FURTHER READING

The references serve as a good resource for further reading. Stretch processing is covered in radar and waveform texts [3, 4] and in several SAR texts [5, 6, 40]. Stepped chirp waveforms are relatively new and are not addressed in most radar texts. The reader is encouraged to start with the papers by Lord and others [7, 8, 10–13]. The initial work in NLFM design performed by Key and others [19–21] is summarized in two excellent texts [26, 50]. Papers by Johnston [24, 25] are also recommended for those interested in the Doppler intolerance associated with NLFM waveforms.

Stepped frequency waveforms are presented in a coherent fashion in the textbook by Wehner [18] and in the chapter by Lane [17]. The original paper by Taylor and Blinchikoff [27] provides background on the motivation behind the development of the quadriphase waveform as well as derivations for some of the equations in this text. Levanon and Mozeson [51] describe other band-limiting techniques, in addition to quadriphase, and describe the ambiguity surface for a quadriphase waveform. The various MMF de-signs are covered at length in [32–35]. Early approaches to MMF design are covered in [52, 53], and more recently an adaptive approach was described in [54].

2.9 REFERENCES

[1] Keel, B.M., “Fundamentals of Pulse Compression Waveforms,” Chapter 20 in Principles of Modern Radar, Basic Principles, Ed. M. A. Richards, J. A. Scheer, and W. A. Holm, Scitech Publishing, Raleigh, NC, 2010.

[2] Caputi, Jr., W.J., “Stretch: A Time-Transformation Technique,” IEEE Trans. AES, vol. AES-7, no. 2, pp. 269–278, March 1971.

[3] Skolnik, M., Radar Handbook, 3d ed., McGraw-Hill, New York, 2008.

[4] Stimson, G.W., Introduction to Airborne Radar, 2d ed., Scitech Publishing, Raleigh, NC, 1998.

[5] Jakowatz, Jr., C.V., Wahl, D.E., Eichel, P.H., Ghiglia, D.C., and Thompson, P.A., Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach, Kluwer Academic Publishers, Boston, 1996.

[6] Curlander, J.C. and McDonough, R.N., Synthetic Aperture Radar, Systems and Signal Pro-cessing, New York, John Wiley & Sons, 1991.

[7] Nel, W., Tait, J., Lord, R., and Wilkinson, A., “The Use of a Frequency Domain Stepped Frequency Technique to Obtain High Range Resolution on the CSIR X-Band SAR System,”

in Proceedings of the IEEE 2002 Africon Conference, vol. 1, pp. 327–332, 2002.

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[8] Wilkinson, A.J., Lord, R.T., and Inggs, M.R., “Stepped-Frequency Processing by Reconstruc-tion of Target Reflectivity Spectrum,” in Proceedings of the 1998 South African Symposium on Communications and Signal Processing, pp. 101–104, 1998.

[9] Berens, P., “SAR with Ultra-High Range Resolution Using Synthetic Bandwidth,” in Pro-ceedings of the IEEE 1999 International Geoscience and Remote Sensing Symposium, vol. 3, pp. 1752–1754, 1999.

[10] Lord, R.T. and Inggs, M.R., “High Resolution SAR Processing Using Stepped-Frequencies,”

in Proceedings of the 1997 IEEE International Geoscience and Remote Sensing Conference, pp. 490–492, August 1997.

[11] Lord, R.T. and Inggs, M.R., “High Range Resolution Radar using Narrowband Linear Chirps Offset in Frequency,” in Proceedings of the 1997 South African Symposium on Communica-tions and Signal Processing, pp. 9–12, September 1997.

[12] Hongxing, D., “Stepped Frequency Chirp Signal SAR Imaging,” in Proceedings of the First Asian and Pacific Conference on Synthetic Aperture Radar, pp. 14–18, 2007.

[13] Haojuan, Y., Meiguo, G., and Guoman, L., “Coherent Spectrum Synthesis of Frequency-Stepped Chirp Signal,” in Proceedings of the 2009 IET International Radar Conference, pp. 1–4, April 2009.

[14] McGroary, F.X., Lindell, K., and Greenspan, M., “Multi-Pulse Pulse Compression Radar System,” US Patent Number 5,128,681, July 7, 1992.

[15] McGroary, F. and Lindell, K., “A Stepped Chirp Technique for Range Resolution Enhance-ment”, in Proceedings of the National Telesystems Conference, pp. 122–126, 1991.

