Element efficiency: a unifying concept for array antennas

The efficiency of the mth elementary (lossless, reciprocal) antenna within the environment of an entire array of N terminated antenna elements may be defined as the ratio of the realized gain, g, relative to power available at the mth element, to the directive gain, g_d relative to the power radiated from that element. A physical arrangement of such a general array of N elements is indicated. With respect to the N antenna ports the array is characterized by its normalized voltage scattering matrix.