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We consider a power-controlled wireless network with an established networktopology in which the communication links (transmitter-receiver pairs) arecorrupted by the co-channel interference and background noise. We have fairlygeneral power constraints since the vector of transmit powers is confined tobelong to an arbitrary convex polytope. The interference is completelydetermined by a so-called gain matrix. Assuming irreducibility of this gainmatrix, we provide an elegant characterization of the max-min SIR-balancedpower allocation under such general power constraints. This characterizationgives rise to two types of algorithms for computing the max-min SIR-balancedpower allocation. One of the algorithms is a utility-based power controlalgorithm to maximize a weighted sum of the utilities of the link SIRs. Ourresults show how to choose the weight vector and utility function so that theutility-based solution is equal to the solution of the max-min SIR-balancingproblem. The algorithm is not amenable to distributed implementation as theweights are global variables. In order to mitigate the problem of computing theweight vector in distributed wireless networks, we point out a saddle pointcharacterization of the Perron root of some extended gain matrices and discusshow this characterization can be used in the design of algorithms in which eachlink iteratively updates its weight vector in parallel to the power controlrecursion. Finally, the paper provides a basis for the development ofdistributed power control and beamforming algorithms to find a global solutionof the max-min SIR-balancing problem.

A Characterization of Max-Min SIR-Balanced Power Allocation with Applications