Random and partially random acoustic arrays

Statistical properties of the beampatterns of three‐dimensional random arrays of arbitrary geometry are derived. The class of random arrays studied differs from those previously analyzed in that it includes partially random arrays. A partially random array is defined, for purposes of this paper, as a random array in which the various element positions may have different probability density functions and may be interdependent. Results presented include the expected value and variance of the pattern function, expected array power and the associated directivity index, and the variance of the array power. The results are applied to random and partially random disk arrays. The partially random disk array is assumed to have elements arranged in vertical strings. It is found that an array with M‐element strings is characterized by a region corresponding in elevation to the main lobe and extending 360° in azimuth in which the side‐lobe variance is a factor of M greater than that in the rest of the side‐lobe region.