Combining Phase and Linear Frequency Modulations to Design Unimodular Doppler-Tolerant Radar Pulses

The problem of designing unimodular Dopplertolerant radar pulses and corresponding minimum peak sidelobe pulse compression filters is considered. A two stage approach is adopted, where the pulse is designed first, and the filter afterwards. The pulse is constructed by distorting a linear frequency modulated pulse with a suitable smooth phase modulation. The smoothness of the phase modulation is ensured by interpolating between the values of phases that are coded on a regularly spaced time grid. The code is found by numerical optimization using a derivative-free algorithm. The adopted cost function combines, among others, terms responsible for good spectral properties, tolerance to Doppler shift, and sidelobe level. The corresponding minimum peak sidelobe filter is also found using derivative-free optimization and similarly constructed cost function. Multiple dissimilar pulses can be found using the proposed approach.