  In this paper, we investigate the downlink transmission of a multiuser
multiple-input single-output (MISO) channel under a symbol-level precoding
(SLP) scheme, having imperfect channel knowledge at the transmitter. In
defining the SLP problem, a general category of constructive interference
regions (CIR) called distance preserving CIR (DPCIR) is adopted. In particular,
we are interested in the robust SLP design minimizing the total transmit power
while satisfying the users' quality-of-service (QoS) requirements. We consider
two common models for the channel uncertainty region, namely, norm-bounded
spherical and stochastic. For the spherical uncertainty model, a worst-case
robust precoder is proposed, while for the stochastic uncertainties, we define
a convex optimization problem with probabilistic constraints. We simulate the
performance of the proposed robust approaches, and compare them with the
existing methods. Through the simulation results, we also show that there is an
essential trade-off between the two robust approaches.
