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Previous authors have shown that the asymptotic capacity of a multiple-element-antenna (MEA) system with N transmit and N receive antennas [termed an (N,N) MEA] grows linearly with N if, for all l, the correlation of the fading for two antenna elements whose indices differ by l remains fixed as antennas are added to the array. However, in practice, the total size of the array is often fixed, and thus the correlation of the fading for two elements separated in index by some value l will change as the number of antenna elements is increased. In this paper, under the condition that the size of an array of antennas is fixed, and assuming that the transmitter does not have access to the channel state information (CSI) while the receiver has perfect CSI, the asymptotic properties of the instantaneous mutual information IN,N of an (N,N) MEA wireless system employing uniform linear arrays in a quasi-static fading channel are derived analytically and tested for accuracy for finite N through simulations. For many channel correlation structures, it is demonstrated that the asymptotic performance converges almost surely, implying that such MEA systems have a certain strong robustness to the instantiation of the channel fading values.