The polarized electromagnetic waves have significant impact on the performance of adaptive antenna arrays. In this paper we investigate the effect of polarized desired and undesired signals on the performance of electronically steered beam adaptive antenna arrays. To achieve this goal, we built an analytical signal model for the adaptive array, in order to analyze, and compare the effect of polarized signals on the output SINRs (signal to interference plus noise ratios) of single-dipole, and cross-dipole adaptive antenna arrays. Based on a proof-of-concept experiment, and on MATLAB simulation results, it will be shown that cross-dipole adaptive antenna arrays exhibit better performance in comparison with single-dipole adaptive antenna arrays in presence of randomly polarized signals. However, single-dipole arrays show better performance under certain operating conditions.