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We address the problem of designing jointly the linear transmit and receive beamformers in a single-cell multiuser multiple-input multiple-output (MIMO) downlink system. The optimization is based on maximizing the weighted harmonic mean of the combiner output's signal-to-interference-and-noise ratio (SINR). When the linear minimum mean-squared error (MMSE) receivers are employed, we show that the maximization of the proposed objective leads to the minimization of an upper-bound on the weighted sum mean-squared error (MSE).We propose a reduced complexity solution which finds the transmit beamformers without relying on interior point methods. The solution supports the transmission of multiple substreams to each user, and handles multiple antennas at both the base station (BS) and the mobiles. Power allocation schemes based on the sum-power constraint (SPC) and the per-antenna power constraint (PAPC) are also investigated in this paper.