Optimal Transmission over a Fading Channel with Imperfect Channel State Information

This paper considers a wireless channel when the probability distribution of fading is unknown and the transmitter has access to imperfect channel state information (CSI). Transmitted power and coding mode are adapted to the available imperfect CSI through the use of a backoff function in order to maximize the expected transmission rate subject to an average power constraint. Determination of the optimal power allocation and backoff function is a non-convex stochastic optimization problem with infinitely many variables. Despite its non-convexity, the duality gap of this problem has been shown to be null. Exploiting this property, we show that the optimal power allocation and channel backoff functions are uniquely determined by the optimal dual variable. This affords considerable simplification because the dual optimization problem is convex and one-dimensional -- whereas the original primal problem is non-convex and infinite-dimensional. Iterative algorithms that find the optimal power and backoff function based on imperfect CSI without having access to the channel probability distribution are further developed. Numerical results are provided to corroborate theoretical findings.