Maximixing the Directivity of Arrays of Non-directional Acoustic Receivers

The conditions under which maximum directive gain and receiving directivity are equivalent are reviewed. Then a fundamental method of calculating directivity from given correlation functions for signal and noise based on the original treatise by Faran and Hills is presented. Numerical results are given for line arrays and a particular class of two-dimensional arrays that appear to have optimal realizable directivity of significance in the design of small receiving arrays. Empirical relationships are given for nominal values of directivity and beamwidth of uniform line arrays used for the reception of broadband signals in a background of broadband isotropic noise.