On the receiving cross section of an antenna in infinite linear and planar arrays

A rigorous derivation is given for the receiving cross section of an antenna located in infinite linear and planar arrays. For linear arrays the result involves the active input impedance and the azimuthal directivity of the array. For planar arrays it depends on the active input impedance and on geometrical parameters of the array. The expression of the receiving cross section of an element can be used to derive the generally accepted expression for the active element pattern without, however, making use of intuitive arguments. Results are first presented for conditions without grating lobes; they are then generalized to conditions where grating lobes enter the visible space.