Article,
Suppression of Chirp Interferers in GPS Using the Fractional Fourier Transform
Signal Processing: An International Journal (SPIJ), 13 (1): 1-10 (June 2020)
Abstract
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).
