Adaptive transmit policies for cost-efficient power allocation in multi-carrier systems

In this paper, we examine the problem of cost/energy-efficient power allocation in uplink multi-carrier orthogonal frequency-division multiple access (OFDMA) wireless networks. In particular, we consider a set of wireless users who seek to maximize their transmission rate subject to pricing limitations and we show that the resulting non-cooperative game admits a unique equilibrium for almost every realization of the system´s channels. We also propose a distributed exponential learning scheme which allows users to converge to the game´s equilibrium exponentially fast by using only local channel state information (CSI) and signal to interference-plus-noise ratio (SINR) measurements. Given that such measurements are often imperfect in practical scenarios, a major challenge occurs when the users´ information is subject to random perturbations. In this case, by using tools and ideas from stochastic convex programming, we show that the proposed learning scheme retains its convergence properties irrespective of the magnitude of the observational errors.