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.Comment: 19 pages, 9 figures, Submitted to IEEE Transactions in Signal
Processin
