  We consider a power-controlled wireless network with an established network
topology in which the communication links (transmitter-receiver pairs) are
corrupted by the co-channel interference and background noise. We have fairly
general power constraints since the vector of transmit powers is confined to
belong to an arbitrary convex polytope. The interference is completely
determined by a so-called gain matrix. Assuming irreducibility of this gain
matrix, we provide an elegant characterization of the max-min SIR-balanced
power allocation under such general power constraints. This characterization
gives rise to two types of algorithms for computing the max-min SIR-balanced
power allocation. One of the algorithms is a utility-based power control
algorithm to maximize a weighted sum of the utilities of the link SIRs. Our
results show how to choose the weight vector and utility function so that the
utility-based solution is equal to the solution of the max-min SIR-balancing
problem. The algorithm is not amenable to distributed implementation as the
weights are global variables. In order to mitigate the problem of computing the
weight vector in distributed wireless networks, we point out a saddle point
characterization of the Perron root of some extended gain matrices and discuss
how this characterization can be used in the design of algorithms in which each
link iteratively updates its weight vector in parallel to the power control
recursion. Finally, the paper provides a basis for the development of
distributed power control and beamforming algorithms to find a global solution
of the max-min SIR-balancing problem.
