By considering the large-system regimes, we analyze the asymptotic performance of a multiple-input multiple-output (MIMO) multiple-access (MA) wireless network in the presence of spatial correlation at the transmitters (i.e., mobile stations) and the receiver (i.e., base station) with particular emphasis on the receive antennas utilizing pattern diversity. Using the replica method originally developed in statistical physics, we are able to derive analytical solutions to the spectral efficiency of the MIMO-MA systems for any given arbitrary input signal distributions at the transmitters assuming the information-theoretic optimum decoding at the receivers. Our results are general in that they encompass lots of previously published results for degenerate cases. In addition, based on the asymptotic solution, we propose a computation-efficient algorithm to determine the asymptotic optimum transmit signal covariance matrices that can maximize the spectral efficiency of the MA network when only the slow-varying channel spatial covariance information is available at the transmitters.