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Resource Allocation in Wireless Networks: Theory and Algorithms [Pehme köide]

  • Formaat: Paperback / softback, 211 pages, kõrgus x laius: 235x155 mm, kaal: 318 g, Illustrations
  • Sari: Lecture Notes in Computer Science v.4000
  • Ilmumisaeg: 30-Oct-2006
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540462481
  • ISBN-13: 9783540462484
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  • Formaat: Paperback / softback, 211 pages, kõrgus x laius: 235x155 mm, kaal: 318 g, Illustrations
  • Sari: Lecture Notes in Computer Science v.4000
  • Ilmumisaeg: 30-Oct-2006
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540462481
  • ISBN-13: 9783540462484
Teised raamatud teemal:
Resource Allocation in Wireless Networks demonstrates that emerging applications and directions require fundamental understanding on how to design and control wireless networks that lie far beyond what the currently existing theory can provide. It is shown that mathematics is the key technology to cope with central technical problems in their design. The book provides the tools for better understanding the fundamental tradeoffs in wireless networks.

The wireless industry is in the midst of a fundamental shift from providing voice-only services to offering customers an array of multimedia services, including a wide variety of audio, video and data communications capabilities. Future wireless networks will be integrated into every aspect of daily life, and therefore could affect our life in a magnitude similar to that of the Internet and cellular phones.This monograph demonstrates that these emerging applications and directions require fundamental understanding on how to design and control wireless networks that lies far beyond what the currently existing theory can provide. It is shown that mathematics is the key technology to cope with central technical problems in the design of wireless networks since the complexity of the problem simply precludes the use of engineering common sense alone to identify good solutions.The main objective of this book is to provide tools for better understanding the fundamental tradeoffs and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these interdependencies to achieve significant performance gains. The book consists of three largely independent parts: theory, applications and appendices. The latter contain foundational apects to make the book more understandable to readers who are not familiar with some basic concepts and results from linear algebra and convex analysis.
List of Symbols XIX
Part I Theory
1 On the Perron Root of Irreducible Matrices
3
1.1 Some Basic Definitions
3
1.2 Some Bounds on the Perron Root and Their Applications
4
1.2.1 Concavity of the Perron Root on Some Subsets of Irreducible Matrices
11
1.2.2 Kullback–Leibler Divergence Characterization
14
1.2.3 Some Extended Perron Root Characterizations
15
1.2.4 Collatz–Wielandt-Type Characterization of the Perron Root
18
1.3 Convexity of the Perron Root
22
1.3.1 Some Definitions
22
1.3.2 Sufficient Conditions
24
1.3.3 Convexity of the Feasibility Set
26
1.3.4 Necessary Conditions
28
1.4 Special Classes of Matrices
30
1.4.1 Symmetric Matrices
31
1.4.2 Symmetric Positive Semidefinite Matrices
32
1.5 The Perron Root Under the Linear Mapping
34
1.5.1 Some Bounds
35
1.5.2 Disproof of the Conjecture
38
1.6 Some Remarks on Arbitrary Nonnegative Matrices
41
1.6.1 Log-Convexity of the Spectral Radius
42
1.6.2 Characterization of the Spectral Radius
43
1.6.3 Collatz- Wielandt-Type Characterization of the Spectral Radius
46
1.7 Bibliograpical Notes
47
2 On the Positive Solution to a Linear System with Nonnegative Coefficients
51
2.1 Basic Concepts and Definitions
51
2.2 Feasibility Sets
53
2.3 Convexity Results
56
2.3.1 Log-Convexity of the Positive Solution
56
2.3.2 Convexity of the Feasibility Set
59
2.3.3 Strict Log-Convexity
60
2.3.4 Strict Convexity of the Feasibility Sets
65
2.4 The Linear Case
66
Part II Applications and Algorithms
3 Introduction
71
4 Network Model
75
4.1 Basic Definitions
75
4.2 Medium Access Control
76
4.3 Wireless Communication Channel
79
4.3.1 Signal-to-Interference Ratio
81
4.3.2 Power Constraints
83
4.3.3 Data Rate Model
84
4.3.4 Two Examples
85
5 Resource Allocation Problem in Communications Networks
91
5.1 End-to-End Rate Control in Wired Networks
91
5.1.1 Fairness Criteria
92
5.1.2 Algorithms
95
5.2 Problem Formulation for Wireless Networks
97
5.2.1 Joint Power Control and Link Scheduling
98
5.2.2 Feasible Rate Region
101
5.2.3 End-to-End Window-Based Rate Control for Wireless Networks
103
5.2.4 MAC Layer Fair Rate Control for Wireless Networks
105
5.2.5 Utility-Based Power Control
107
5.3 Interpretation in the QoS Domain
112
5.4 Remarks on Joint Power Control and Link Scheduling
115
5.4.1 Optimal Joint Power Control and Link Scheduling
115
5.4.2 High SIR Regime
118
5.4.3 Low SIR Regime
119
5.4.4 Wireless Links with Self-Interference
122
5.5 Remarks on the Efficiency–Fairness Trade Off
123
5.5.1 Efficiency of the Max-Min Fair Power Allocation
125
5.5.2 Axiom-Based Interference Model
128
6 Power Control Algorithm
129
6.1 Some Basic Definitions
130
6.2 Convex Statement of the Problem
131
6.3 Strong Convexity Conditions
133
6.4 Gradient Projection Algorithm
137
6.4.1 Global Convergence
138
6.4.2 Rate of Convergence
140
6.4.3 Diagonal Scaling
142
6.4.4 Projection on a Closed Convex Set
142
6.5 Distributed Implementation
143
6.5.1 Local and Global Parts of the Gradient Vector
143
6.5.2 Adjoint Network
145
6.5.3 Distributed Handshake Protocol
148
6.5.4 Noisy Measurements
150
Part III Appendices
A Some Concepts and Results from Matrix Analysis
155
A.1 Vectors and Vector Norms
155
A.2 Matrices and Matrix Norms
157
A.3 Square Matrices and Eigenvalues
158
A.3.1 Spectral Radius and Neumann Series
159
A.3.2 Orthogonal, Symmetric and Positive Semidefinite Matrices
160
A.4 Perron—Frobenius Theory
161
A.4.1 Perron—Frobenius Theorem for Irreducible Matrices
162
A.4.2 Perron—Frobenius Theorem for Primitive Matrices
165
A.4.3 Some Remarks on Reducible Matrices
166
A.4.4 The Existence of a Positive Solution p to (αI — X)p = b
168
B Some Concepts and Results from Convex Analysis
171
B.1 Sets and Functions
171
B.2 Convex Sets and Functions
175
B.2.1 Strong Convexity
176
B.3 Log-Convex Functions
177
B.3.1 Inverse Functions of Monotonic Log-Convex Functions
179
B.4 Convergence of Gradient Projection Algorithms
180
References
185