Nearfield beamforming using radial reciprocity

We establish the asymptotic equivalence, up to complex conjugation, of two problems: 1) determining the nearfield performance of a farfield beampattern specification and 2) determining the equivalent farfield beampattern corresponding to a nearfield beampattern specification. Using this reciprocity relationship, we develop a computationally simple procedure to design a beamforming array to achieve a desired nearfield beampattern 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.