## Fundamentals of Resource Allocation in Wireless Networks: Theory and AlgorithmsThe purpose of this book is to provide tools for a better understanding of the fundamental tradeo?s and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these int- dependencies to achieve signi?cant performance gains. Two facts prompted us to write it: First, future wireless applications will require a fundamental understanding of the design principles and control mechanisms in wireless networks. Second, the complexity of the network problems simply precludes the use of engineering common sense alone to identify good solutions, and so mathematics becomes the key avenue to cope with central technical problems in the design of wireless networks. In this book, two ?elds of mathematics play a central role: Perron-Frobenius theory for non-negative matrices and optimization theory. This book is a revised and expanded version of the research monograph “Resource Allocation in Wireless Networks” that was published as Lecture Notes in Computer Sciences (LNCS 4000) in 2006. Although the general structure has remained unchanged to a large extent, the book contains - merous additional results and more detailed discussion. For instance, there is a more extensive treatment of general nonnegative matrices and interf- ence functions that are described by an axiomatic model. Additional material on max-min fairness, proportional fairness, utility-based power control with QoS (quality of service) support and stochastic power control has been added. |

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### Contents

Part II Principles of Resource Allocation in Wireless Networks | 79 |

Part III Algorithms | 258 |

Part IV Appendices | 345 |

### Other editions - View all

Fundamentals of Resource Allocation in Wireless Networks Slawomir Stanczak,Marcin Wiczanowski,Holger Boche No preview available - 2009 |

### Common terms and phrases

adjoint network algorithm arbitrary assume beamforming channel concave condition convergence convex function convex set Corollary data rate deﬁned Deﬁnition denote diﬀerent diﬀerentiable eﬀective eigenvalue equal equivalent exists fair Fe(s feasibility set feasible rate region ﬁrst ﬁxed ﬂows gain matrix given gradient IEEE implies inequality irreducible matrices iteration Lagrangian Lemma linear link scheduling Lipschitz continuous log-convex max-min SIR power maximal min-max node nonnegative matrices Note Observation optimal Perron root positive right eigenvector power constraints power control algorithm power control problem power vector primal primal-dual Proof QoS support receiver right eigenvector saddle point satisﬁed Sect sequence SIR power allocation SIR targets SIRk(p spectral radius stationary point strictly convex strictly increasing subnetwork suﬃcient Theorem transmit powers unique utility function utility-based power control valid power weight vector wireless networks