This study introduces an extended optimal filtering technique for adaptive-on-transmit radar based on the transmission of pseudorandom noise waveforms as a method to simultaneously achieve low sidelobe level and spectral purity without degrading the main peak of the cross-correlation function. The proposed method is an extended version of the classical optimal filtering technique, resulting in longer codes with three simultaneously improved features that usually work in trade-off: 1) the cross-correlation function (CCF) sidelobe level is reduced in direct proportion to the filter length, K; 2) the out-of-band spectral suppression is at least 40 dB for pseudorandom binary sequences (PRBS); and 3) the frequency spectrum tail presents a decay given by K-4, offering larger out-of-band frequency suppression. The proposed technique provides skewsymmetry to the input signal and is tested on PRBS, Barker, and Golay pair of complementary codes. The proposed codes are also demonstrated to be Doppler resistant and offer better multipath capability.
2. Griep, K. R., J. A. Ritcey, and J. J. Burlingame, "Polyphase codes and optimal filters for multiple user ranging," IEEE Transactions on Aerospace and Electronic Systems, Vol. 31, No. 2, 752-767, April 1995.
3. Levanon, N. and E. Mozeson, Radar Signals, John Wiley & Sons.
4. Chen, C.-Y., C.-H. Wang, and C.-C. Chao, "Complete complementary codes and generalized Reed-Muller codes," IEEE Communications Letters, Vol. 12, No. 11, 849-851, November 2008.
5. Golay, M. J. E. and D. J. Harris, "A new search for skew symmetric binary sequences with optimal merit factors," IEEE Transactions on Information Theory, Vol. 36, No. 5, 1163-1166, September 1990.
6. Golay, M. J. E., "The merit factor of long low autocorrelation binary sequences with optimal merit factors," IEEE Transactions on Information Theory, Vol. 28, 543-549, 1982.
7. Helleseth, T., D. Sarwate, H.-Y. Song, and K. Yang, "Third International Conference on Sequences and Their Applications-SETA," revised selected papers, Seoul, Korea, October 24-28, 2004.
8. Lecture Notes in Computer Science, , Vol. 3486, Tod Helleseth Ed., Springer, 2005.
9. Guerci, J. R. and S. U. Pillai, "Theory and application of optimum transmit-receive radar," IEEE International Radar Conference, 705-709, 2000.
10. Van Trees, H. L., Optimum Array Processing, Wiley Interscience, New York, 2002, ISBN 0471093904.
11. Van Trees, H. L., "Optimum signal design and processing for reverberation-limited environments," IEEE Transactions on Military Electronics, Vol. 9, No. 3, 212-229, 1965.
12. Athans, M. and F. C. Schweppe, "Optimal waveform design via control theoretic principles," Information Control, Vol. 10, 335-377, 1967.
13. DeLong, D. and E. Hofstetter, "On the design of optimum radar waveforms for clutter rejection," IEEE Transactions on Information Theory, Vol. 13, No. 3, 454-463, 1967.
14. Kincaid, T. G., "Optimum waveforms for correlation detection in the sonar environment noise-limited conditions," The Journal of the Acoustical Society of America, Vol. 44, No. 3, 787-796, 1968.
15. Gjessing, D. T., "Target Adaptive Matched Illumination Radar: Principles and Application," Peter Peregrinus Ltd., 1986, ISBN: 0-86341-057-X.
16. Schreiber, H. H. and M. G. O'Connor, "Adaptive waveform radar," United States Patent 4,901,082, February 1990.
17. Bell, M. R., "Information theory and radar waveform design," IEEE Transaction on Information Theory, Vol. 39, No. 5, 1578-1597, September 1993.
18. Lee, S. P. and J. L. Uhran, "Optimum signal and filter design in underwater acoustic echo ranging systems," IEEE Transactions on Aerospace and Electronic Systems, Vol. 9, No. 5, 701-713.
19. Kayani, J. K., "Development and application of spread spectrum ultrasonic evaluation technique," Ph.D. Dissertation, Iowa State University, Ames, IA, 1996.
20. Narayanan, R. M., X. Xu, and J. A. Henning, "Radar penetration imaging using ultra-wideband (UWB) random noise waveforms," IEE Proc. on Radar, Sonar and Navigation, Vol. 151, No. 3, 143-148, June 2004.
21. Richards, M. A., et al., Principles of Modern Radar: Basic Principles, Scitech Publishing, Inc., 2010.
22. Lewis, B. L., F. F. Kretschmer, and Jr., "A new class of polyphase pulse compression codes and techniques," IEEE Transactions on Aerospace and Electronics Systems, Vol. 17, No. 3, May 1981.
