We study the problem of minimizing the sum transmit power in mutliple-input multiple-output (MIMO) downlink channels with linear transceivers if per-user quality of service (QoS) constraints (expressed in terms of rates) have to be fulfilled. To find a suboptimal solution of the arising non-convex optimization problem, we introduce new auxiliary variables representing the division of the per-user rate constraints into per-stream rate targets, and we optimize these variables by means of gradient-projection steps. This new method is combined with alternating updates of the transmit and receive filters. Furthermore, the proposed algorithm ensures that the mean square error (MSE) matrices of all users are diagonal, and in the course of the execution of the algorithm, it is possible that inactive streams get activated if this leads to a decreased sum transmit power. In numerical simulations, the new algorithm turns out to be superior to the various existing methods since these methods either lead to a higher sum transmit power than the proposed scheme or have a higher computational complexity or make restrictive assumptions on the system parameters.
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