volume | PIER Journals

Abstract

Developed initially for military applications, radar technology is rapidly spreading to areas as diverse as natural resource monitoring, civil infrastructure assessment, and homeland security. Waveform design is a critical component to extract maximum information about the targets or features being probed. Waveforms derived from noiselets, one of the family functions of wavelets, can be advantageous in certain applications owing to their random and uncorrelated properties. In this work, radio frequency (RF) noiselet waveforms are introduced and their performance related to detection of arbitrary target interfaces using the cross-correlation method, a form of matched filtering, is assessed. The application of the RF noiselet waveform for nondestructive testing (NDT) of the multilayered dielectric structures is discussed. The application of wideband noiselet waveforms for multiresolution analysis (MRA) is demonstrated.

1. Coifman, R., F. Geshwind, and Y. Meyer, "Noiselets," Appl. Comput. Harmon. Anal., Vol. 10, No. 1, 27-44, 2001.
doi:10.1006/acha.2000.0313 Google Scholar

2. Candes, E. and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Prob., Vol. 23, 969-985, 2007.
doi:10.1088/0266-5611/23/3/008 Google Scholar

3. Keep, D. N., "Frequency-modulation radar for use in the mercantile marine," Proc. IEE --- Part B: Radio Electr. Electron., Vol. 103, No. 10, 519-523, 1956.
doi:10.1049/pi-b-1.1956.0203 Google Scholar

4. Narayanan, R. M., "Through-wall radar imaging using UWB noise waveforms," J. Franklin Inst., Vol. 345, No. 6, 659-678, 2008.
doi:10.1016/j.jfranklin.2008.03.004 Google Scholar

5. Ferguson, B., S. Mosel, W. Brodie-Tyrrell, M. Trinkle, and D. Gray, "Characterisation of an L-band digital noise radar," Proc. 2007 IET International Conf. on Radar Systems, Edinburgh, UK, Oct. 2007, doi: 10.1049/cp:20070634. Google Scholar

6. Axelsson, S. R., "Noise radar using random phase and frequency modulation," IEEE Trans. on Geoscience and Remote Sensing, Vol. 42, No. 11, 2370-2384, 2004.
doi:10.1109/TGRS.2004.834589 Google Scholar

7. Foucher, S., G. B. Benie, and J. M. Boucher, "Multiscale MAP filtering of SAR images," IEEE Trans. Image Process., Vol. 10, No. 1, 49-60, 2001.
doi:10.1109/83.892442 Google Scholar

8. Graps, A., "An introduction to wavelets," IEEE Comput. Sci. Eng., Vol. 2, No. 2, 50-61, 1995.
doi:10.1109/99.388960 Google Scholar

9. Peng, Z. K. and F. L. Chu, "Application of the wavelet transform in machine condition monitoring and fault diagnostics: A review with bibliography," Mech. Syst. Sig. Process., Vol. 18, No. 2, 199-221, 2004.
doi:10.1016/S0888-3270(03)00075-X Google Scholar

10. Walnut, D. F., An Introduction to Wavelet Analysis, Springer Science & Business Media, 2014.

11. Akansu, A. N. and R. A. Haddad, Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets, Academic Press, 2001.

12. Rajaraman, P., N. A. Sundaravaradan, R. Meyur, M. J. B. Reddy, and D. K. Mohanta, "Fault classification in transmission lines using wavelet multiresolution analysis," IEEE Potentials, Vol. 35, No. 1, 38-44, 2016.
doi:10.1109/MPOT.2015.2468775 Google Scholar

13. Rohwer, C., "Multiresolution analysis of sequences," Nonlinear Smoothing and Multiresolution Analysis, Chapter 7, 71-90, Birkhauser Verlag, Basel, Switzerland, 2005. Google Scholar

14. Sadiku, M. N. O., C. Akujuobi, and R. C. Garcia, "An introduction to wavelets in electromagnetics," IEEE Microwave Mag., Vol. 6, No. 2, 63-72, 2005.
doi:10.1109/MMW.2005.1491268 Google Scholar

15. Wang, N., Y. Zhang, and S. Wu, "Radar waveform design and target detection using wavelets," Proc. 2001 CIE International Conf. on Radar, 506-509, Beijing, China, Oct. 2001. Google Scholar

