Passive radar detection and imaging using low-rank matrix recovery

Abstract

The objective of this thesis is to develop passive radar imaging methods in an optimization framework that utilize prior information. Passive radar relies on transmitters of opportunity such as commercial television, radio, and cell phone base stations, or satellites as a source of illumination. It offers several advantages such as reduced cost, simplicity, and stealth.

Then we study the structure of orthogonal frequency division multiplexed (OFDM) waveforms used by common television and cellular illuminators of opportunity. Using this waveform model, we pose joint estimation as maximum a posteriori (MAP) estimation problem. We propose an alternating minimization algorithm to obtain the MAP estimator and prove convergence to a local minimizer.

Next, we study the performance of the convex LRMR based approach. We show that at sufficiently high center frequencies and commonly used imaging configurations the convex LRMR method recovers the scene reflectivity exactly. Furthermore, we derive a sufficient condition for exact recovery in terms of the resolution, showing that our method is a super-resolution technique. Additionally, we show that using cross-correlated measurements provably provides superior performance than auto-correlated or phaseless measurements.

First, this thesis presents a non-linear optimization based reconstruction method for passive radar that overcomes the drawbacks of currently used Fourier based methods, such as passive coherent localization (PCL) and time difference of arrival (TDOA) backprojection. Observing that the relationship between cross-correlated data from two different receivers and the unknown scene reflectivity can be recast as a linear mapping of a rank-one operator, we pose image formation as a convex nuclear-norm minimization using low-rank matrix recovery (LRMR) framework.

We then use non-convex optimization methods to reduce computational complexity and enforce the rank-one structure directly. We derive a descent algorithm using the majorization-minimization framework and prove convergence to an optimal solution when the step-size satisfies an easily computable bound.