Nearfield beamforming using radial reciprocity

We establish the asymptotic equivalence, up to complex conjugation, of two problems: 1) determining the near-field performance of a far-field beam pattern specification and 2) determining the equivalent far-field beam pattern corresponding to a near-field beam pattern specification. Using this reciprocity relationship, we develop a computationally simple procedure to design a beamforming array to achieve a desired near-field beam pattern response. The superiority of this approach to existing methods, both in ease of design implementation and performance obtained, is analyzed and then illustrated by a design example.