[16] Ruttenberg, K. and Chanzit, L., “High Range Resolution by Means of Pulse to Pulse Frequency Shifting,” in Proceedings of the EASCON, Radar Systems, vol. 2, pp. 153–157, 1968.

[17] Lane, T. L., “Stepped-Frequency and ISAR Imaging Systems,” Chapter 11, in Coherent Radar Performance Estimation, Ed. J. A. Scheer and J. L. Kurtz, Artech House, Norwood, MA, 1993.

[18] Wehner, D. R., “Synthetic High-Range-Resolution Radar”, Chapter 5, in High-Resolution Radar, 2d ed., Artech House, Boston, MA, 1995.

[19] Key, E.L., Fowle, E.N., and Haggarty, R.D., “A Method of Designing Signals of Large Time-Bandwidth Product,” in Proceedings of the IRE International Convention Record, vol. 9, pt. 4, pp. 146–154, 1961.

[20] Fowle, E.N., “The Design of FM Pulse Compression Signals,” IEEE Trans. on Information Theory, pp. 61–67, January 1964.

[21] Newton, C.O., “Nonlinear Chirp Radar Signal Waveforms for Surface Acoustic Wave Pulse Compression Filters,” Wave Electronics, pp. 387–401, 1974.

[22] Brandon, M.A., “The Design of a Non-linear Pulse Compression System to Give a Low Loss High Resolution Radar Performance,” Marconi Review, vol. 36, no. 188, pp. 1–45, 1973.

[23] Brandon, M.A., “The Spectra of Linear and Non-linear F.M. Used in Pulse Compression, and the Effects on the Resultant Compressed Pulse,” Marconi Review, vol. 36, no. 188, pp. 69–92, 1973.

[24] Johnston, J.A., “Analysis of the Pulse Compression of Doppler Shifted Nonlinear Frequency Modulated Signals,” Electronic Letters, vol. 20, pp. 1054–1055, December 1984.

[25] Johnston, J.A. and Fairhead, A.C., “Waveform Design and Doppler Sensitivity Analysis for Nonlinear FM Chirp Pulses,” IEE Proceedings–F, vol. 133, no. 2, pp. 163–175, April 1986.

[26] Cook, C.E. and Bernfeld, M., Radar Signals: An Introduction to Theory and Application, Artech House, Boston, 1993.

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2.9 References 83

[27] Taylor, Jr., J.W. and Blinchikoff, H.J., “Quadriphase Code—A Radar Pulse Compression Signal with Unique Characteristics,” IEEE Trans. on AES, vol. 24, no.2, pp. 156–170, March 1988.

[28] Faust, H., Connolly, B., Firestone, T.M., Chen, R.C., Cantrell, B.H., and Mokole, E.L., “A Spectrally Clean Transmitting System for Solid-State Phased-Array Radars,” in Proceedings of the IEEE Radar Conference, pp. 140–144, April 26–29, 2004.

[29] Blinkchikoff, H.J., “Range Sidelobe Reduction for the Quadriphase Codes,” IEEE Trans. AES, vol. 32, no. 2, pp. 668–675, April 1996.

[30] Levanon, N. and Freedman, A., “Ambiguity Function of Quadriphase Coded Radar Pulse,”

IEEE Trans. AES, vol. 25, no. 6, pp. 848–853, November 1989.

[31] Vale, C.R., “SAW Quadriphase Code Generator,” IEEE Trans. on Sonics and Ultrasonics, vol. SU-28, no. 3, pp. 132–136, May 1981.

[32] Stoica, P., Li, J., and Xue, M., “Transmit Codes and Receive Filters for Pulse Compression Radar Systems,” in Proceedings of the IEEE 2008 International Conference on Acoustics, Speech and Signal Processing, pp. 3649–3652, March 31–April 4, 2008.

[33] Nunn, C. and Kretschmer, F.F., “Performance of Pulse Compression Code and Filter Pairs Optimized for Loss and Integrated Sidelobe Level,” in Proceedings of the 2007 IEEE Radar Conference, pp. 110–115, April 17–20, 2007.

[34] Baden, J.M. and Cohen, M.N., “Optimal Peak Sidelobe Filters for Biphase Pulse Compres-sion,” in Proceedings of the IEEE 1990 International Radar Conference, pp. 249–252, May 7–10, 1990.

[35] Griep, K.R., Ritcey, J.A., and Burlingame, J.J., “Design of Mismatched Filters for Pulse Compression in a Multiple User Sonar Ranging System, in Proceedings of the 1993 Conference Record of The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers, vol. 2, pp. 1111–1115, November 1–3, 1993.

