Stochastic transceiver design in multi-antenna channels with statistical channel state information

The problem of stochastic robust sum mean square error (MSE) minimization transceiver design is addressed for multiple-input multiple-output (MIMO) broadcast channels (BCs). The transmitter has only distribution knowledge of the doubly correlated Gaussian channels and the receivers have complete channel state information (CSI). The design is based on an alternating optimization (AO) of the transmit and receive filters. For the users' minimum MSEs (MMSEs), i.e., the achieved MSEs using MMSE equalizers, and the expectations in the AO procedure, novel closed form expressions are calculated via first and second order derivatives of suitable ergodic mutual information expressions.