Design and Evaluation of Stochastic Processes as Physical Radar Waveforms

Abstract

Recent advances in waveform generation and in computational power have enabledthe design and implementation of new complex radar waveforms. Still despite these advances, in a waveform agile mode where the radar transmits unique waveforms for every pulse or a nonrepeating signal continuously, effective operation can be difficult due the waveform design requirements. In general, for radar waveforms to be both useful and physically robust they must achieve good autocorrelation sidelobes, be spectrally contained, and possess a constant amplitude envelope for high power operation. Meeting these design goals represents a tremendous computational overhead that can easily impede real-time operation and the overall effectiveness of the radar. This work addresses this concern in the context of random FM waveforms (RFM) that have been demonstrated in recent years in both simulation and in experiments to achieve low autocorrelation sidelobes through the high dimensionality of coherent integration when operating in a waveform agile mode. However, while they are effective, the approaches to design these waveforms require optimization of each individual waveform, making them subject to costly computational requirements. This dissertation takes a different approach. Since RFM waveforms are meant to be noise like in the first place, the waveforms here are instantiated as the sample functions of an underlying stochastic process called a waveform generating function (WGF). This approach enables the convenient generation of spectrally contained RFM waveforms for little more computational cost than pulling numbers from a random number generator (RNG). To do so, this work translates the traditional mathematical treatment of random variables and random processes to a more radar centric perspective such that the WGFs can be analytically evaluated as a function of the usefulness ofthe radar waveforms that they produce via metrics such as the expected matched filter response and the expected power spectral density (PSD). Further, two WGF models denoted as pulsed stochastic waveform generation (Pulsed StoWGe) and continuouswave stochastic waveform generation (CW-StoWGe) are devised as means to optimize WGFs to produce RFM waveform with good spectral containment and design flexibility between the degree of spectral containment and autocorrelation sidelobe levels for both pulsed and CW modes. This goal is achieved by leveraging gradient descent optimization methods to reduce the expected frequency template error (EFTE) cost function. The EFTE optimization is shown analytically using the metrics above, as well as others defined in this work and through simulation, to produce WGFs whose sample functions achieve these goals and thus produce useful random FM waveforms. To complete the theory-modeling-experimentation design life cycle, the resultant StoWGe waveforms are implemented in a loop-back configuration and are shown to be amenable to physical implementation.