Defense Notices

The Doppler tolerance of a waveform refers to its behavior when subjected to a fast-time Doppler shift imposed by scattering that involves nonnegligible radial velocity. While previous efforts have established decision-based criteria that lead to a binary judgment of Doppler tolerant or intolerant, it is also useful to establish a measure of the degree of Doppler tolerance. The purpose in doing so is to introduce a Doppler "quasi-tolerant" trade-space that can ultimately inform automated/cognitive waveform design in increasingly complex and dynamic radio frequency (RF) environments. This idea of Doppler quasi-tolerance leads to the development of random FM (RFM) waveforms that retain a degree of Doppler tolerance while still providing the diversity of a nonrepeating waveform structure. The ensuing ambiguity functions split the delay/Doppler ridge into a variety of different patterns. Since these patterns are known at transmission, a strategy for appropriate coherent slow time combining is demonstrated in simulation. Separately, the application of slow-time coding (STC) to the Doppler-tolerant linear FM (LFM) waveform has been examined for disambiguation of multiple range ambiguities. However, using STC with non-adaptive Doppler processing often results in high Doppler "cross-ambiguity" side lobes that can hinder range disambiguation despite the degree of separability imparted by STC. To enhance this separability, a gradient-based optimization of STC sequences is developed, and a "multi-range" (MR) modification to the reiterative super-resolution (RISR) approach that accounts for the distinct range interval structures from STC is examined. The efficacy of these approaches is demonstrated using open-air measurements. Pulse agility is an alternative range disambiguation technique that relies on pulse-to-pulse waveform separability. Although pulse-agile waveforms are often uncorrelated and therefore amenable to range disambiguation, they may exhibit poor Doppler tolerance. To preserve Doppler tolerance and achieve separability, a class of hybrid waveforms is developed whereby a phase code is embedded on an LFM base waveform. A gradient-based optimization is developed for this waveform structure to achieve enhanced suppression of range-folded scattering in desired delay/Doppler regions. The Doppler tolerance and separability of the optimized waveforms are examined in simulation, and open-air measurements are used to demonstrate the range disambiguation capability.