A characterization of max-min SIR-balanced power allocation with applications

We consider a power-controlled wireless network with an established network topology in which the communication links (transmitter-receiver pairs) are subject to some constraints on transmit powers and corrupted by the cochannel interference and background noise. The interference is completely determined by a so-called gain matrix. Assuming irreducibility of the gain matrix, we provide an elegant characterization of the max-min SIR-balanced power allocation under general power constraints. This characterization gives rise to two types of algorithms for computing the max-min SIR-balanced power allocation. It also allows for an interesting saddle point characterization of the Perron root of extended gain matrices.