Derivation of Beam Interpolation Coefficients with Application to the K- omega Beamformer

摘要

A problem of general interest is to be able to use a set of L beams, steered and focused respectively at the bearing-range pairs Theta1, R1, Theta2, R2,..., Theta(sub L), R(sub L), to approximate a beam steered and focused at a given angle-range pair Theta0, R0. A problem of particular interest is to be able to use L beams focused at infinite range (i.e., a plane wave) to approximate the beam steered and focused at the angle-range pair Theta0, R0. To accomplish the latter, a set of L appropriate coefficients, which are complex in general, must be computed and then used to scale and combine the beams to generate an approximation of the beam in question. These coefficients are derived in this report via mean square error minimization. The number of coefficients needed for a given error value is examined as a function of frequency and focusing range. The beam interpolation scheme is applied to the K- alpha; line array.