We consider a multiuser multiple-input multiple-output (MIMO) communication system using code-division multiple access (CDMA) and multiuser detection to discriminate the different users. Our focus is on the CDMA uplink of a frequency-nonselective Rayleigh fading channel. We study two types of receivers: joint receivers, which address simultaneously both spatial and multiple-access interference; and separate receivers, addressing the two types of interference individually. This approach allows assessing the benefits of adding MIMO processing capabilities to existing multiuser single-input single-output systems. For both receiver types, we analyze solutions based on linear (matched filter, decorrelator, minimum mean-square error) and maximum-likelihood receivers. For all the receivers considered, we provide closed-form expressions (as expectations of given functions) of the resulting pairwise error probabilities. Performance results are obtained in terms of frame-error rate versus E(b)/N(0), following two different approaches. An analytic approach using large-system asymptotic methods, whereby the system parameters (number of users and antennas, spreading gain) are assumed to grow to infinity with finite limiting ratios. A computer-simulation approach is used to illustrate the differences between asymptotic and simulation results.