Compressively Sampled Radar Using Random Waveforms

Open Access
Author:
Shastry, Mahesh Chandramouli
Graduate Program:
Electrical Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
March 26, 2013
Committee Members:
  • Ram Mohan Narayanan, Dissertation Advisor
  • Vishal Monga, Committee Member
  • John F Doherty, Committee Member
  • James Joseph Brannick, Committee Member
Keywords:
  • compressive sensing
  • radar
  • sparsity
  • signal processing
  • noise radar
Abstract:
Compressive sensing (also referred to as compressed sensing) refers to the theory and practice of exploiting sparsity in physical measurements to acquire fewer samples than dictated by the conventional Shannon-Nyquist-Kotelnikov sampling theorem. In this thesis, we explore the utility of compressive sensing in radar imaging problems. In order to achieve good imaging resolution, we seek to build radar systems with hardware and algorithms intended for processing signals of high bandwidth. Traditionally, radar systems utilized analog processing systems. Over the last few years, with advances in computing, it has been possible to process ultra-wideband (UWB) signals digitally. The current state of analog-to-digital converter (ADC) technology limits our ability to effectively acquire UWB radio-frequency (RF) signals in the context of radar imaging. However, radar signals that are scattered from common target scenes are sparse when represented in appropriate basis functions. We can thus apply the theory of compressive sensing to circumvent the limitations of ADC technology and design radar systems capable of imaging at higher resolutions than conventionally thought possible. In this thesis, we study the utility of random, noise-like transmit waveforms in compressive radar imaging. Our focus is on developing the theory and methods for the basic radar signal processing tasks of imaging, detection, and waveform design in the framework of compressive sensing. Compressive radar signal processing systems are more complex and less robust to noise and perturbations than conventional systems. We demonstrate using phase-transition diagrams that compressive noise radar is a feasible technology. Further, phase transition diagrams can be used for calibrating radar systems in real applications. The original contributions of this thesis are in developing the theory of compressive radar imaging using random stochastic waveforms. We demonstrate that compressive sensing works in real scenarios by applying it to experimental data. Hypothesis testing for target detection in the context of compressive radar imaging is different than the conventional setting since signal recovery is iterative and non-linear. We propose a method based on extreme value statistics to characterize the detection performance and determine thresholds for target detection in compressive radar imaging. We validate the effectiveness of this approach by applying it to experimental noise-radar imaging data. Radar systems often require designing waveforms that are optimally suited for specific applications and target scenarios. However, optimizing the transmit waveform can make the system matrix unsuitable for compressive signal recovery. In our work, we propose a waveform design algorithm that optimizes the waveform while keeping the system matrix suitable for compressive sensing. We analyze its performance and demonstrate its effectiveness through numerical simulations.