Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Connections between Spectral Properties of Asymptotic Mappings and Solutions to Wireless Network Problems
 IEEE transactions on signal processing 67 (2019), No.10, pp.27472760 ISSN: 00963518 ISSN: 00189278 ISSN: 00961620 ISSN: 1053587X ISSN: 19410476 

 English 
 Journal Article 
 Fraunhofer HHI () 
Abstract
In this study, we establish connections between asymptotic functions and properties of solutions to important problems in wireless networks. We start by introducing a class of selfmappings (called asymptotic mappings) constructed with asymptotic functions, and we show that spectral properties of these mappings explain the behavior of solutions to some maxmin utility optimization problems. For example, in a common family of maxmin utility power control problems, we prove that the optimal utility as a function of the power available to transmitters is approximately linear in the low power regime. However, as we move away from this regime, there exists a transition point, easily computed from the spectral radius of an asymptotic mapping, from which gains in utility become increasingly marginal. From these results we derive analogous properties of the transmit energy efficiency. In this study, we also generalize and unify existing approaches for feasibility analysis in wireless networks. Feasibility problems often reduce to determining the existence of the fixed point of a standard interference mapping, and we show that the spectral radius of an asymptotic mapping provides a necessary and sufficient condition for the existence of such a fixed point. We further present a result that determines whether the fixed point satisfies a constraint given in terms of a monotone norm.