Directivity Index of Partially Random Sonobuoy Arrays

The directivity index, DI, of partially random arrays is analyzed. A partially random array is an array in which the element positions are random variables subject to constraints that create some degree of either non-randomness or interdependence. The analysis is based on the definition of DI as the ratio in decibels of the power received by a single omnidirectional hydrophone of unity gain to the array power normalized to unity maximum gain. The array power is a random variable. Its expected value is used in the definition of DI to define the "nominal DI". The variance of the array power provides a measure of the variability of the DI among the members of an ensemble.