Robust Design of Power Minimizing Symbol-Level Precoder under Channel Uncertainty

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 design problem, a general category of constructive interference regions (CIR) called distance preserving CIR (DPCIR) is adopted. In particular, we are interested in a robust SLP design minimizing the total transmit power subject to individual quality-of-service (QoS) requirements. We consider two common models for the channel uncertainty region, namely, spherical (norm-bounded) and stochastic. For the spherical uncertainty model, a worst-case robust precoder is proposed, while for the stochastically known uncertainties, we derive 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.