[36] Richards, M.A., Fundamentals of Radar Signal Processing, McGraw-Hill, New York, 2005.

[37] Walden, R.H., “Analog-to-Digital Converter Survey and Analysis,” IEEE Journal on Selected Areas in Communications, vol. 17, no. 4, pp. 539–550, April 1999.

[38] Le, B., Rondeau, T.W., Reed, J.H., and Bostian, C.W., “Analog-to-Digital Converters,” IEEE Signal Processing Magazine, vol. 22, no. 6, pp. 69–77, November 2005.

[39] Jonsson, B.E., “A Survey of A/D-Converter Performance Evolution,” in Proceedings of the 17th IEEE International Conference on Electronics, Circuits, and Systems, pp. 766–769, December 12–15, 2010.

[40] Carrara, W.G., Goodman, R.S., and Majewski, R.M., Spotlight Synthetic Aperture Radar, Signal Processing Algorithm, Artech House, Boston, 1995.

[41] Ludeman, L.C., Fundamentals for Digital Signal Processing, Harper & Row, New York, 1986.

[42] Kellogg, W.C., “Digital Processing Rescues Hardware Phase Errors,” Microwaves and RF, vol. 21, no. 12, pp. 63–64, 66–67, 80, November 1982.

[43] Jedwab, J., “A Survey of the Merit Factor Problem for Binary Sequences,” pp. 30–55 in Lecture Notes in Computer Science vol. 3486, Sequences and their Applications — SETA 2004, Ed.

T. Helleseth et al., Springer-Verlag, Berlin, 2005.

[44] Borwein, P., Ferguson, R., and Knauer, J., “The Merit Factor Problem,” pp. 52–70 in London Mathematical Society Lecture Note Series 352, Ed. J. McKee and C. Smyth, Cambridge University Press, Cambridge, UK, 2008.

[45] Brogan, L.W., Modern Control Theory, 2d ed., Prentice Hall, Englewood Cliffs, NJ, 1985.

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[46] Nunn, C., “Constrained Optimization Applied to Pulse Compression Codes and Filters,” in Proceedings of the 2005 IEEE International Radar Conference, pp. 190–194, May 9–12, 2005.

[47] Levanon, N., “Cross-Correlation of Long Binary Signals with Longer Mismatched Filters,”

IEE Proceedings of Radar, Sonar and Navigation, vol. 152, no. 6, pp. 372–382, 2005.

[48] Cohen, M.N., Fox, M.R., and Baden, J.M., “Minimum Peak Sidelobe Pulse Compression Codes,” in Proceedings of the 1990 IEEE International Radar Conference, Arlington, VA, pp. 633–638, 1990.

[49] Coxson, G. and Russo, J., “Efficient Exhaustive Search for Optimal-Peak-Sidelobe Binary Codes,” IEEE Trans. AES, vol. 41, no. 1, pp. 302–308, January 2005.

[50] Peebles, Jr., P.Z., Radar Principles, John Wiley & Sons, New York, 1998.

[51] Levanon, N. and Mozeson, E., Radar Signals, John Wiley & Sons, Hoboken, NJ, 2004.

[52] Key, E.L., Fowle, E.N., and Haggarty, R.D., “A method of side-lobe suppression in phase-coded pulse compression systems,” Technical Report no. 209, M.I.T. Lincoln Laboratory, Lexington, August 1959.

[53] Ackroyd, M.H. and Ghani, F., “Optimum Mismatched Filters for Sidelobe Suppression,” IEEE Trans. AES, vol. AES-9, no. 2, pp 214–218, March 1973.

[54] Blunt, S.D., and Gerlach, K., “Adaptive Pulse Compression via MMSE Estimation,” IEEE Trans. AES, vol. 42, no. 2, pp. 572–584, April 2006.

2.10 PROBLEMS

1. A synthetic aperture radar employs stretch processing. The radar achieves an un-weighted, Rayleigh range resolution of 0.2 m. The system is designed to support a 200 m range window, and the pulse width is 10 μsec. What is the filter bandwidth required to support the specified range window?

2. In a system employing stretch processing, the range to the center of the window is 25 km. A target is located within the window at a range of 25.02 km. The LFM waveform has 1.2 GHz bandwidth and a pulse width of 150μsec. What is the beat frequency associated with the target?