Alpha-Fair Resource Allocation under Incomplete Information and Presence of a Jammer

Abstract

Abstract. In the present work we deal with the concept of alpha-fair resource allocation in the situation where the decision maker (in our case, the base station) does not have complete information about environment. Namely, we develop a concept of α-fairness under uncertainty to allocate power resource in the presence of a jammer under two types of uncertainty: (a) the decision maker does not have complete knowledge about the parameters of the environment, but knows only their distribution, (b) the jammer can come into the environment with some probability bringing extra background noise. The goal of the decision maker is to maximize the α-fairness utility function with respect to the SNIR (signal to noise-plus-interference ratio). Here we consider a concept of the expected α-fairness utility function (short-term fairness) as well as fairness of expectation (long-term fairness). In the scenario with the unknown parameters of the environment the most adequate approach is a zero-sum game since it can also be viewed as a minimax problem for the decision maker playing against the nature where the decision maker has to apply the best allocation under the worst circumstances. In the scenario with the uncertainty about jamming being in the system the Nash equilibrium concept is employed since the agents have non-zero sum payoffs: the decision maker would like to maximize either the expected fairness or the fairness of expectation while the jammer would like to minimize the fairness if he comes in on the scene. For all the plots the equilibrium strategies in closed form are found. We have shown that for all the scenarios the equilibrium has to be constructed into two steps. In the first step the equilibrium jamming strategy has to be constructed based on a solution of the corresponding modification of the water-filling equation. In the second step the decision maker equilibrium strategy has to be constructed equalizing the induced by jammer background noise.

Multiscale fairness and its application to resource allocation in wireless networks

“…This, as well as other fairness notions can be defined through a set of axioms, see [2]. This paper is inspired by several papers which already observed or derived fairness at different time-scales [3][4][5][6][7][8]. However, we would like to mention that the T -scale fairness (a unifying generalization of long-and short-term fairness) and multiscale fairness are new concepts introduced in the present work.…”

Multiscale Fairness and Its Application to Resource Allocation in Wireless Networks

“…This, as well as other fairness notions can be defined through a set of axioms, see [2]. This paper is inspired by several papers which already observed or derived fairness at different time-scales [3,4,5,6,7,8]. However, we would like to mention that the T -scale fairness (a unifying generalization of long-and short-term fairness) and multiscale fairness are new concepts introduced in the present work.…”

A heterogeneous approach to fair resource allocation and its application in femtocell networks

“…This, as well as other fairness notions can be defined through a set of axioms, see [4]. For a rich literature on concepts of fairness and some interesting applications, the reader is referred to [5], [6], [7], [8], [9]. For the state of art and current research trends in femtocell networks, see [10] and the references therein.…”