In this work, we study the downlink of multiuser multiantenna systems which employ one multiple-input multiple-output (MIMO) relay and the amplify-and-forward (AF) relay strategy. We propose joint constrained optimization frameworks that consider the allocation of power levels between the base station (BS) and the relay station (RS) subject to a total power constraint and the joint design of BS precoders, relay beamformers and mobile station (MS) receivers. In terms of the perfect channel state information (CSI), we derive constrained minimum mean square error (MMSE) expressions for the BS precoding and RS beamforming matrices that determine the optimal power levels across the BS and the RS, and the MS receiver matrices. Simulation results show that the performance of the proposed techniques is significantly better than prior art in terms of perfect CSI.