16. Peele, L. C. and A. N. Pergande, "Wavelet-based radar,", United States Patent No. 5,990,823, 23, Nov. 1999. Google Scholar

17. Wang, L., S. Law, C. Fraker, R. Vela, Y. F. Zheng, R. Ewing, and G. Scalzi, "Development of a new software-defined S-band radar and its use in the test of wavelet-based waveforms," Proc. 2011 IEEE National Aerospace and Electronics Conf. (NAECON), 162-166, Fairborn, OH, USA, Jul. 2011. Google Scholar

18. Cao, S., Y. F. Zheng, and R. L. Ewing, "Wavelet-based radar waveform adaptable for different operation conditions," Proc. 10th European Radar Conf., 149-152, Nuremberg, Germany, Oct. 2013. Google Scholar

19. Cao, S., Y. F. Zheng, and R. L. Ewing, "Wavelet-based waveform for effective sidelobe suppression in radar signal," IEEE Trans. Aerosp. Electron. Syst., Vol. 50, No. 1, 265-284, 2014.
doi:10.1109/TAES.2013.120067 Google Scholar

20. Cao, S., Y. F. Zheng, and R. L. Ewing, "Wavelet-based radar waveform for moving targets detection," Proc. 2014 IEEE Radar Conf., 1149-1154, Cincinnati, OH, USA, May 2014. Google Scholar

21. Cao, S., Y. F. Zheng, and R. L. Ewing, "Wavelet-based Gaussian waveform for spotlight synthetic aperture radar," Proc. 2014 IEEE National Aerospace and Electronics Conf. (NAECON), 267-273, Dayton, OH, USA, Jun. 2014. Google Scholar

22. Cao, S., Y. F. Zheng, and R. L. Ewing, "A wavelet-packet-based radar waveform for high resolution in range and velocity detection," IEEE Trans. Geosci. Remote Sens., Vol. 53, No. 1, 229-243, 2015.
doi:10.1109/TGRS.2014.2321258 Google Scholar

23. Sullivan, E. J., R. P. Goddard, H. A. Greenbaum, and K. P. Bongiovanni, "Generating simulated reverberation using noiselets," J. Acoust. Soc. Am., Vol. 119, No. 5, Pt. 2, 3273, 2006.
doi:10.1121/1.4786158 Google Scholar

24. Matsumoto, M. and N. Takuji, "Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator," ACM Trans. Model. Comput. Simul. (TOMACS), Vol. 8, No. 1, 3-30, 1998.
doi:10.1145/272991.272995 Google Scholar

25. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley & Sons, 1999.

26. Richards, M. A. "Fundamentals of Radar Signal Processing," McGraw-Hill, 2005. Google Scholar

27. Martinez-Lorenzo, J. A., F. Quivira, and C. M. Rappaport, "SAR imaging of suicide bombers wearing concealed explosive threats," Progress In Electromagnetics Research, Vol. 125, 255-272, 2012.
doi:10.2528/PIER11120518 Google Scholar

28. Dehmollaian, M. and K. Sarabandi, "Refocusing through building walls using synthetic aperture radar," IEEE Trans. Geosci. Remote Sens., Vol. 46, No. 6, 1589-1599, 2008.
doi:10.1109/TGRS.2008.916212 Google Scholar

29. Stolt, R. H., "Migration by Fourier transform," Geophys., Vol. 43, No. 1, 23-48, 1978.
doi:10.1190/1.1440826 Google Scholar

30. Lopez-Sanchez, J. M. and J. Fortuny-Guasch, "3-D radar imaging using range migration techniques," IEEE Trans. Antennas Propag., Vol. 48, No. 5, 728-737, 2000.
doi:10.1109/8.855491 Google Scholar

31. Gharamohammadi, A., Y. Norouzi, and H. Aghaeinia, "Optimized UWB signal to shallow buried object imaging," Progress In Electromagnetics Research Letters, Vol. 72, 7-10, 2018.
doi:10.2528/PIERL17091506 Google Scholar

Dr. Tae Hee Kim

Prof. Ram M. Narayanan