Max-Min Utility Fair Power Control in Cognitive Radio Networks

This chapter presents a systematic approach for solvingmax-min utility fair power control problems in cognitive radio networks (CRNs) with general monotonic constraints, such as power constraints and interference temperature constraints. These problems are often challenging to solve due to the complicated nonlinear and nonconvex relation between the users’ transmit powers and their utility functions. By establishing a connection between these problems and the class of conditional eigenvalue problems that can be addressed by a generalized nonlinear Perron-Frobenius theory, we show how these problems can be solved optimally using an iterative algorithm that converges geometrically fast. The proposed framework is general enough to include a broad class of competitive utility functions, such as SINR, MSE, capacity, QoE, outage probability, and can accommodate monotonic constraints on, e.g., power, interference temperature, and outage probability. This framework can also be extended to incorporate the problem of max-min rate assignment of multiple flows in CRNs. Numerical results are presented to demonstrate the fast-convergence behavior of the algorithms to the optimal fixed-point solution characterized by our generalized nonlinear Perron-Frobenius theoretic framework.