Robust Maximin MIMO Precoding for Arbitrary Convex Uncertainty Sets

We consider a worst-case robust precoding design for multi-input multi-output (MIMO) communication systems with imperfect channel state information at the transmitter (CSIT). Instead of a particular choice, we consider a general imperfect CSIT model that only assumes the channel errors to be within a convex set, which includes most common imperfect CSIT models as special cases. The robust precoding design is formulated as a maximin problem, aiming at maximizing the worst-case received signal-to-noise ratio or minimizing the worst-case error probability. It is shown that the robust precoder can be easily obtained by solving a convex problem. We further provide an equivalent but more practical form of the convex problem that can be efficiently handled with common optimization methods and software packages.