Random Sampling for Radar Signals: Random Noise Radar Ambiguity Functions, Covert Noise Radar Analysis and Particle Filter Tracking Using Diversity Waveforms

Wenwei Zhou, Purdue University

Abstract

This thesis consists of three works in the area of radar engineering: probabilistic analysis of random noise radar waveforms, analysis of joint detection performance of radar and electronic warfare receivers, and particle filter based radar target tracking using diversity waveforms. Probabilistic Analysis of Random Noise Radar Waveforms: Noise waveforms are an important class of radar waveforms. Because the waveforms are random noise, we must have a probabilistic understanding of how their ambiguity function delay-Doppler sidelobes behave in order to understand the likelihood of an appearance of higher than usual sidelobes; In this work, we probabilistically characterize the behavior of the sidelobes of Gaussian random noise waveforms. Among other things, we demonstrated the application of the central limit theorem and weak/strong law of large numbers to the sidelobe of any given Doppler and delay. In the case where the baseband data is real, we also rigorously show that maximum of N sidelobes has a Gumble distribution and give a Chernoff bound which can be used to upper bound the large deviation of the sidelobes. The result indicates that high sidelobes are a very rare phenomenon. Joint Radar and EW Receiver Detection Performance for Random Noise Waveforms: We explore the potential and limitations of using random noise waveform for covert operation. We found that if we can transmit arbitrarily low power, then in theory we can make probability of detection of the matched filter in radar receiver arbitrarily close to one while limiting the probability of detection of an energy detector in an Electronic Warefare(EW) receiver close to what a coin toss would achieve. However, we also discovered that in practice, due to limitations on the duration of the waveform a radar can process, covert operation using a noise waveform is limited to targets within certain distance. We put forth both a general formula and a ball park estimate of an upper bound on range as a function of upper bound on waveform duration if successful covert operation is intended. Radar Target Tracking: We propose a novel radar target tracking method using a combination of diversity waveforms and a particle filter. We demonstrate in simulation that our method converges quickly, provides superior resolution of targets compared to a single waveform, and maintains tracking on multiple moving targets. We can further apply the expectationmaximization algorithm together with minimum description length criteria to automatically estimate the target locations.

Degree

Ph.D.

Advisors

Bell, Purdue University.

Subject Area

Engineering|Electrical engineering

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