The steady-state antenna patterns of adaptive arrays

A decomposition of the adapted pattern generated by an adaptive array operating in an environment with one narrowband signal, K-1 narrowband jammers, and programmed to produce the maximum SNR is presented. The antenna voltage pattern is demonstrated to be a linear combination of K (or less) basis patterns, each from a sole source, and the kth basis pattern becomes the desired signal realized by the array. Isotropic array patterns result in retrodirective basis patterns, and the decomposition can be configured to obtain the retrodirective beams for all K.