Linear precoding for the wireless MIIMO broadcast channel with multiple antennas at the transmitter and non cooperative single antenna receivers is considered. For statistical channel state information (CSI) at the transmitter a novel opti mization problem for adaptive precoding based on the mean square error (MSE) is solved, which can also deal with incomplete CSI at the receivers, i.e., the receivers' channel estimates rely on a common pilot channel. We explicitly model the receivers' (limited) processing capabilities, which leads to a performance advantage over existing signal-tointerference-and-noise-ratio (SINR) approaches.