 241–265.MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Almeida, L. B., The fractional Fourier transform and time-frequency representations, IEEE Trans. on SP, 1994, 42(11): 3084–3091.CrossRefGoogle Scholar
  16. 16.
    Dong Yongqiang, Tao Ran, Zhou Siyong et al., The fractional Fourier analysis of multicomponent LFM signal, Chinese Journal of Electronics, 1999, 8(3): 326–329.Google Scholar
  17. 17.
    Qi Lin, Tao Ran, Zhou Siyong et al., Adptive time-varying filter for linear FM signal in fractional Fourier domain, Proc. Of the 6th International Conference on Signal Processing, Beijing: Posts & Telecom. Press, 2002, 1425–1428.Google Scholar
  18. 18.
    Dong Yongqiang, Tao Ran, Zhou Siuong et al., SAR moving target detection and imaging based on fractional Fourier transform, Acta Armamentarii (in Chinese), 1999, 20(2): 132–136.Google Scholar
  19. 19.
    Ozaktas, H. M., Arikan, O., Kutay, M. A. et al., Digital computation of the fractional Fourier transform. IEEE Trans. on SP, 1996, 44(9): 2141–2150.CrossRefGoogle Scholar
  20. 20.
    Ristic, B., Boashash, B., Comments on “The Cramer-Rao Lower Bounds for Signals with Constant Amplitude and Polynomial Phase”, IEEE Trans. On SP, 1998, 46(6): 1708–1709.CrossRefGoogle Scholar
  21. 21.
    Peleg, S., Porat, B., The Cramer-Rao lower bounds for signals with constant amplitude and polynomial phase, IEEE Trans. on SP, 1991, 39(5): 749–752.CrossRefGoogle Scholar

Copyright information

© Science in China Press 2004

Authors and Affiliations

  1. 1.Department of Electronic EngineeringBeijing Institute of TechnologyBeijingChina
  2. 2.School of Information EngineeringZhengzhou UniversityZhengzhouChina

Personalised recommendations