A general theory for SIR balancing

We study the problem of maximizing the minimum signal-to-interference ratio ( SIR) in a multiuser system with an adaptive receive strategy. The interference of each user is modelled by an axiomatic framework, which reflects the interaction between the propagation channel, the power allocation, and the receive strategy used for interference mitigation. Assuming that there is a one-to-one mapping between the QoS and the signal-to-interference ratio ( SIR), the feasible QoS region is completely characterized by the max-min SIR balancing problem. In the first part of the paper, we derive fundamental properties of this problem for the most general case, when interference is modelled with an axiomatic framework. In the second part, we show more specific properties for interference functions based on a nonnegative coupling matrix. The principal aim of this paper is to provide a deeper understanding of the interaction between power allocation and interference mitigation strategies. We show how the proposed axiomatic approach is related to the matrix-based theory.