A different perspective on taper efficiency for array antennas

Taper efficiency is a relative figure of merit for antenna arrays giving the loss of directivity due to array amplitude and phase weighting. The derivation of the standard formula for antenna array taper efficiency proceeds from the definition of antenna directivity given the assumption that the array elements are spaced a multiple of half wavelengths apart. We derive a more physically intuitive definition of the taper efficiency of an array by starting from the communication link range equation. We do not require any assumption regarding element spacing. We find that the taper efficiency is equal to the ratio of beamformer signal gain to noise gain divided by the ratio of the same gains when the beamformer is uniformly weighted, where gain includes the contributions from all active and passive components within the beamformer. This definition is edifying, since an array's amplitude weighting and directivity are manifested primarily within the beamformer. We show that our formula reduces to the standard formula for three examples.