Optimal amplitude shading for arrays of irregularly spaced or non-coplanar elements

Abstract

The majority of optimal amplitude shading methods for arrays of irregularly spaced or non-coplanar elements rely on numerical optimizations and iterative techniques to compute the desired weighting function because analytic solutions generally do not exist. Optimality is meant here in the Dolph–Chebyshev sense to provide the narrowest mainlobe width for a given sidelobe level. A simpler and more efficient technique to compute the shading weights for arbitrary line array shapes or element spacings is presented and it is shown that it is sufficient to sample the optimal Dolph–Chebyshev window, computed for a uniform line array of equivalent aperture length, at the element position of the nonuniform array. Examples are given for narrow-band plane-wave beamforming with curved arrays in which phase compensation is achieved by projecting the elements on a line tangent to the array. For the same mainlobe width, the resulting peak sidelobe levels are within 3 dB of a 30-dB Dolph–Chebyshev weighted uniform line array of equal aperture length and number of elements. Results are presented for computer simulations and for data collected at sea with the Toroidal Volume Search Sonar by the Coastal Systems Station, Panama City, Florida. [Work sponsored by ONR-NRL (Contract No. N00014-96-1-G913).]