Sparsity-based signal processing for noise radar imaging

Noise radar systems transmitting incoherent signal sequences have been proposed as powerful candidates for implementing compressively sampled detection and imaging systems. This paper presents an analysis of compressively sampled noise radar systems by formulating ultrawideband (UWB) compressive noise radar imaging as a problem of inverting ill-posed linear systems with circulant system matrices. The nonlinear nature of compressive signal recovery presents challenges in characterizing the performance of radar imaging systems. The suitability of noise waveforms for compressive radar is demonstrated using phase transition diagrams and transform point spread functions (TPSFs). The numerical simulations are designed to provide a compelling validation of the system. Nonidealities occurring in practical compressive noise radar systems are addressed by studying the properties of the transmit waveform. The results suggest that waveforms and system matrices that arise in practical noise radar systems are suitable for compressive signal recovery. Field imaging experiments on various target scenarios using a UWB millimeter wave noise radar validate our analytical results and the theoretical guarantees of compressive sensing.