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This paper is concerned with the integration of compact antenna arrays for MIMO into handheld devices, where the antenna properties are influenced by the housing of the device and the user's head and hand. An accurate model that allows for the analysis of the performance of antenna arrays with mutual coupling in MIMO systems is presented. The impact on the MIMO system performance is investigated with regard to the capacity, correlation properties and the power transmission gain. It is shown that the performance is strongly influenced by a reduced efficiency of the arrays, rather than by the correlation properties of the signals.