Array gain is not the same thing as "gain," "power gain," "directive gain," or "directivity," but if the noise environment around the array is isotropic and the array input signal is from an isotropic radiator, then array gain is equal to gain defined in the usual way from the array beam pattern.
Array gain is distinct from "gain," "power gain," "directive gain," or "directivity." If the noise environment surrounding the array is uniform and the input signal comes from a uniformly radiating source, then array gain corresponds to the standard gain calculated using the array's beam pattern.