  We consider the design of linear precoders and receivers in a Multiple-Input
Single-Output (MISO) Broadcast Channel (BC). We aim at minimizing the transmit
power while fullfiling a set of per-user Quality-of-Service (QoS) constraints
expressed in terms of per-user average rate requirements. The Channel State
Information (CSI) is assumed to be perfectly known at the receivers but only
partially at the transmitter. To solve the problem we transform the QoS
constraints into Minimum Mean Square Error (MMSE) constraints. We then leverage
the MSE duality between the BC and the Multiple Access Channel (MAC), as well
as standard interference functions in the dual MAC, to perform power
minimization by means of an Alternating Optimization (AO) algorithm. Problem
feasibility is also studied to determine whether the QoS constraints can be
fulfilled or not. Finally, we present an algorithm to balance the average rates
and manage situations that may be unfeasible or lead to an unacceptably high
transmit power.
