The Structures of SINR Regions for Standard Interference Mappings

Abstract

In 1995, Yates proposed an axiomatic framework of standard interference mappings and examined the iterative power control algorithm for a system with interference constraints. In 2000s, Boche and Schubert built on a generalization of the theory of standard interference mappings and considered feasibility of the constraints by the interference mapping in their sense. In this paper, we consider the SINR (Signal to Interference and Noise Ratio) region of any continuous and standard interference mapping, i.e., the set of all realizable values of SINR and make clear the structure of the SINR region. We also show the relations between the SINR regions for any continuous and standard interference mapping and its asymptotic mapping. In addition, we discuss an optimization problem with SINR constraints. Under the assumption of feasibility of the problem, we prove that there exists a unique fixed point which is at the same time a unique optimal solution. Furthermore, we show the so-called max min balancing property holds at the optimal solution.