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In this paper, we propose two robust precoder designs for multiple-input multiple-output (MIMO) broadcast channels with imperfect channel state information (CSI). First,we consider a precoder design for a multiuser multiple-input single-output (MISO) downlink, where a base station (BS) equipped with multiple transmit antennas communicates with user terminals which are equipped with a single receive antenna. For this scenario, we propose a robust precoder design based on the minimization of the total BS transmit power under constraints on individual user signal-to-interference-plus-noise ratio (SINR). We show that this problem can be formulated as a second order cone program (SOCP) that can be solved efficiently. Next, we consider a precoder design for a multiuser MIMO downlink, where the user terminals are equipped with multiple receive antennas. For this scenario, we propose a robust joint precoder/receive filter design based on the minimization of a stochastic function of the sum mean square error (SMSE), under a constraint on the total BS transmit power. We solve this problem through an iterative algorithm, wherein the optimization is performed with respect to the transmit precoder and the receive filter in an alternating fashion.