Coarray synthesis with circular and elliptical boundary arrays

An elliptical boundary aperture is a collection of points lying on an ellipse from which energy is transmitted and/or received. The aperture may be composed of a discrete set of points or a continuum, and an important special case is the circular boundary aperture. Such apertures are of interest because they can span a wide region while requiring a relatively small amount of sensor resources. When these apertures are used with the process of beamforming to produce a narrow-band image of a far-field source, the corresponding point spread function (PSF) is characterized by high sidelobes. In this paper, we use the concept of the coarray of an imaging system to develop new techniques which synthesize the effect of a more desirable PSF with an elliptical boundary aperture. Techniques are given for use in active imaging of spatially coherent sources, as well as passive imaging of spatially incoherent sources. Discrete arrays and continuous apertures are considered separately, and explicit results are provided for each case. Our approach to PSF synthesis based on coarrays shows that the problem can be solved in many more ways than previously recognized, and we exploit this fact to develop procedures which have a least-squares optimality property.