volume | PIER Journals

Abstract

Multi-path time delay spread is a very important factor in the bit error rate of high-frequency ionospheric communication channels and in the target detection performance of over-the-horizon radars. In this study, the probability density distribution of multi-path time delay and Doppler shift of ionospheric radio signal are derived using Rayleigh fading. Moreover, the probability density distribution of time delay, average power of the received signal, and received signal variance are discussed in detail. Using a designed experimental circuit, the measured value of the multi-path time delay spread is obtained from three given radio paths by the sweep-frequency pulse sounding technique. The average value of the multi-path time delay spread that changes with the ratio K, which is the operating frequency of the basic maximum usable frequency, is also analyzed and fitted using the least-squares fitting method. Theoretical and statistical research shows that for a given radio path and specific frequency, the multi-path time delay spread approximately follows a normal distribution. The average time delay spread decreases with the increase in the ratio K; however, it eventually approaches a steady value. The results of this research provide an empirical reference for further prediction and estimation of the time delay spread of a radar wave propagating through the ionosphere.

1. Kandic, , M., G. E. Bridges, and , "Limits of negative group delay phenomenon in linear causal media," Progress In Electromagnetics Research, Vol. 134, 227-246, 2013. Google Scholar

2. Bello, , P. A., "Characterization of randomly time-variant linear channels," IEEE Transactions on Communications Systems,, Vol. 11, No. 4, 360- 393, 1963.
doi:10.1109/TCOM.1963.1088793 Google Scholar

3. Maresca, , J. W., T. M. Georges, and , "Measuring rms wave height and the scalar ocean wave spectrum with HF skywave radar," J. Geophys. Res., Vol. 85, No. 26, 2759-2771, 1980.
doi:10.1029/JC085iC05p02759 Google Scholar

4. Bell, , B. M., T. E. Ewart, and , "Separating multipaths by global optimization of multidimensional matched filter," IEEE Transaction on Acoustics, Speech, and Signal Processing, Vol. 34, No. 5, 1029-1037, 1986.
doi:10.1109/TASSP.1986.1164940 Google Scholar

5. Zhang, , W., A. Hoorfar, and L. Li, "Through-the-wall target location with time reversal MUSIC method," Progress In Electromagnetics Research, Vol. 106, 75-89, 2010.
doi:10.2528/PIER10052408 Google Scholar

6. Zhang, , X., G. Feng, and D. Xu, "Blind direction of angle and time delay estimation algorithm for uniform linear array employing multi-invariance MUSIC," Progress In Electromagnetics Research Letters, Vol. 13, 11-20, 2010.
doi:10.2528/PIERL09102611 Google Scholar

7. Lizzi, L., F. Viani, M. Benedetti, P. Rocca, and A. Massa, "The M-DSO-ESPRIT method for maximum likelihood DOA estimation," ress In Electromagnetics Research, Vol. 80, 477-497, 2008.
doi:10.2528/PIER07121106 Google Scholar

8. Ching, , P. C., H. C. So, and , "Two adaptive algorithms for multipath time delay estimation," IEEE Journal of Oceanic Symposium on Circuits and Systems, Vol. 19, No. 3, 458-463, 1994. Google Scholar

9. Qi, , C., Z. Zhao, W. Yang, Z.-P. Nie, and G. Chen, "Electromagnetic scattering and Doppler analysis of three-dimensional breaking wave crests at low-grazing angles," Progress In Electromagnetics Research, Vol. 119, 239-252, 2011.
doi:10.2528/PIER11062401 Google Scholar

10. Zhang, , G. G., J. Wang, H. W. Li, and H. Huang, "Improved blind source extraction for time delay estimate in passive coherent location system," Progress In Electromagnetics Research B, Vol. 37, 257-274, 2012.
doi:10.2528/PIERB11102202 Google Scholar

11. Shin, D. C., C. L. Nikias, and , "Estimation of frequency-delay of arrival (FDOA) using fourth-order statistics in unknown correlated Gaussian noise source," IEEE Transactions on Signal Processing, Vol. 42, No. 10, 2771-2780, 1994.
doi:10.1109/78.324742 Google Scholar

12. Cheng, J., G. Gao, W. Ding, X. Ku, and J. Sun, "An improved scheme for parameter estimation of G± distribution model in high-resolution SAR images," Progress In Electromagnetics Research, Vol. 134, 23-46, 2013. Google Scholar

13. Booker, , H. G., J. A. Rateliffe, and D. H. Shinn, "Diffraction from an irregular screen with application to ionosphere problem," Phil. Trans. Roy. Soc., Vol. 242, No. 856, 579-607, 1950.
doi:10.1098/rsta.1950.0011 Google Scholar

14. Essex, , E. A., F. H. Hibberd, and , "Auto-correlation of the fading of multiple echoes from the ionosphere," J. Atmos. Terr. Phys., Vol. 29, No. 8, 1025-1027, 1967.
doi:10.1016/0021-9169(67)90253-X Google Scholar

15. Baussard, , A., M. Rochdi, and A. Khenchaf, "PO/MEC-based scattering model for complex objects on a sea surface," Progress In Electromagnetics Research, Vol. 111, 229-251, 2011.
doi:10.2528/PIER10083005 Google Scholar

