Statistical patterns of a general array

The present analysis considers the effects of Gaussian errors upon the antenna pattern of any array of elements. Analytical solutions for an average pattern and the standard deviation about this average are found. The errors are described in terms of the rms amplitude and phase errors at each element, with a correlation function relating errors in neighboring elements. The results are applied to the case of an array consisting of a sector of a circular array, with the resulting statistical patterns plotted. Then the problem of assigning probabilities to statements about the actual antenna pattern, based upon the statistical plots, is discussed.