Optimal Wireless Communications With Imperfect Channel State Information

This paper studies optimal transmission over wireless channels with imperfect channel state information available at the transmitter side in the context of point-to-point channels, multiuser orthogonal frequency division multiplexing, and random access. Terminals adapt transmitted power and coding mode to channel estimates in order to maximize expected throughput subject to average power constraints. To reduce the likelihood of packet losses due to the mismatch between channel estimates and actual channel values, a backoff function is further introduced to enforce the selection of more conservative coding modes. Joint determination of optimal power allocations and backoff functions is a nonconvex stochastic optimization problem with infinitely many variables that despite its lack of convexity is part of a class of problems with null duality gap. Exploiting the resulting equivalence between primal and dual problems, we show that optimal power allocations and channel backoff functions are uniquely determined by optimal dual variables. This affords considerable simplification because the dual problem is convex and finite dimensional. We further exploit this reduction in computational complexity to develop iterative algorithms to find optimal operating points. These algorithms implement stochastic subgradient descent in the dual domain and operate without knowledge of the probability distribution of the fading channels. Numerical results corroborate theoretical findings.