Concave resource allocation problems for interference coupled wireless systems

The paper characterizes the class of all concave resource allocation problems in interference coupled wireless systems. An axiomatic framework for interference functions proposed by Yates in 1995 is used to model interference coupling in our paper. The paper shows that there exists no transformation, which ensures concavity for all linear interference functions for all functions of SINR. The paper then characterizes the largest class of utility functions under a certain requirement, such that the corresponding class of utility functions functions, which are a function of SINR in the s-domain are concave. The paper shows that such a class of utility functions is a restricted class due to a requirement, which ensures concavity. Furthermore, the paper shows that the largest class of interference functions, which ensures concavity for resource allocation problems are the log-convex interference functions. These results differ from the convex case, where we are interested in minimizing utility functions of inverse SINR.