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 contrasts with "gain," "power gain," "directive gain," or "directivity." If the noise around the array is isotropic and the input signal originates from an isotropic radiator, then array gain aligns with the usual gain determined by the array's beam pattern.