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The ability of a least mean square (LMS) adaptive array to adapt to the electromagnetic polarization of incoming signals is considered. An array of two pairs of crossed dipoles is studied. A desired signal and an interference signal are assumed to arrive from arbitrary directions with arbitrary elliptical polarizations. The output signal-to-interference-plus-noise ratio (SINR) from the array is computed as a function of the signal angles of arrival and polarizations. It is shown that as long as certain special desired signal polarizations are avoided, the array is difficult to jam with a single interference signal. To produce a poor SINR, an interference signal must both arrive from the same direction and have the same polarization as the desired signal.
R. Compton (1981) studied this question.