Optimization Algorithm for Spectral Notching Based on Analytical Frequency Spectrum of Ultrawideband Throb Signal Represented by Chirp-Fourier Series

Ultrawideband (UWB)-throb signal has the potentials and many applications for high-resolution radar. In this paper, an optimization algorithm for spectral notching and compatibility is developed for cognitive radar systems using UWB-throb signals in a spectrally dense radio frequency (RF) environment. The existing mathematical model of the UWB-throb signal is expressed in terms of a finite chirp-Fourier series with real-value Fourier coefficients. An analytical expression for the frequency spectrum of the UWB-throb signal is derived by calculating the Fourier transform of the chirp-Fourier series. A spectral optimization algorithm is presented that utilizes the analytical frequency spectrum to generate transmit UWB signals with spectral notches, of acceptable depths, existing over different specified frequency subbands. Computer simulation plots are generated for the UWB-throb signal represented by the chirp-Fourier series, its analytical power spectral density (PSD), and the corresponding autocorrelation function (ACF), prior to and after performing spectral optimization for creating notches over different frequency subbands. The effects of shifting the notch subbands to higher frequencies, and creating multiple nulls within the spectrum, on the structure of the spectrally optimized UWB-throb signal are illustrated too. The spectral notching algorithm will allow cognitive radar systems to operate with UWB-throb signals in a spectrally dense radio frequency (RF) environment.