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This letter derives and analyzes the spatial correlation based on a physically intuitional stochastic channel model for multiple-input-multiple-output (MIMO) systems using polarized and isolated antenna arrays. Simulations for a 2 times 2 MIMO system were performed using dipole antennas with various configurations to investigate the effects of polarization, pattern of elements, and cross-polarization discrimination (XPD) on the spatial correlation. Results show that the correlation is very sensitive to the orthogonality of pattern and polarization. Furthermore, XPD slightly affects the spatial correlation.