Fourier-Based Methods for Passive Sensing and Imaging

Abstract

Sensor arrays play an instrumental role in a variety of applications, including radar, sonar, radio astronomy, and wireless communications. Employing an array of sensors permits direction-of-arrival (DOA) estimation, interference suppression, and imaging of spatial distributions of sources or scatterers. Linear and planar array geometries can have sensors with uniform or non-uniform spacings. Non-uniform arrays require much fewer sensors to achieve comparable performance to uniform arrays in terms of the spatial resolution and the number of resolvable sources or scatterers. This dissertation proposes novel signal processing methods for narrowband passive (receive-only) sensing and imaging. The focus is on source estimation using linear and planar passive arrays with uniform and non-uniform geometries. Algorithm development for the non-uniform arrays is facilitated by a virtual array structure, called the difference coarray, which comprises pairwise differences of physical sensor positions. The difference coarray naturally arises from the passive sensing signal model. High-resolution DOA estimation techniques, such as the subspace-based methods, are computationally expensive, especially for arrays that span large apertures. Further, performance of such methods deteriorates for coherent sources. We propose efficient and effective Fourier-based iterative techniques for DOA estimation of coherent and uncorrelated sources using linear and planar arrays with both uniform and non-uniform geometries. The considered non-uniform arrays include those with uniform and non-uniform difference coarrays. The proposed DOA estimation techniques build on the iterative interpolated beamformer, which employs an estimate-and-subtract strategy to successively extract the sources and refines the estimates via an interpolation and spectral leakage subtraction scheme. We enable iterative beamforming in the coarray domain for linear and rectangular arrays, specifically compensating for non-uniformity of difference coarrays to yield asymptotically unbiased DOA estimates. We also design the iterative interpolated beamformer for oversampled and undersampled uniform circular arrays under the manifold separation framework, which permits the application of DOA estimation techniques that were developed for uniform linear arrays to arbitrary array geometries, such as circular arrays. The proposed iterative beamforming techniques not only estimate the source DOAs, but also provide source power/amplitude estimates. As such, these Fourier-based methods are applicable to narrowband passive imaging systems for providing an accurate estimate of the distribution of source intensity or amplitude as a function of angle.