Application of the singular value decomposition to aperture synthesis with boundary arrays

It is shown how arrays consisting of sensors arranged only on the boundary of a planar region can be used to synthesize the effect of a more densely populated array. Such boundary arrays can simultaneously achieve good resolution and low sidelobes, using relatively few sensor elements compared with ´filled´ arrays. One essentially compensates for the missing elements from the interior of the boundary array by performing extra processing of the data. The authors focus on aperture synthesis techniques for passive imaging of spatially incoherent sources for some particular array geometries, namely the cross array and rectangular and triangular boundary arrays. Results are stated purely in terms of discrete arrays, and it is shown that the singular value decomposition provides a convenient solution to the aperture synthesis problem in this framework.<>