Generalised multi-receiver radio network: capacity and asymptotic stability of power control through Banach's fixed-point theorem

Authors:
Virgilio Rodriguez;Rudolf Mathar;Anke Schmeink
Affiliations:
Institute for Theoretical Information Technology;Institute for Theoretical Information Technology;UMIC Research Centre, RWTH Aachen, Aachen, Germany
Venue:
WCNC'09 Proceedings of the 2009 IEEE conference on Wireless Communications & Networking Conference
Year:
2009

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Abstract

We introduce a model of a generalised multi-receiver radio network with quality-of-service (QoS) constraints. There are two key functions: (1) Ni is non-decreasing and homogeneous and gives i's QoS as function of its carrier-to-interference ratios at each of K receivers, (2) nu_ik is a semi-norm that gives the interference experienced by transmitter i at receiver k as function of the power vector. We utilise "norm" concepts and Banach's well-known fixed-point theorem to characterise the conditions under which a QoS vector is feasible, and the corresponding power-adjustment process converges. The critical power levels equal a_i/h_i where a_i is the QoS target, and h_i is the 'average' channel gain. hi=Ni(h_i1,..., h_i,K) where h_ik is the channel gain from transmitter i to receiver k. If the interference experienced by each transmitter i at each receiver k is less than 1 when each power is set to the critical level (i.e., nu_ik(a_1/h_1, a_2/h_2,..., a_N/h_N)