Low-Complexity Robust MISO Downlink Precoder Design Under Imperfect CSI

We consider the design of the linear precoder for a multiple-input single-output (MISO) downlink system with quality-of-service (QoS) constraints. The broad goal is to develop low-complexity techniques that mitigate the impact of the uncertainty in the transmitter's channel state information (CSI) by incorporating probabilistic models for the uncertainty into the design. The proposed techniques are developed for systems based on limited feedback, and they can be easily adapted to systems that acquire CSI using estimation on the uplink and channel reciprocity. We consider the conventional problem of minimizing the transmitted power under probability of outage constraints for a target signal-to-interference-and-noise ratio (SINR), and the related problem of minimizing the outage probability under a transmitted power constraint. By approximating the outage constraint by a zero-outage region, employing a semidefinite relaxation, and applying an extension of the S-Lemma that is derived herein, these problems are converted into convex and quasi-convex problems, respectively. Insights into the structure of the solution of those problems are then used to generate an alternate design formulation that provides greater robustness in the presence of significant uncertainties and has a quasi-closed-form solution. As illustrated by simulations, the proposed alternate design provides significantly better performance than the conventional designs that do not incorporate uncertainty models, and better performance than existing robust designs in the presence of large uncertainties, and does so at a computational cost that is close to that of the conventional designs.