Optimal wireless multiuser channels with imperfect channel state information

This paper considers algorithms for optimal transmission over wireless multiuser channels where the transmitter has access to imperfect channel state information (CSI). We focus on downlink orthogonal frequency division multiple access and multiuser uplink random access. In both cases, frequency assignment, transmitted power, and coding mode are adapted to imperfect CSI in order to maximize expected transmission rate subject to average power constraints. Determination of optimal solutions is a non-convex stochastic optimization problem with infinitely many variables. Exploiting its property of null duality gap, we show that optimal solutions are determined by optimal dual variables. This affords considerable simplification because the dual optimization problem is convex and finite-dimensional. Iterative algorithms that find the optimal operating point based on imperfect CSI without having access to the channels´ probability distributions are further developed.