Alpha-fair resource allocation under incomplete information and presence of a jammer

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 fo