Radar detection of high-energy cosmic rays in non-Gaussian background using a time-frequency technique

Cosmic rays are the highest-energy observable particles in the universe. Their study opens a new frontier for scientists to better understand the nature of the universe. This paper reports our study of a bistatic radar approach that is being developed for remote sensing of cosmic-ray induced air showers. In this context, we propose a robust detection technique based on time-frequency domain for the received radar echoes. These echoes are modeled as linear-downward chirp signals, characterized by very short sweep periods, low energies, and corrupted by non-stationary and non-Gaussian background noise. In addition, the related parameters of the received echoes are variable within some expected ranges, determined by the physical parameters of the air showers. In this paper, we explore the performance of the proposed detection method through an extensive theoretical analysis. We derive formulae for probability of the correct detection, as well as false-alarm rate. Numerical simulations and experimental results that corroborate our analysis are also presented.

[1]  Peter Willett,et al.  Tracking a general, frequency modulated signal in noise , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[2]  S. Kay,et al.  On the optimality of the Wigner distribution for detection , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[3]  Peter Willett,et al.  Detection of hidden Markov model transient signals , 2000, IEEE Trans. Aerosp. Electron. Syst..

[4]  W. Rhodes,et al.  Cross terms of the Wigner distribution function and aliasing in numerical simulations of paraxial optical systems. , 2010, Optics letters.

[5]  H H Barrett,et al.  Two-dimensional complex Fourier transform via the Radon transform. , 1985, Applied optics.

[6]  H. O. Lancaster.  The chi-squared distribution , 1971 .

[7]  T. Gaisser.  Cosmic rays and particle physics , 2016 .

[8]  Andrea Trucco,et al.  Experimental validation of a chirp-based underwater acoustic communication method , 2008 .

[9]  Behrouz Farhang-Boroujeny,et al.  On radar detection of chirp signals with nondeterministic parameters in challenging noise background , 2013, 2013 IEEE Radar Conference (RadarCon13).

[10]  B. Boashash,et al.  Application of the Wigner–Ville Distribution to Temperature Gradient Microstructure: A New Technique to Study Small-Scale Variations , 1986 .

[11]  Jae S. Lim,et al.  Advanced topics in signal processing , 1987 .

[12]  T. Yildirim,et al.  A parameter extraction technique for FMCW radar signals using Wigner-Hough-Radon transform , 2012, 2012 IEEE Radar Conference.

[13]  Louis-Gilles Durand,et al.  Nonlinear transient chirp signal modeling of the aortic and pulmonary components of the second heart sound , 2000, IEEE Transactions on Biomedical Engineering.

[14]  Yingning Peng,et al.  Radon-Fourier Transform for Radar Target Detection, I: Generalized Doppler Filter Bank , 2011, IEEE Transactions on Aerospace and Electronic Systems.

[15]  J. Lafferl,et al.  A Spread-Spectrum Concept Combining Chirp Modulation and Pseudonoise Coding , 1983, IEEE Trans. Commun..

[16]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[17]  Odile Macchi,et al.  Adaptive recovery of a chirped sinusoid in noise. II. Performance of the LMS algorithm , 1991, IEEE Trans. Signal Process..

[18]  Daisuke Ikeda,et al.  On site calibration for new fluorescence detectors of the telescope array experiment , 2009 .

[19]  B. Carlson,et al.  Search radar detection and track with the Hough transform. II. detection statistics , 1994 .

[20]  Sergio Barbarossa,et al.  A combined Wigner-Ville and Hough transform for cross-terms suppression and optimal detection and parameter estimation , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[21]  Odile Macchi,et al.  Adaptive recovery of a chirped sinusoid in noise. I. Performance of the RLS algorithm , 1991, IEEE Trans. Signal Process..

[22]  Josef Kittler,et al.  A survey of the hough transform , 1988, Comput. Vis. Graph. Image Process..

[23]  R. A. Altes,et al.  Echolocation as Seen from the Viewpoint of Radar/Sonar Theory , 1984 .

[24]  Robert Weigel,et al.  Spread spectrum communications using chirp signals , 2000, IEEE/AFCEA EUROCOMM 2000. Information Systems for Enhanced Public Safety and Security (Cat. No.00EX405).

[25]  Abbas Jamalipour,et al.  Wireless communications , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[26]  James R. Zeidler,et al.  Comparative tracking performance of the LMS and RLS algorithms for chirped narrowband signal recovery , 2002, IEEE Trans. Signal Process..

[27]  R. Mjelde,et al.  Semiperiodic chirp sequences reduce autocorrelation side lobes of pulsed signals , 2008 .

[28]  E. D. Evans,et al.  Search Radar Detection and Track with the Hough Transform , 1994 .

[29]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[30]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[31]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[32]  Peter Händel,et al.  Two algorithms for adaptive retrieval of slowly time-varying multiple cisoids in noise , 1995, IEEE Trans. Signal Process..

[33]  John C. Curlander,et al.  Synthetic Aperture Radar: Systems and Signal Processing , 1991 .

[34]  Charles E. Cook,et al.  Radar Signals: An Introduction to Theory and Application , 1967 .

[35]  Boualem Boashash,et al.  Time-frequency features for pattern recognition using high-resolution TFDs: A tutorial review , 2015, Digit. Signal Process..

[36]  M. Barbu,et al.  Fractional Fourier transform for sonar signal processing , 2005, Proceedings of OCEANS 2005 MTS/IEEE.