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We consider the design of linear precoders and receivers in a Multiple-InputSingle-Output (MISO) Broadcast Channel (BC). We aim at minimizing the transmitpower while fullfiling a set of per-user Quality-of-Service (QoS) constraintsexpressed in terms of per-user average rate requirements. The Channel StateInformation (CSI) is assumed to be perfectly known at the receivers but onlypartially at the transmitter. To solve the problem we transform the QoSconstraints into Minimum Mean Square Error (MMSE) constraints. We then leveragethe MSE duality between the BC and the Multiple Access Channel (MAC), as wellas standard interference functions in the dual MAC, to perform powerminimization by means of an Alternating Optimization (AO) algorithm. Problemfeasibility is also studied to determine whether the QoS constraints can befulfilled or not. Finally, we present an algorithm to balance the average ratesand manage situations that may be unfeasible or lead to an unacceptably hightransmit power.

QoS Constrained Power Minimization in the MISO Broadcast Channel with Imperfect CSI