2020 Volume 13 Issue 3 Pages 50-56
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 the 2000s, Boche and Schubert built on a generalization of the theory of standard interference mappings and considered the feasibility of the constraints by the interference mapping in their sense. In this paper, we consider the signal to interference and noise ratio (SINR) region for any continuous and standard interference mapping, i.e., the set of all attainable values of SINR and make clear some properties 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 give a new and simple proof of the existence of positive eigenvalues and positive eigenvectors for any continuous and standard interference mapping making use of the properties of the SINR region and show there is an order relation among positive eigenvectors. Furthermore, we discuss an optimization problem with SINR constraints. Under the assumption of the feasibility of the problem, we prove that there exists a unique fixed point which is, at the same time, a unique optimal solution. We also provide a sufficient condition for the feasibility of the problem, based on a unique eigenvalue of the asymptotic mapping.