There has been significant interest in the capacity of multiple element antenna (MEA) wireless systems. Previous authors have shown that the asymptotic capacity of a 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 antennas 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 changes as the number of antenna elements is increased. In this paper, under the condition that the length of a linear array of antennas is fixed, the asymptotic properties of the instantaneous mutual information I/sub N,N/ of an (N,N) MEA wireless system are derived analytically and tested for accuracy for finite N through simulations. Two different cases are considered: (1) when the fixed array size constraint is imposed at the mobile unit, and (2) when the fixed array size constraint is imposed at both the base station and the mobile unit. For the first case, simulation results indicate that the analytical approximations are very accurate for moderate values of N, especially at high signal-to-noise-ratios (SNR). For the second case, the predicted non-convergence of I/sub N,N/ is observed in simulations, as well.