Decentralized Admission Control and Resource Allocation for Power-Controlled Wireless Networks S lawomir Sta´ nczak 1,2 joint work with Holger Boche 1,2 , Marcin Wiczanowski 1 and Angela Feistel 2 1 Fraunhofer German-Sino Lab for Mobile Communications (MCI) Berlin, Germany 2 Heinrich Hertz Chair for Mobile Communications Faculty of EECS Technical University of Berlin 22 September 2009 UCLA, 22.09.2009 Fraunhofer German-Sino Lab Mobile Communications MCI 1/43
53
Embed
Decentralized Admission Control and Resource Allocation for Power
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Decentralized Admission Control and ResourceAllocation for Power-Controlled Wireless Networks
S lawomir Stanczak1,2
joint work with
Holger Boche1,2, Marcin Wiczanowski1 and Angela Feistel2
1Fraunhofer German-Sino Lab for Mobile Communications (MCI)Berlin, Germany
2Heinrich Hertz Chair for Mobile CommunicationsFaculty of EECS
Technical University of Berlin
22 September 2009
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI1/43
Outline
1 Introduction
2 Physical-Layer Abstraction by Interference Functions
3 User-centric Approaches
4 Network-centric approachesDistributed Power Control AlgorithmsIncorporating QoS requirements
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI2/43
Outline
1 Introduction
2 Physical-Layer Abstraction by Interference Functions
3 User-centric Approaches
4 Network-centric approachesDistributed Power Control AlgorithmsIncorporating QoS requirements
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI3/43
Wireless Networks
Goal: Study resource allocation and interference management
Focus: High data rates, low or moderate channel dynamics
Energy supply is not a bottleneck.Wireless mesh networks, cellular networks
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI4/43
Wireless Channel Characteristics
Radio propagation channel is unreliable.
channel fading, path loss, channel conditions are time-varying ...
Power and bandwidth are limited.
Wireless spectrum is a shared medium.
Link capacities are elastic.Network cannot be regarded as a collection of point-to-point links.Performance is maximized by tolerating interference in a controlled way.
Resource allocation and interference management are necessary.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI5/43
Wireless Network Resources and Mechanisms
Wireless resources: power, time, frequency, space, codes, routes...
Mechanisms for resource allocation and interference management
Multiple antenna techniquesMAC: power control and schedulingrouting...
Cross-layer protocols
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI6/43
Applications
Voice transmission
Inelastic traffic: QoS requirements need to be satisfied permanently.
Data applications (WWW browsing,e-mail,ftp)
Low QoS levels are temporarily acceptable.Elastic traffic: Applications modify their data rates according to availableresources in communication networks.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI7/43
Quality of Service
User-centric approaches (inelastic applications):
Satisfy strict QoS requirements of applications permanently.
Find a class of strictly increasing and concave utility functions Ψ with
γ(Ψ(x)) = x , x ≥ 0
so that Fγ is a convex set.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI24/43
Convexity of Feasible QoS Region: Sufficient Conditions
Theorem (Convexity under a Linear Interference Function)
If γ with γ(Ψ(x)) = x , x ≥ 0, is log-convex, then the feasible QoS region is aconvex set, regardless of the type of power constraints
Observation:γ is log-convex if and only if Ψe(x) := Ψ(ex) is concave.
Further related results:
Log-convexity of γ(x) is necessary for the region to be convex in general.Convexity of γ(x) is sufficient if V is confined to belong to some subset ofnonnegative matrices.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI25/43
Examples of Function Classes
Ψα(x) =
{x1−α
1−α α > 1
log(x) α = 1Ψα(x) =
log x α = 1
log x1+x α = 2
log x1+x +
α−2∑j=1
1j(1+x)j α > 2
α = 1: Throughput maximization
α→∞: Max-min fairness
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI26/43
Arbitrarily Close Approximation of Max-Min Fairness
Let ω∗k = Ψα(SIR∗k) and let ν∗k = log(1 + SIR∗k). Then, ν∗ converges to themax-min rate allocation as α→∞.
Flow 1
Flow 2 Flow 3 Flow 4
8
8.2
8.42.4
1.8
1 6 11 16
Sou
rce
Rat
es
α
Sum of Source Rates
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI27/43
Efficiency of the Max-Min SIR Power Allocation
Theorem
If p and q are positive right and left eigenvectors of B(k0) = V + 1Pk0
zeTk0
, then
(i) p is max-min fair power allocation if and only if p = p.
