  We consider the downlink of a cellular system in which the base station
employs multiple transmit antennas, each receiver has a single antenna, and the
users specify. We consider communication schemes in which the users have
certain Quality of Service (QoS) requirements. We study the design of robust
broadcasting schemes that minimize the transmission power necessary to
guarantee that the QoS requirements are satisfied for all channels within
bounded uncertainty regions around the transmitter's estimate of each user's
channel. Each user's QoS requirement is formulated as a constraint on the mean
square error (MSE) in its received signal, and we show that these MSE
constraints imply constraints on the received SINR. Using the MSE constraints,
we present a unified design approach for robust linear and non-linear
transceivers with QoS requirements. The proposed designs overcome the
limitations of existing approaches that provide conservative designs or are
only applicable to the case of linear precoding. Furthermore, we provide
computationally-efficient design formulations for a rather general model of
channel uncertainty that subsumes many natural choices for the uncertainty
region. We also consider the problem of the robust counterpart to precoding
schemes that maximize the fidelity of the weakest user's signal subject to a
power constraint. For this problem, we provide quasi-convex formulations, for
both linear and non-linear transceivers, that can be efficiently solved using a
one-dimensional bisection search. Our numerical results demonstrate that in the
presence of CSI uncertainty, the proposed designs provide guarantees for a
larger range of QoS requirements than the existing approaches, and consume
require less transmission power in providing these guarantees.
