Distributed stochastic power control for time-varying long-term and short-term fading wireless networks

In this paper, new time-varying wireless channel models that capture both the space and time variations of longterm and short-term fading wireless networks are developed. The proposed models are based on stochastic differential equations. These models are more realistic than the static ones usually encountered in the literature. Moreover, optimal power control algorithms based on the new models are proposed. A centralized power control algorithm is shown to reduce to a simple linear programming problem if predictable power control strategies are used. In addition, an iterative distributed stochastic power control algorithm is used to solve for the optimization problem using stochastic approximations. The latter solely requires each mobile to know its received signal to interference ratio unlike common stochastic algorithms found in the literature. Numerical results show that the proposed distributed stochastic power control algorithm under the new time-varying channels provides better power stability and consumption than the deterministic ones.