A basic question in wireless networking is how to optimize the
wireless network resource allocation for utility maximization and
interference management. How can we overcome interference to
efficiently optimize fair wireless resource allocation, under
various stochastic constraints on quality of service demands?
Network designs are traditionally divided into layers. How does
fairness permeate through layers? Can physical layer innovation be
jointly optimized with network layer routing control? How should
large complex wireless networks be analyzed and designed with
clearly-defined fairness using beamforming? Wireless Network
Optimization by Perron-Frobenius Theory provides a comprehensive
survey of the models, algorithms, analysis, and methodologies using
a Perron-Frobenius theoretic framework to solve wireless utility
maximization problems. This approach overcomes the notorious
non-convexity barriers in these problems, and the optimal value and
solution of the optimization problems can be analytically
characterized by the spectral property of matrices induced by
nonlinear positive mappings. It can even solve several previously
open problems in the wireless networking literature. This survey
will be of interest to all researchers, students and engineers
working on wireless networking.
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