Max-min fair rate control based on a saddle-point characterization of some perron roots

We consider a power-controlled wireless network with an established network topology in which the communication links (transmitter-receiver pairs) are subject to general constraints on transmit powers and corrupted by the co-channel interference and background noise. In this paper, we characterize the max-min SIR power allocation and provide a saddle point characterization of this power allocation under weaker conditions. This characterization is a basis for novel algorithms for computing a max-min SIR power allocation.