Waveform Design and Generalized Ambiguity Function for Ultrawideband Nonsinusoidal Signals

The classical theory of radar resolution is based on narrowband sinusoidal waveforms and cannot directly be applied to ultrawideband (UWB) impulse radar. The concept of a generalized ambiguity function, which is a two-dimensional autocorrelation function in the range-Doppler domain, was first introduced by Harmuth in 1981 as a convenient design tool for the performance analysis of carrier-free radar. In 1989, we derived a generalized ambiguity function for coded waveforms represented by a sequence of (positive and negative) ideal Gaussian pulses. In this paper, the concepts of waveform design and ambiguity function are presented based on a physically realizable nonsinusoidal signal. The time variation of the nonsinusoidal signal is that of a generalized Gaussian pulse (GGP) having UWB frequency spectrum that is free from dc component. Therefore, the GGP signal can be radiated by a broadband antenna. For resolution enhancement, a sidelobe canceller is devised to eliminate the undesirable sidelobes of the autocorrelation function of the GGP signal without any significant reduction in signal energy. The generalized ambiguity function for UWB coded signals that are composed of a finite sequence of GGP signals is derived too. Computer plots of the generalized ambiguity function are generated for different design parameters. The plots demonstrate to what extend the generalized ambiguity function of the coded GGP signals can achieve the target resolution and clutter suppression capabilities of an ideal thumbtack ambiguity function.