Optimal Max-min Fairness Rate Control in Wireless Networks: Perron-Frobenius Characterization and Algorithms
Rate adaptation and power control are two key resource allocation mechanisms in multiuser wireless networks. In the presence of interference, how do we jointly optimize end-to-end source rates and link powers to achieve weighted max-min rate fairness for all sources in the network? This optimization problem is hard to solve as physical layer link rate functions are nonlinear, nonconvex, and coupled in the transmit powers. We show that the weighted max-min rate fairness problem can, in fact, be decoupled into separate fairness problems for flow rate and power control. For a large class of physical layer link rate functions, we characterize the optimal solution analytically by a nonlinear Perron-Frobenius theory (through solving a conditional eigenvalue problem) that captures the interaction of multiuser interference. We give an iterative algorithm to compute the optimal flow rate that converges geometrically fast without any parameter configuration. Numerical results show that our iterative algorithm is computationally fast for both the Shannon capacity, CDMA, and piecewise linear link rate functions.
© 2012 IEEE. Date of Current Version: 10 May 2012. The work in this paper was partially supported by grants from the Research Grants Council of Hong Kong, Project No. RGC CityU 112909, Qualcomm Inc., the ARO under MURI Grant W911NF-08-1-0233, the NSF under NetSE Grant CNS 0911041, Bell Labs, Lucent-Alcatel, and the Okawa Foundation.