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We consider the limits to the capacity of the multiple-input-multiple-output wireless channel as modeled by the finite scatterers channel model, a generic model of the multipath channel which accounts for each individual multipath component. We assume a normalization that allows for the array gain due to multiple receive antenna elements and, hence, can obtain meaningful limits as the number of elements tends to infinity. We show that the capacity is upper bounded by the capacity of an identity channel of dimension equal to the number of scatterers. Because this bound is not very tight, we also determine an estimate of the capacity as the number of transmit/receive elements tends to infinity which is asymptotically accurate.