23. Lewis, B. L., F. F. Kretschmer, and Jr., "Linear frequency modulation derived polyphase pulse compression codes and techniques," IEEE Transactions on Aerospace and Electronics Systems, Vol. 18, No. 5, May 1981.
24. Lee, W. K., H. D. Gri±ths, and L. Vinagre, "Developments in radar waveform design," 12th International Conference on Microwaves and Radar (MIKON), Vol. 4, 56-76, May 1998.
25. Lee, W. K., H. D. Gri±ths, and R. Benjamin, "Integrated sidelobe energy reduction technique using optimal polyphase codes ," Electronics Letters, Vol. 35, No. 24, November 1999.
26. Nunn, C. J. and G. E. Coxson, "Polyphase pulse compression codes with optimal peak and integrated sidelobes," IEEE Transactions on Aerospace and Electronic Systems, Vol. 45, No. 2, 775-781, April 2009.
27. Nunn, C. and G. Coxson, "Best known autocorrelation peak sideobe levels for binary codes of length 71 to 105," IEEE Transactions on Aerospace and Electronic Systems, Vol. 44, No. 1, 392-395, January 2008.
28. Ackroyd, M. H. and Ghani, "Optimum mismatched filters for sidelobe suppression," IEEE Transactions on Aerospace and Electronic Systems, Vol. 9, No. 2, 214-218, March 1973.
29. Molina, A. and P. C. Fannin, "Application of mismatched filter theory to bandpass impulse response measurements," Electronics Letters, Vol. 29, No. 2, 162-163, January 1993.
30. Levanon, N., "Cross-correlation of long binary signals with longer mismatched filters," IEE Proc. Radar, Sonar and Navigation, 1-6, 2005.
31. Levanon, N. and A. Scharf, "Range sidelobes blanking by comparing outputs of contrasting mismatched filters," IET Radar Sonar Navig., Vol. 3, No. 3, 265-277, 2009.
32. Levanon, N., "Noncoherent radar pulse compression based on complementary sequences," IEEE Trans. on Aerospace and Electronic Systems, Vol. 45, No. 2, 742-747, April 2009.
33. Bhatt, T. D., E. G. Rajan, and P. V. D. S. Rao, "Design of frequency-coded waveforms for target detection," IET Radar Sonar Navig., Vol. 2, No. 5, 388-394, 2008.
34. Shinriki, M., H. Takase, and H. Susaki, "Periodic binary codes with zero and small time sidelobe levels," IEE Proc. --- Radar Sonar Navig., Vol. 153, No. 6, December 2006.
35. Lee, W.-K., "A pair of asymmetric weighting receivers and polyphase codes for e±cient aperiodic correlations," IEEE Communications Letters, Vol. 10, No. 5, 387-389, May 2006.
36. Sebt, M. A., A. Sheikhi, and M. M. Nayebi, "Orthogonal frequency-division multiplexing radar signal design with optimized ambiguity function and low peak-to-average power ratio," IET Radar Sonar Navig., Vol. 3, No. 2, 122-132, 2009.
37. Liu, B., "Orthogonal discrete frequency-coding waveform set design with minimized autocorrelation sidelobes," IEEE Transactions on Aerospace and Electronic Systems, Vol. 45, No. 4, 1650-1657, October 2009.
38. Searle, S. J., S. D. Howard, and W. Moran, "Formation of ambiguity functions with frequency-separated Golay coded pulses," IEEE Transactions on Aerospace and Electronic Systems, Vol. 45, No. 4, 1580-1597, October 2009.
39. Liu, J. and W. Chu, "Design of binary multiple level sequences," IEEE Transactions on Aerospace and Electronic Systems, Vol. 47, No. 1, 26-36, January 2011.
40. Alejos, A. V., M. G. Sánchez, and I. Cuiñas, "Improvement of wideband radio channel swept time cross-correlation sounders by using golay sequences," IEEE Transactions on Vehicular Technology, Vol. 56, No. 1, January 2007.
41. Zakeri, B. G., M. Zahabi, and S. Alighale, "Sidelobes level improvement by using a new scheme used in microwave pulse compression radars," Progress In Electromagnetics Research Letters, Vol. 30, 81-90, 2012.
42. Lee, H. and Y.-H. Kim, "Weather radar network with pulse compression of arbitrary nonlinear waveforms: Ka-band test-bed and initial observations," Progress In Electromagnetics Research B, Vol. 25, 75-92, 2010.