Interaction of adaptive antenna arrays in an arbitrary environment

This paper deals with adaptive transmitting arrays in which the excitations of the elements are varied in response to a pilot field incident on the array from a distant source. General theorems, some quite simple, are obtained relating to optimal power transfer from an adaptive array in an arbitrary reciprocal medium to either a single receiver or a receiving array. We assume first that the amplitudes and phases of the transmitting elements are separately adjustable, and afterward that only the phases are adjustable. The results involve in particular the matrix which represents the pilot fields produced at the elements of the transmitting array by currents at the locations of the receiving elements. In some important special cases, optimal power transfer results from making the phase of each transmitting element equal to the negative of the phase of the pilot field at that element. We also consider the dynamic behavior of two adaptive arrays which simultaneously transmit and receive, the phases on transmission being made equal to the negatives of the received phases. Analysis of an idealized model indicates that the arrays will reach a unique steady state which is in practical cases identical with or very close to the condition for optimal power transfer. Some numerical simulations of 2- and 3-element interacting arrays have been made to show how such arrays approach an essentially steady state under moderately realistic assumptions.