Perron-root minimization for interference-coupled systems with adaptive receive strategies

Interference in multiuser systems is often characterized by a non-negative and irreducible coupling matrix. The maximum eigenvalue (Perron root) of the weighted coupling matrix provides a single measure for the joint achievability of certain signal-to-interference ratios (SIR). In this paper, we address the more general case where the users are coupled by concave interference functions. This corresponds to a system with adaptive receive strategies which minimize the interference received by each user. A necessary and sufficient condition for feasibility is obtained by minimizing the Perron root over the set of possible receive strategies. This type of problem is directly related to the problem of (weighted) max-min-SIR balancing. This paper provides an analytical framework and an iterative algorithm that converges monotonically to a global optimum. We also study an alternative approach based on a fixed point iteration. This iteration is shown to converge to the global optimum if the SIR targets lie on the boundary of the region.