Time-limited waveform synthesis for range-Doppler radar

Abstract

Summary form only given. An exact expression has been derived for the continuous ambiguity function of a time-limited waveform in terms of the discrete ambiguity function of the same waveform, and the resulting aliasing problem has been studied. The results have been used to solve the problem of least-squares synthesis of ambiguity functions for time-limited waveforms. The optimal waveform is specified by its Fourier transform samples taken at the Nyquist rate. Since the waveform is time limited, in general there are infinitely many nonzero frequency samples. Therefore, for practical purposes, all but a finite number of samples are specified to be zero. With this constraint, the design problem is solved by optimally choosing the nonzero Fourier-transform samples. This is accomplished by finding the eigenvector corresponding to the largest eigenvalue of a Hermitian matrix generated from the desired ambiguity function. The corresponding time waveform is then obtained by inverse transforming the optimal Fourier samples using the fast Fourier transform (FFT). Weighting of the Fourier samples prior to the FFT reduces the Gibbs' phenomenon.<>