Gain of an array of sensors subjected to processor perturbations

Arrays of distributed transducers are employed in such areas as acoustics, seismology, or radar. An array is generally designed for a certain array gain. However, the actual performance may be less than the value expected on the basis of design calculations. Thus, the actual array gain of a given processor will depend on the particular errors present. The current investigation is concerned with the effect of amplitude and phase errors on array gain. An exact expression is developed for the expected value of array gain when subjected to amplitude and phase errors of the form considered in the equation of a perturbation model. Several approximations are developed to provide insight into the relative importance of individual terms. The considered procedure makes it possible to avoid expensive Monte Carlo simulations.