While the capacity of a single-user, point-to-point, multiple-input multiple-output (MIMO) channel has been well known, the achievable capacity of a MIMO channel in the presence of other co-channel users is much less understood. One such important scenario is the multiple-access (MA) channel where communication occurs from many uncoordinated mobile users to a common base station receiver (i.e., multipoint-to-point). Unlike previous studies whose emphases were on the idealized spatially uncorrelated channels with Gaussian signaling inputs from users, this paper derives a general analytical expression for the asymptotic (in the sense of large-system limit) sum-rate of a MIMO-MA system where the transmitters and the receiver can have different spatial correlations, and the users' inputs are not necessarily Gaussian. In addition to the sum-rate formula that assumes optimal joint decoding at the base station, we also derive the asymptotic sum-rate of a more practical system which performs separate decoding (multiuser detection followed by a bank of temporal error-correction decoders). Our analytic formulae are important in that they reveal the sum-rate one's system can achieve given the spatial correlation structures at the transmitters and receiver, and the input signal distributions. For special cases that users are homogeneous or users have Gaussian inputs, our results degenerate to previously published results. Furthermore, through computer simulations, we see that the proposed asymptotic solution gives good estimates for the ergodic sum-rate of the systems even with only a few antenna elements at each transmitter and receiver
