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E-raamat: Utility Maximization in Nonconvex Wireless Systems

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Utility Maximization in Nonconvex Wireless SystemsSuurem pilt
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This book offers a framework for modeling and solving utility maximization problems in nonconvex wireless systems, presenting a general model for utility optimization in wireless systems, methods for solving problems, and case studies showing the model in use.

This monograph develops a framework for modeling and solving utility maximization problems in nonconvex wireless systems. The first part develops a model for utility optimization in wireless systems. The model is general enough to encompass a wide array of system configurations and performance objectives. Based on the general model, a set of methods for solving utility maximization problems is developed in the second part of the book. The development is based on a careful examination of the properties that are required for the application of each method. This part focuses on problems whose initial formulation does not allow for a solution by standard methods and discusses alternative approaches. The last part presents two case studies to demonstrate the application of the proposed framework. In both cases, utility maximization in multi-antenna broadcast channels is investigated.
1 Introduction
1(6)
2 General Problem Setup
7(28)
2.1 Parameter Optimization Problems
7(7)
2.2 Utility Maximization Problems
14(4)
2.3 Rate Region and Rate Space Problem
18(17)
2.3.1 Proper Rate Regions
20(4)
2.3.2 Intersection Problems
24(1)
2.3.3 The Pareto Manifold
25(4)
2.3.4 Outer-Approximation of a Proper Rate Region
29(2)
2.3.5 Convex Rate Regions
31(4)
3 Solution Methods
35(64)
3.1 A Simple Utility Maximization Problem
36(1)
3.2 Rate Space Formulation
37(1)
3.3 Lagrange Duality
38(15)
3.3.1 Generic Approach
39(2)
3.3.2 Solving the Dual Problem
41(4)
3.3.3 Verifying Slater's Condition
45(1)
3.3.4 Special Case: Affine u and h
46(3)
3.3.5 Lagrange Duality and Nonconvexities
49(2)
3.3.6 Related Work
51(2)
3.4 Monotonic Optimization
53(16)
3.4.1 Polyblock Algorithm
54(4)
3.4.2 Projection Rules
58(3)
3.4.3 Extended Polyblock Algorithm
61(3)
3.4.4 Solving the Intersection Problem
64(1)
3.4.5 Complexity of the Polyblock Algorithm
65(1)
3.4.6 Related Work
66(3)
3.5 Local Methods on the Pareto Manifold
69(30)
3.5.1 Optimality Conditions
70(7)
3.5.2 Computing a KKT Point on the Pareto Manifold
77(3)
3.5.3 A Generic Global Parameterization
80(7)
3.5.4 A Varying Parameterization Approach
87(2)
3.5.5 Boundary Points
89(8)
3.5.6 Related Work
97(2)
4 Physical Layer Models
99(24)
4.1 MISO Broadcast Channel with Linear Precoding
99(16)
4.1.1 PHY Layer Parameterization
100(1)
4.1.2 Rate Region
101(2)
4.1.3 Intersection Problem
103(4)
4.1.4 An Alternative Parameterization
107(1)
4.1.5 Global Parameterization of the Pareto Set
107(8)
4.2 MIMO Broadcast Channel with Dirty Paper Coding
115(8)
4.2.1 PHY Layer Parameterization
116(1)
4.2.2 Rate Region
117(1)
4.2.3 Weighted Sum Rate Maximization
118(1)
4.2.4 Global Parameterization of the Pareto Boundary
119(4)
5 Utility Models
123(6)
5.1 Concave Utility Functions
124(3)
5.1.1 Sum-Throughput and Max-Min Fairness
124(1)
5.1.2 Logarithmic Utility Functions
124(1)
5.1.3 Generalized Max-Min
125(2)
5.2 Nonconcave Utility Functions
127(2)
6 Case Studies
129(26)
6.1 Utility Maximization in the MISO Broadcast Channel with Linear Precoding
129(14)
6.1.1 Parameter Space Formulation
130(1)
6.1.2 Globally Optimal Solutions
131(3)
6.1.3 Local Solutions
134(1)
6.1.4 Numerical Results
135(8)
6.2 Nonconcave Utility Maximization in the MIMO Broadcast Channel
143(12)
6.2.1 Parameter Space Problem
144(1)
6.2.2 Globally Optimal Solutions
144(1)
6.2.3 Local Solutions
145(1)
6.2.4 Numerical Results
146(9)
A Appendix
155(22)
A.1 Mathematical Preliminaries
155(4)
A.1.1 Sets
155(1)
A.1.2 Spaces
155(2)
A.1.3 Functions
157(1)
A.1.4 Order Relations, Monotonicity, and Pareto Optimality
158(1)
A.2 Elementary Topology
159(1)
A.3 Pareto Sets
160(3)
A.4 Comprehensive Sets
163(2)
A.5 Convex Analysis
165(4)
A.6 The Set of Extended Real Numbers
169(1)
A.7 Optimality Conditions
170(1)
A.8 Differentiable Manifolds
171(5)
A.9 Yates' Framework for Power Control
176(1)
References 177(4)
Index 181
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