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Weakly Standard Interference Mappings: Existence of Fixed Points and Applications to Power Control in Wireless Networks

: Cavalcante, R.L.G.; Stańczak, S.


Sanei, Saeid (General Chair) ; Institute of Electrical and Electronics Engineers -IEEE-; IEEE Signal Processing Society:
ICASSP 2019, IEEE International Conference on Acoustics, Speech and Signal Processing. Proceedings : May 12-17, 2019, Brighton
Piscataway, NJ: IEEE, 2019
ISBN: 978-1-4799-8131-1
ISBN: 978-1-4799-8132-8
International Conference on Acoustics, Speech, and Signal Processing (ICASSP) <44, 2019, Brighton>
Bundesministerium für Bildung und Forschung BMBF (Deutschland)
Fraunhofer HHI ()

We propose novel approaches to identify the existence of fixed points of the so-called weakly standard interference mappings, which include the well-known standard and general interference mappings as particular cases. The approaches are based on the concept of spectral radius of asymptotic mappings, a mathematical tool recently introduced to study the behavior of wireless networks. We show that, for arbitrary weakly standard interference mappings, knowledge of the spectral radius of an associated asymptotic mapping gives a sufficient condition to determine the existence of fixed points or their absence in the positive orthant. If the mapping has a fixed point, we further prove that the set of fixed points has a minimal element that can be easily computed with a simple fixed point algorithm. The theory developed here is applied to the problem of power control for load planning in LTE networks. Unlike previous approaches in the literature, the proposed solution takes into account the limited number of modulation and coding schemes of practical transceivers.