A Stochastic Stability Characterization of the Foschini-Miljanic Algorithm in Random Wireless Networks

Robust Power Management via Learning and Game Design

“…This last property is particularly appealing because it incorporates elements of both stability and optimality (and hence robustness): the former because the proposed algorithms converge almost surely to a fixed constant power vector (despite the persistent, random fluctuations in the network); the latter because the algorithm's end state is an optimal solution of the network's power management problem with respect to the network's mean value. This comes in sharp contrast to the FM algorithm which, when the channel is feasible on average, may fail to converge altogether -or, at best, only converges in distribution to a power profile that is not optimal in any way (Zhou et al 2016).…”

“…In a stochastic and time-varying channel, the power iterates generated by FM will be random variables and may fail to converge altogether. Even when FM does converge, it will at best, under uncertain conditions of the channel, converge to a stationary distribution (Zhou et al (2016)), as opposed to a deterministic power vector, which is more desirable. This reveals two main drawbacks of FM.…”

“…Before stating the algorithm, we shall first present the model of the stochastic and time-varying channel within which the algorithm will operate. We adopt the same stochastic model of a wireless network channel as in Zhou et al (2016):…”

Power Control with Random Delays: Robust Feedback Averaging

“…One foremost power control method in such a distributed wireless network was developed by Foschini and Miljanic (FM) [3]. Since its development, the FM algorithm has proved applicable and stable in far more general environments than originally considered [4]. As a clean and polished control scheme which possesses several strong and useful convergence properties, the FM algorithm has heavily inspired subsequent research in the field [5], [6], [7].…”