Robust MMSE transceiver designs for uplink MIMO systems subject to arbitrary linear equality power constraints

Two numerical approaches, the Robust-Generalized Iterative Approach (R-GIA) and the Robust-Transmit Covariance Optimization Approach (R-TCOA), are proposed for jointly designing the minimum mean square error (MMSE) precoders and decoders of uplink multiuser multiple-input-multiple-output (MIMO) systems with arbitrary linear equality power constraints and possibly imperfect channel state information (CSI). The R-TCOA always gives optimum solutions but is only applicable when the rank constraints on the precoders are relaxed, the spatial correlation matrix for the transmit antennas of each user is an identity matrix, and there exists a scalar such that squaring the source covariance matrices is the same as multiplying them by it. The statistics of the CSI error also need to be the same for all users if the power constraints of the users are interdependent. The R-GIA, on the other hand, has no such restrictions. But whenever the R-TCOA is applicable, both approaches converge, and all the transmit covariance matrices are full rank, the two solutions are actually equivalent (i.e. the R-GIA is also optimum)! Numerical results show that these two robust approaches, for the most part, outperform their non-robust counterparts in various different channel correlation scenarios.