Home   >   CSC-OpenAccess Library   >    Manuscript Information
Full Text Available

This is an Open Access publication published under CSC-OpenAccess Policy.
Publications from CSC-OpenAccess Library are being accessed from over 74 countries worldwide.
Suppression of Chirp Interferers in GPS Using the Fractional Fourier Transform
Seema Sud
Pages - 1 - 10     |    Revised - 30-04-2020     |    Published - 01-06-2020
Volume - 13   Issue - 1    |    Publication Date - June 2020  Table of Contents
Chirp, Fractional Fourier Transform, Interferer, Global Positioning System.
In this paper we apply the Fractional Fourier Transform (FrFT) to remove chirp interferers that corrupt Global Positioning System (GPS) signals. The concept is based on the fact that in the time-frequency plane, known as the Wigner Distribution (WD), chirps are represented as lines. Using an FrFT with some rotational parameter ‘a’, we rotate to a new time axis ta that transforms the chirp to a tone, in which the energy of the tone is contained in usually just one or two samples. The best `a', and the correct time sample along the ta axis, may be found without a priori knowledge by searching for the peak in the FrFT, since compression to one or two time samples results in an energy spike. Once the peak is found, we zero out the tone, and hence the underlying chirp. Rotation back to the original time domain via an inverse FrFT produces an improved GPS signal. This method can apply to multiple chirp interferers, and we describe how to easily determine the number of interferers, K, by finding peaks in the FrFT space over the parameter `a'. We also describe how to easily notch the interferers once converted to tones by computing a threshold based on the power of the coarse acquisition (C/A) code and noise. We show that for signal-to-noise ratios (SNRs) greater than at least 10 dB, interferers can be notched regardless of the ratio of the C/A code power to the combined interferer power, denoted as carrier-to-interference ratio (CIR).
1 H. Liu and M. Zhu, "Applying Fractional Fourier Transform to Radar Imaging of Moving Targets", Proc. IEEE Geoscience and Remote Sensing Symp. (IGARSS), Toulouse, France, Jul. 21-25, 2003.
2 Q. Meng and Z. Zhulin, "A New Method of Moving Targets Detection and Imaging for Bistatic SAR", Proc. IEEE 7th Int. Symp. on Computational Intelligence and Design, Hangzhou, China, Dec. 13-14, 2014.
3 S. Sud, "A Simple Method for Separating Weak and Strong Moving Targets in Clutter for a Radar System Using the Fractional Fourier Transform", Signal Processing: An Int. Journal (SPIJ), Vol. 10, No. 3, pp. 31-40, Oct. 2016.
4 H.-B. Sun, G.-S. Liu, H. Gu, and W.-M. Su, "Application of the Fractional Fourier Transform to Moving Target Detection in Airborne SAR", IEEE Trans. on Aerosp. and Electr. Systems, Vol. 38, No. 4, Oct. 2002.
5 S. Subramaniam, B.W. Ling, and A. Georgakis, "Filtering in Rotated Time-Frequency Domains with Unknown Noise Statistics", IEEE Trans. on Sig. Proc., Vol. 60, No. 1, Jan. 2012.
6 K. D. Rao and M. N. S. Swamy, "New Approach for Suppression of FM Jamming in GPS Receivers," IEEE Transactions on Aerospace and Electronic Systems, Vol. 42, No. 4, pp. 1464-1474, Oct. 2006.
7 R. Abimoussa and R. Landry, "Anti-jamming Solution to Narrowband CDMA Interference Problem", Canadian Conference on Electrical and Computer Engineering, Halifax, NS, Canada, Vol. 2, pp. 1057-1062, 2000.
8 W.L. Mao, "Novel SREKF-based Recurrent Neural Predictor for Narrowband/FM Interference Rejection in GPS', AEU Int. Journal of Electronics and Communications, Vol. 62, No. 3, pp. 216-222, Mar. 2008.
9 A. Rügamer, S. Joshi, Merwe, J. R. van der Merwe, F. Garzia, W. Felber, J. Wendel, and F.M. Schubert, "Chirp Mitigation for Wideband GNSS Signals with Filter Bank Pulse Blanking," Proc. of the 30th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION), Portland, Oregon, pp. 3924-3940, Sep. 2017.
10 H.M. Ozaktas, Z. Zalevsky, and M.A. Kutay, "The Fractional Fourier Transform with Applications in Optics and Signal Processing", John Wiley and Sons: West Sussex, England, 2001.
11 C. Candan, M.A. Kutay, and H.M. Ozaktas, "The Discrete Fractional Fourier Transform", IEEE Trans. on Sig. Proc., Vol. 48, pp. 1329-1337, May 2000.
12 M.A. Kutay, H.M. Ozaktas, O. Arikan, and L. Onural, "Optimal Filtering in Fractional Fourier Domains", IEEE Trans. on Sig. Proc., Vol. 45, No. 5, May 1997.
13 M.A. Kutay, H.M. Ozaktas, L. Onural, and O. Arikan, "Optimal Filtering in Fractional Fourier Domains", Proc. IEEE Int. Conf. on Acoustics, Speech, and Sig. Proc. (ICASSP), Detroit, MI, Vol. 2, pp. 937-940, 1995.
14 J.M. O'Toole, M. Mesbah, and B. Boashash, "Discrete Time and Frequency Wigner-Ville Distribution: Properties and Implementation", Proc. Int. Symp. on Digital Sig. Proc. and Comm. Systems, Noosa Heads, Australia, Dec. 19-21, 2005.
Dr. Seema Sud
The Aerospace Corporation - United States of America
sud_seema@yahoo.com, seema.sud@aero.org