A mathematical tutorial on synthetic aperture radar (Q2726315)

Radar signal processing represents an important and fascinating sensor technology because it provides an all-weather, day/night capability to not only detect and locate remote objects, but to generate a spatial, visual representation, that is an image, of the radar reflectivity of an illuminated scenery. A radar system has all-weather capability because microwave radiation propagates through clouds and rain with only limited attenuation. A radar system has day/night capability because it actively supplies its own microwave illumination. Nearly 50 years have passed since C.A. Wiley first observed that a side-looking radar system can improve its azimuth resolution by utilizing the Doppler spread of the echo signal. His landmark observation that the key to better vision is a larger radar antenna aperture signified the birth of a technology now referred to as synthetic aperture radar (SAR). The principal idea behind the SAR imaging modality to synthesize the effect of a large-aperture physical radar system whose physical radar antenna construction is infeasible has also been used since the former radar engineer Sir Martin Ryle (Nobel prize 1974) introduced the Very Large Array (VLA) technique into astrophysics.NEWLINENEWLINE The synthetic aperture technique of VLA which is based on the Keplerian moving platform method finally led to the Very Long Baseline Array (VLBA), and the Very Long Baseline Interferometry (VLBI) of quasars and radio galaxies in modern radio astronomy [J. P. Fitch, Synthetic Aperture Radar. Springer-Verlag, New York (1988); N. Levanon, Radar Principles. Wiley, New York (1988); J. Detlefsen, Radartechnik. Springer-Verlag, Berlin (1989); J.C. Curlander, R.N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing. Wiley, New York (1991); B. Edde, Radar: Principles, Technology, Applications. Prentice--Hall, New York (1993); W.G. Carrara, R.S. Goodman, and R.M. Majewski, Spotlight Synthetic Radar: Signal Processing Algorithms. Artech House, Boston (1995); E. Prestini, Applicazioni Dell'Analisi Armonica. Editore Ulrico Hoepli, Milano (1996); C. Oliver, S. Quegan, Understanding Synthetic Aperture Radar Images. Artech House, Boston, London (1998); B. Borden, Radar Imaging of Airborne Targets: A Primer for Applied Mathematicians and Physicists. Institute of Physics Publishing, Bristol (1999); G. Franceschetti, R. Lanari, Synthetic Aperture Radar Processing. CRC Press, Boca Raton (1999); R. Nitzberg, Radar Signal Processing and Adaptive Systems. Artech House, Boston (1999); R.J. Sullivan, Microwave Radar: Imaging and Advanced Concepts. Artech House, Boston (2000)].NEWLINENEWLINENEWLINEThe survey paper presents some mathematical aspects of conventional strip-mode SAR imaging such as matched filter processing and chirp signals. On the theoretical side the author does not refer to the Heisenberg nilpotent Lie group background of harmonic analysis and radar imagery [\textit{W. Schempp}, Radar ambiguity functions, the Heisenberg group, and holomorphic theta series. Proc. Am. Math. Soc. 92, 103--110 (1984; Zbl 0525.43007); Harmonic Analysis on the Heisenberg Nilpotent Lie Group, with Applications to Signal Theory. Longman, London (1986; Zbl 0632.43001); \textit{A. Terras}, Fourier Analysis on Finite Groups and Applications. Cambridge University Press, Cambridge (1999; Zbl 0928.43001)] and therefore misses the relation to the imaging modalities of optical holography [E.N. Leith, Synthetic aperture radar. In: Optical Data Processing, D. Casasent (eds.) Springer-Verlag, Berlin Topics in Applied Physics, Vol. 23, 89--117, (1978); Optical processing of synthetic aperture radar data. In: Photonic Aspects of Modern Radar, H. Zmuda, E.N. Toughlian (eds.), Artech House, Boston, London, 381--401 (1994)], and clinical magnetic resonance tomography [\textit{W.J. Schempp}, Magnetic Resonance Imaging: Mathematical Foundations and Applications. Wiley--Liss, New York (1998; Zbl 0930.92015)]. Due to the fact that the concept of rotating planar coadjoint orbit of the Heisenberg Lie group is beyond the range of the paper under review, there is no reference to the VLA, VLBA, and VLBI techniques.NEWLINENEWLINE NEWLINEOn the practical side, there is no reference to companion software which is of importance for the effective implementation of radar systems [ M. Soumekh, Synthetic Aperture Radar Signal Processing with MATLAB Algorithms. Wiley, New York (1998); B. R. Mahafza, Radar Systems Analysis and Design Using MATLAB. Chapman \& Hall/CRC, Boca Raton, London (2000)].