Foundations in Signal Processing, Communications and Network

Theory and Algorithms

By: Holger Boche, Slawomir Stanczak, Marcin Wiczanowski

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Hardcover | 7 July 2009 | Edition Number 2

At a Glance

Hardcover
456 Pages

Edition Type
Revised

Dimensions(cm)
23.7 x 16.3 x 3.0

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The 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.

Industry Reviews

From the reviews of the second edition:

"In a world of ubiquitous wireless services there is constant demand for reliable and fast connections. ... The book Fundamentals of Resource Allocation in Wireless Networks: Theory and Algorithms written by Stanczak, Wiczanowski, and Boche, all from Technical University of Berlin, is a great example of a book that presents such a formal analysis toolbox. ... The book is well organized, and the typography is of high standard. For all engineers and scientists interested in advanced concepts in resource allocation this book is a must-read." (Przemyslaw Pawelczak, IEEE Communications Magazine, February, 2010)

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Published: 29th November 2011

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List of Symbols	p. XXI
Mathematical Framework
On the Perron Root of Irreducible Matrices	p. 3
Some Basic Definitions	p. 3
Some Bounds on the Perron Root and their Applications	p. 4
Concavity of the Perron Root on Some Subsets of Irreducible Matrices	p. 11
Kullback-Leibler Divergence Characterization	p. 14
A Rate Function Representation for Large Deviations of Finite Dimensional Markov Chains	p. 15
Some Extended Perron Root Characterizations	p. 20
Collatz-Wielandt-Type Characterization of the Perron Root	p. 22
Convexity of the Perron Root	p. 25
Some Definitions	p. 26
Sufficient Conditions	p. 28
Convexity of the Feasibility Set	p. 30
Necessary Conditions	p. 32
Special Classes of Matrices	p. 34
Symmetric Matrices	p. 35
Symmetric Positive Semidefinite Matrices	p. 36
The Perron Root under the Linear Mapping	p. 37
Some Bounds	p. 39
Disproof of the Conjecture	p. 42
The Perron Root Under Exponential Mapping	p. 45
A Necessary and Sufficient Condition on Strict Convexity of the Feasibility Set	p. 45
Graph-theoretic Interpretation	p. 48
Generalizations to Arbitrary Nonnegative Matrices	p. 51
Log-Convexity of the Spectral Radius	p. 52
Characterization of the Spectral Radius	p. 52
Existence of Positive Eigenvectors	p. 56
Collatz-Wielandt-Type Characterization of the Spectral Radius	p. 57
Bibliographical Notes	p. 59
On the Positive Solution to a Linear System with Nonnegative Coefficients	p. 61
Basic Concepts and Definitions	p. 61
Feasibility Sets	p. 63
Convexity Results	p. 66
Log-Convexity of the Positive Solution	p. 67
Convexity of the Feasibility Set	p. 69
Strict Log-Convexity	p. 70
Strict Convexity of the Feasibility Sets	p. 75
The Linear Case	p. 76
Principles of Resource Allocation in Wireless Networks
Introduction	p. 81
Network Model	p. 85
Basic Definitions	p. 85
Medium Access Control	p. 87
Wireless Communications Channel	p. 90
Signal-to-Interference Ratio	p. 94
Different Receiver Structures	p. 98
Power Constraints	p. 104
Data Rate Model	p. 107
Examples	p. 111
Resource Allocation Problem in Communications Networks	p. 119
End-to-End Rate Control in Wired Networks	p. 119
Fairness Criteria	p. 120
Algorithms	p. 124
Problem Formulation for Wireless Networks	p. 125
Joint Power Control and Link Scheduling	p. 126
Feasible Rate Region	p. 129
End-to-End Window-Based Rate Control	p. 132
MAC Layer Fair Rate Control	p. 134
Utility-Based Power Control	p. 136
Efficiency-Fairness Trade-Off	p. 141
Kuhn-Tucker Conditions	p. 146
Interpretation in the QoS Domain	p. 150
Remarks on Joint Power Control and Link Scheduling	p. 160
Optimal Joint Power Control and Link Scheduling	p. 160
High SIR Regime	p. 163
Low SIR Regime	p. 163
Wireless Links with Self-Interference	p. 167
QoS-based Power Control	p. 168
Some Definitions	p. 169
Axiomatic Interference Functions	p. 174
QoS-Based Power Control Algorithms	p. 180
Max-Min SIR Balancing Power Control	p. 191
Some Preliminary Observations	p. 192
Characterization under Sum Power Constraints	p. 195
General Power Constraints	p. 199
Some Consequences and Applications	p. 204
Utility-based Power Control with QoS Support	p. 210
Hard QoS Support	p. 212
Soft QoS Support	p. 213
Utility-Based Joint Power and Receiver Control	p. 222
Problem Statement	p. 222
Perfect Synchronization	p. 224
Decentralized Alternating Computation	p. 226
Max-Min SIR Balancing	p. 227
Additional Results for a Noiseless Case	p. 228
The Efficiency-Fairness Trade-off	p. 229
Existence and Uniqueness of Log-SIR Fair Power Allocation	p. 241
Proofs	p. 246
Algorithms
Power Control Algorithms	p. 261
Introduction	p. 261
Some Basic Definitions	p. 262
Convex Statement of the Problem	p. 264
Strong Convexity Conditions	p. 266
Gradient Projection Algorithm	p. 270
Global Convergence	p. 270
Rate of Convergence	p. 273
Diagonal Scaling	p. 275
Projection on a Closed Convex Set	p. 275
Distributed Implementation	p. 276
Local and Global Parts of the Gradient Vector	p. 276
Adjoint Network	p. 278
Distributed Handshake Protocol	p. 282
Some Comparative Remarks	p. 283
Noisy Measurements	p. 285
Incorporation of QoS Requirements	p. 288
Hard QoS Support	p. 289
Soft QoS Support	p. 300
Primal-Dual Algorithms	p. 302
Improving Efficiency by Primal-Dual Methods	p. 304
Generalized Lagrangian	p. 311
Primal-Dual Algorithms	p. 319
Decentralized Implementation	p. 322
Min-max Optimization Framework	p. 326
Simulation Results	p. 342
Appendices
Some Concepts and Results from Matrix Analysis	p. 347
Vectors and Vector Norms	p. 347
Matrices and Matrix Norms	p. 349
Square Matrices and Eigenvalues	p. 351
Matrix Spectrum, Spectral Radius and Neumann Series	p. 353
Orthogonal, Symmetric and Positive Semidefinite Matrices	p. 355
Perron-Frobenius Theory	p. 357
Perron-Frobenius Theorem for Irreducible Matrices	p. 358
Perron-Frobenius Theorem for Primitive Matrices	p. 362
Some Extensions to Reducible Matrices	p. 363
The Existence of a Positive Solution p to (¿I - X)p = b	p. 371
Some Concepts and Results from Convex Analysis	p. 377
Sets and Functions	p. 377
Convex Sets and Functions	p. 383
Strong Convexity	p. 384
Majorization and Schur-Convexity	p. 386
Log-Convex Functions	p. 386
Inverse Functions of Monotonic Log-Convex Functions	p. 388
Basics of Optimization Theory	p. 389
Characterization of Numerical Convergence	p. 390
Convergence of Gradient Projection Algorithms	p. 392
Basics of Lagrangian Optimization Theory	p. 395
Saddle Points, Saddle Functions, Min-Max Functions	p. 398
References	p. 401
Index	p. 411
Table of Contents provided by Ingram. All Rights Reserved.

Foundations in Signal Processing, Communications and Network

Theory and Algorithms

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Hardcover

Industry Reviews

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