Finite-array validity of infinite-array coupling asymptotics

Establish whether the asymptotic coupling properties proved for infinite phased arrays—specifically, the inverse-square decay of coupling coefficients with element distance—extend to finite array antennas.

Background

Infinite-array analyses cited in the paper establish that coupling coefficients decay asymptotically as the inverse square of element distance and suggest that this behavior may be universal for phased arrays. The paper applies this theory heuristically to finite arrays in order to predict passive coupling and the resulting error in center-element active impedance.

The authors explicitly distinguish the established infinite-array result from the finite-array case: the asymptotic property has not been demonstrated for finite arrays, and their numerical results indicate that finite bowtie and BoR arrays can exhibit decay rates different from the infinite-array prediction. Determining whether, and in what sense, the infinite-array asymptotics extend to finite arrays therefore remains unresolved.