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The principle of a one-dimensional self-steering array system for beam forming with nonsinusoidal waves has been developed previously. In this paper, an adaptive antenna system consisting of a two-dimensional planar array of sensor elements and a real-time adaptive receiver processor is described. The sensor elements of the planar array are arranged into rows and columns so that the steering commands for the azimuth ald elevation directions can be generated separately. The array system electronically steers a beam in the direction of the source from which the waves are arriving without prior knowledge of the source location.