# Robust SINR-Constrained Symbol-Level Multiuser Precoding with Imperfect Channel Knowledge

## TL;DR

This paper develops a robust symbol-level multiuser precoding method for MIMO systems that accounts for imperfect channel knowledge, using convex approximations to ensure reliable performance under uncertainty.

## Contribution

It introduces convex robust precoding constraints for both bounded and Gaussian CSI errors, improving reliability in multiuser MIMO downlink systems.

## Key findings

- Robust precoding reduces power consumption under CSI uncertainty.
- Convex approximations outperform benchmark methods.
- Robust design increases computational complexity with more users.

## Abstract

In this paper, we address robust design of symbol-level precoding for the downlink of multiuser multiple-input multiple-output wireless channels, in the presence of imperfect channel state information (CSI) at the transmitter. In particular, we consider two common uncertainty models for the CSI imperfection, namely, spherical (bounded) and stochastic (Gaussian). Our design objective is to minimize the total (per-symbol) transmission power subject to constructive interference (CI) constraints as well as users' quality-of-service requirements in terms of signal-to-interference-plus-noise ratio. Assuming bounded channel uncertainties, we obtain a convex CI constraint based on the worst-case robust analysis, whereas in the case of Gaussian uncertainties, we define probabilistic CI constraints in order to achieve robustness to statistically-known CSI errors. Since the probabilistic constraints of actual interest are difficult to handle, we resort to their convex approximations, yielding tractable (deterministic) robust constraints. Three convex approximations are developed based on different robust conservatism approaches, among which one is introduced as a benchmark for comparison. We show that each of our proposed approximations is tighter than the other under specific robustness conditions, while both always outperform the benchmark. Using the developed CI constraints, we formulate the robust precoding optimization as a convex conic quadratic program. Extensive simulation results are provided to validate our analytic discussions and to make comparisons with existing robust precoding schemes. We also show that the robust design increases the computational complexity by an order of the number of users in the large system limit, compared to its non-robust counterpart.