Analysis and design of wide-band imaging arrays based on the coarray

Spatial arrays of sensor elements deployed over a plane region are often used to process propagating signals from sources of radiated or reflected power. The aim of array processing is to extract desired characteristics of the received signal. This dissertation deals primarily with linear array processing in the context of wide-band far-range imaging. The array systems are considered in terms of the coarray formalism, which provides a convenient and elegant framework for understanding narrow-band far-field imaging and is extended here to apply to wide-band imaging. The coarray concept is fundamental to passive and active imaging since it determines the class of PSFs that the imaging system can achieve. In this dissertation, we present a new interpretation based on the coarray formalism for frequency diversity or wide-band passive imaging of spatially incoherent source distributions. A characterization of the wide-band PSF is developed for incoherent imaging of far-field scenes. We also exploit this understanding of wide-band operation to design passive imaging arrays. In the field of active imaging, previous analysis has been focused on narrow-band far-range active imaging. Surprisingly few closed-form results exist for imaging performance characterization for wide-band active imaging. We use the sum coarray concept to show that for wide-band far-field active imaging, the reflectivity estimate is the convolution of the true reflectivity distribution and a basic characteristic of the imaging system, which we call the wide-band PSF. We develop an expression for the wide-band PSF. Our expression helps us understand the effect of bandwidth, pulse shape, array weights and array locations on the angular resolution. We demonstrate that the closed-form expression can be used to our advantage by adjusting these parameters optimally to design transmit and receive arrays. In addition to characterization of wide-band active and passive PSFs, we also investigate an issue of great interest in many imaging applications (both active and passive). That is, what array configurations should be used so that maximum angular resolution is achieved with a limited number of array elements. Active/Passive arrays that provide maximum resolution with a given number of elements are called minimum redundancy active/passive arrays. We show that it is possible to remove elements from minimum redundancy arrays and still achieve the same performance by filling in the missing elements through operation at multiple frequencies. This work also provides a basic conceptual framework in terms of the postage stamp problem within which many apparently isolated signal processing techniques can be understood. Moreover, we propose a new scheme, the retransmit strategy, for narrow-band active imaging, which allows a major expansion of the sum coarray using small arrays, resulting in high-resolution images