Study of the first-order curvature of array manifold for spherical-wave propagation

Superresolution array processing an in particular signal subspace-type techniques are based effectively on the searching of the array manifold in order to estimate signal parameter. The differential geometry of the manifold of a general array of isotropic sensors receiving signals from near-field sources was investigated. Expressions for the rate of change of manifold arc length and first curvature as a function of source bearing and range were presented and their behaviour was discussed for the special case of a uniform linear array. It was thereby shown that the shape of the azimuth (θ-parameter) curves deviates from that of a hyperhelix for decreasing values of range