Diversity waveform sets for delay-Doppler imaging

The properties of the ambiguity function and the uncertainty relation of Fourier transforms assert fundamental limitations on the ability of any single radar waveform of constrained time-bandwidth product to distinguish two or more targets closely spaced in both time-delay (range) and Doppler-shift (radial velocity). These same mechanisms place fundamental limits on the ability radar imaging systems to distinguish separate scatterers in delay and Doppler. In this paper, the problem of using multiple waveform sets to make enhanced discrimination delay-Doppler measurements is considered. While small coded waveform sets for enhanced discrimination delay-only measurement are known (e.g., the Golay sequences), these waveforms do not have good Doppler discrimination properties. The problem of designing multiple waveform sets for enhanced discrimination delay-Doppler measurement is investigated, and the composite ambiguity function (CAF) is introduced as a tool to measure the delay-Doppler discrimination characteristics of these waveform sets. The problem of designing optimal coded waveform sets under a time-bandwidth product constraint is considered, and explicit optimal phase, frequency, and joint phase-frequency coded waveform sets having constant amplitude are presented. Algorithms for the construction of such waveform sets of arbitrary size and practical implementation issues are also presented