(ii) ω∗ is max-min fair ω if and only if w = w∗ = q ◦ p > 0.
α2α3 α1 = 1∞ α4
maxω∈Fγ(P) wTω
w
α1 < α2 < α3 < α4
ω1 = log(SIR1)
ω2 = log(SIR2)
max-min fairness
w∗
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI28/43
Joint Power and Receiver Control
Alternating optimization1 Given U(t − 1) compute p(t)
(i) Compute the weight vector: w = y(B(m)) ◦ x(B(m)), m = arg maxk ρ(B(k))(ii) Compute the QoS vector: ω∗ = arg maxω∈Fγ wTω(iii) p(t) = (I− Γ(ω∗)V)−1Γ(ω∗)z,Γ(ω) = diag(γ(ω1), . . . , γ(ωK ))
2 Given p(t) compute U(t)
(i) ∀k uk(t) = arg max‖x‖2=1 SIRk(p(t),x)
monotonic convergence to max-min SIR-balancing solution
But: not amenable to distributed implementation
Theory provides a basis for novel decentralized algorithms for finding a saddlepoint of the aggregate utility function.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI29/43
Joint Power and Receiver Control
Alternating optimization1 Given U(t − 1) compute p(t)
(i) Compute the weight vector: w = y(B(m)) ◦ x(B(m)), m = arg maxk ρ(B(k))(ii) Compute the QoS vector: ω∗ = arg maxω∈Fγ wTω(iii) p(t) = (I− Γ(ω∗)V)−1Γ(ω∗)z,Γ(ω) = diag(γ(ω1), . . . , γ(ωK ))
2 Given p(t) compute U(t)
(i) ∀k uk(t) = arg max‖x‖2=1 SIRk(p(t),x)
monotonic convergence to max-min SIR-balancing solution
But: not amenable to distributed implementation
Theory provides a basis for novel decentralized algorithms for finding a saddlepoint of the aggregate utility function.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI29/43
Joint Power and Receiver Control
Alternating optimization1 Given U(t − 1) compute p(t)
(i) Compute the weight vector: w = y(B(m)) ◦ x(B(m)), m = arg maxk ρ(B(k))(ii) Compute the QoS vector: ω∗ = arg maxω∈Fγ wTω(iii) p(t) = (I− Γ(ω∗)V)−1Γ(ω∗)z,Γ(ω) = diag(γ(ω1), . . . , γ(ωK ))
2 Given p(t) compute U(t)
(i) ∀k uk(t) = arg max‖x‖2=1 SIRk(p(t),x)
monotonic convergence to max-min SIR-balancing solution
But: not amenable to distributed implementation
Theory provides a basis for novel decentralized algorithms for finding a saddlepoint of the aggregate utility function.
Dynamic optimization over finiteand infinite time horizon.
Stochastic power control.
...
This book series presents monographs about fundamental topics and trends in signal processing, communications and networking in the field of information technology. The main focus of the series is to contribute on mathematical foundations and methodologies for the understanding, modeling and optimization of technical systems driven by information technology. Besides classical topics of signal processing, communications and networking the scope of this series includes many topics which are comparably related to information technology, network theory, and control. All monographs will share a rigorous mathematical approach to the addressed topics and an information technology related context.
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 thus could affect our life in a magnitude similar to that of the Internet and cellular phones. However, the emerging applications and directions require a fundamental understanding of how to design and control the wireless networks that lies beyond what the existing communication theory can provide. In fact, the complexity of the 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. That’s why, two fields of mathematics play a central role in this book: Perron-Frobenius theory for non-negative matrices and optimization theory. Here these theories are applied and extended 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. This revised and expanded second edition consists of four largely independent parts:the mathematical framework, principles of resource allocation in wireless networks, power control algorithms and appendices. The latter contain foundational aspects to make the book more understandable to readers who are not familiar with key concepts and results from linear algebra and convex analysis.
Foundations in Signal Processing, Communications and NetworkingVol. 3W. Utschick · H. Boche · R. MatharSeries Editors
Fundamentals of Resource Allocation in Wireless NetworksTheory and AlgorithmsSecond Expanded EditionSławomir Stańczak · Marcin Wiczanowski · Holger Boche
Fundamentals of Resource Allocation in Wireless Networks
AB
StańczakW
iczanowski · Boche
Fundamentals of Resource
Allocation in Wireless Networks
1 23
Foundations in signal Processing, communications and networking