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.
2. Candes, E. and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Prob., Vol. 23, 969-985, 2007.
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.
4. Narayanan, R. M., "Through-wall radar imaging using UWB noise waveforms," J. Franklin Inst., Vol. 345, No. 6, 659-678, 2008.
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.
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.
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.
8. Graps, A., "An introduction to wavelets," IEEE Comput. Sci. Eng., Vol. 2, No. 2, 50-61, 1995.
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.
10. Walnut, D. F., An Introduction to Wavelet Analysis, Springer Science & Business Media, New York, NY, USA, 2014.
11. Akansu, A. N. and R. A. Haddad, Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets, Academic Press, San Diego, CA, USA, 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.
13. Rohwer, C., "Multiresolution analysis of sequences," Nonlinear Smoothing and Multiresolution Analysis, Chapter 7, 71-90, Birkhauser Verlag, Basel, Switzerland, 2005.
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.
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.
16. Peele, L. C. and A. N. Pergande, "Wavelet-based radar,", United States Patent No. 5,990,823, 23, Nov. 1999.
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.
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.
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.
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.
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.
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.
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.
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.
25. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley & Sons, New York, NY, USA, 1999.
26. Richards, M. A., "Fundamentals of Radar Signal Processing," McGraw-Hill, 2005.
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.
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.
29. Stolt, R. H., "Migration by Fourier transform," Geophys., Vol. 43, No. 1, 23-48, 1978.
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.
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.