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A very fast and efficient method for designing compact antenna arrays preserving the maximum channel capacity of multi input multi output (MIMO) systems using infinitesimal dipole model (IDM) theory is presented. Using this method each antenna element is replaced by a set of infinitesimal dipoles producing the same electric fields of the antenna. The recently introduced Invasive weed optimization (IWO) algorithm is employed to find the infinitesimal dipole models. The algorithm is applied to a planar inverted F-antenna designed as an element of a compact array for MIMO applications. Using the obtained IDMs, self and mutual admittances between the antennas are predicted. Therefore, correlation coefficients of the MIMO array system are achieved using S-parameters. Having the correlation of the system, the location and orientation of each antenna are optimized to find the minimum correlation value for the MIMO antenna system. Using the optimization technique, very low cross correlation coefficient is obtained for very close antennas over a finite ground plane.