Two complementary numerical approaches, the generalized iterative approach (GIA) and the transmit covariance optimization approach (TCOA) are proposed for jointly designing the minimum mean square error (MMSE) precoders and decoders in uplink multiuser multiple-inputmultiple- output (MIMO) systems with a per-antenna power constraint. The TCOA always give optimum solution but works only when the source covariance matrices are projection matrices multiplied by the same constant and the rank constraint on the precoders is relaxed. On the other hand, the GIA does not have these restrictions. Furthermore, it is able to deal with arbitrary source covariances and allows arbitrary numbers of data streams. However, under these more general conditions, the GIA results are only guaranteed to be locally optimum. Regarding computational efficiency, the TCOA is more efficient at high transmission power and the GIA is more efficient at low transmission power when both approaches are applicable. Furthermore, the GIA and the TCOA are equivalent and both are optimum if the transmit covariance matrices obtained from the MMSE design are full rank. Numerical results show that the MSE and BER performances of the two approaches with the more practical per-antenna power constraint are very similar to those with the less practical peruser power constraint.