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We address the problem of minimum mean square error (MMSE) transceiver design for point-to-multipoint transmission in multiuser multiple-input-multiple-output (MIMO) systems. We focus on the problem of minimizing the downlink sum-MSE under a sum power constraint. It is shown that this problem can be solved efficiently by exploiting a duality between the downlink and uplink MSE feasible regions. We propose two different optimization frameworks for downlink MMSE transceiver design. The first one solves an equivalent uplink problem, then the result is transferred to the original downlink problem. Duality ensures that any uplink MMSE scheme, e.g., linear MMSE reception or MMSE-decision feedback equalization (DFE), has a downlink counterpart. We propose two globally optimum algorithms based on convex optimization. The basic idea of the second framework is to perform optimization in an alternating manner by switching between the virtual uplink and downlink channels. This strategy exploits that the same MSE can be achieved in both links for a given choice of transmit and receive filters. This iteration is proven to be convergent.