16. Wang, , Y., Y.-M. Zhang, and L.-X. Guo, "Microwave Doppler spectra of sea echoes at high incidence angles: Influences of large-scale waves," Progress In Electromagnetics Research B, Vol. 48, 99-113, 2013. Google Scholar

17. Nie, D., M. Zhang, X. Geng, and P. Zhou, "Investigation on Doppler spectral characteristics of electromagnetic backscattered echoes from dynamic nonlinear surfaces of finite-depth sea," Progress In Electromagnetics Research, Vol. 130, 169-186, 2012. Google Scholar

18. From, , W. R., D. H. Meehan, and , "Mid-latitude spread-F structure," J. Atmos. Terr. Phys., Vol. 50, , No. 7, 629-638, 1988.
doi:10.1016/0021-9169(88)90061-X Google Scholar

19. Cornelius, , D. W., E. A. Essex, and , "HF Doppler observations associated with spread F," J. Geophys. Res., , Vol. 84, No. 4, 1361-1368, 1979.
doi:10.1029/JA084iA04p01361 Google Scholar

20. Long, , X. L. and J. C. Hou, "On the frequency variation of radio waves reflected from the ionosphere," Acta Geophysica Sinica, Vol. 22, No. 4, 388-395, 1979 . Google Scholar

21. Ma, , L., Z.-F. Li, and G. Liao, "System error analysis and calibration methods for multi-channel SAR," Progress In Electromagnetics Research, Vol. 112, 309-327, 2011. Google Scholar

22. Davies, K., D. M. Baker, and , "On frequency variations of ionospherically propagated HF radio signals," Radio Science, Vol. 1, No. 5, 545-556, 1966. Google Scholar

23. Lee, , J.-H., S.-W. Cho, S.-H. Park, and K.-T. Kim, "Performance analysis of radar target recognition using natural frequency: Frequency domain approach," Progress In Electromagnetics Research, , Vol. 132, 315-345, 2012. Google Scholar

24. Liu, , Z.-Y., L.-X. Guo, and , "A quasi three-dimensional ray tracing method based on the virtual source tree in urban microcellular environments," Progress In Electromagnetics Research, Vol. 118, 397-414, 2011.
doi:10.2528/PIER11041602 Google Scholar

25. Bennet, , J. A., "The calculation of Doppler shifts due to a changing ionosphere," J. Atmos. Terr. Phys., Vol. 29, No. 887--891, 1967. Google Scholar

26. Papoulis, , A., , Probability, Random Variables and Stochastic Processes,, 4th Ed., January 2002.

27. Ma, , X. Y., C. L. Nikias, and , "Joint estimation of time delay and frequency delay in impulsive noise using fractional lower-order statistics," IEEE Transactions on Signal Processing, Vol. 44, No. 11, 2669-2686, 1996.
doi:10.1109/78.542175 Google Scholar

28. Davies, , K., , Ionospheric Radio Wave, , Peter Peregrinus Ltd., 1990.
doi:10.1049/PBEW031E

29. Stein, , S., , "Statistical characterization of fading multipath channels," Report No. 321, Sylvania Applied Research Lab.,, 1963. Google Scholar

30. CCIR, "Ionospheric propagation and noise characteristics perti nent to terrestrial radio communication systems design and serice planning (Fading)," Reports of the CCIR, Vol. VI, No. 266-7, 298-316, 1990. Google Scholar

31. Zhong, , X.-M, C. Liao, and W. Lin, "Time-delay-based multi-target detection and power delivering," Progress In Electromagnetics Research M, Vol. 19, 25-28, 2011.
doi:10.2528/PIERM11042502 Google Scholar

32. Asiyo, M. O., T. J. O. Afullo, and , "Statistical estimation of fade depth and outage probability due to multipath propagation on southern Africa," Progress In Electromagnetics Research B,, Vol. 46, 251-274, 2013. Google Scholar

33. Daly, , R. F., K. D. Felperin, T. I. Dayharsh, et al., "Curts phase II automatic frequency selection system-signal processing," Application and Evaluation. Final Report, AD-815884/2, , 1967. Google Scholar

34. CCIR, "Ionospheric sounding at oblique incidence, propagation in ionized media ," Recommendations and Reports of the CCIR, Vol. VI, 1986. Google Scholar

35. CCIR, "Propagation predication Method for HF Broadcasting Propagation in ionized Media," Recommendations and Reports of the CCIR , Vol. VI, 1986. Google Scholar

36. Guier, , W. H., , "Ionospheric contributions to the Doppler shift at VHF from near-earth satellites," Proc. IRE, Vol. 49, No. 11, 1680-1681, 1961. Google Scholar

37. Ignatenko, , M. V. and M. V. Tinin, "Infoluence of ionospheric irregularities on the form of radio signal scattering spectrum in over-the-horizon radar sounding of the rough sea surface," Waves in Random Media, Vol. 13, No. 3, 151-164, 2003..
doi:10.1088/0959-7174/13/3/301 Google Scholar

38. Willman, , J. F., "Frequency-dependent ionospheric refraction effects on the Doppler shift of satellite signals," IEEE Trans. Aerospace and Electronic Systems, Vol. 1, No. 3, 283-289, 1965.
doi:10.1109/TAES.1965.4501697 Google Scholar

Dr. Bao-Ke Ma

Professor Li-Xin Guo

Dr. Hongtao Su