Compressive sensing meets noise radar

In this chapter, we discuss how noise radar systems are suitable for realizing practically the promises of compressive sensing in radar imaging, in general, and in urban-sensing applications, in particular. Noise radar refers to radio frequency imaging systems that employ transmit signals that are generated to resemble random noise waveforms. Noise radar has recently been successfully applied to urban sensing applications such as through-the-wall sensing (Amin 2011). Recent advances in the field of compressive sensing provide us with techniques to overcome the challenges of waveform design, sampling, and bandwidth constraints. We review existing literature related to these problems and present new results that enable for us to leverage compressive sensing and sparsity to improve noise radar systems. We model compressively sampled noise radar imaging as a problem of inverting linear system with a circulant random system matrix. We demonstrate the feasibility of this model by applying it to experimental data acquired using a millimeter wave ultrawideband noise radar system. Our principal contributions lie in developing theory and algorithms for imaging and detection strategies in compressively sampled noise radar imaging. We outline an approach based on extreme value statistics that works by empirically estimating the distribution of the residue of instances of the estimation algorithm. False alarms are treated as statistically rare events for estimating event probabilities in the compressive detection problem. We extrapolate the distribution of the residue from a small number of recovery instances to calibrate compressive noise radar systems. For deploying compressively sensed noise radar systems in real applications, it is necessary to develop convenient approaches to calibrate and characterize recovery performance.