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
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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
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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
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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.
Network-centric approaches (elastic applications):
Maximize the aggregate utility as perceived by the network operator.Address the issue of fairness.
QoS link 1
QoS link 2max-min fairness
maxP
k QoSk (best overall efficiency)
maxP
k αkQoSk (weighted sum optimization)
minimum total power
Feasible QoS region
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI8/43
The focus of this talk
Power control with some aspects of the physical-layer design.
Link Layer
Physical Layer
System
Constraints
Transmit/Receive
Power Control
+
Network Layer
Applications
QoS
Strategies
Single-hop communication with K > 1logical links (users)
Concurrent transmission (works withany scheduling protocol).
Each user is decoded (single-userdecoding).
Combination with routing and networkcoding strategies possible.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI9/43
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
MCI10/43
Feasible QoS Region: Fγ
Given a channel, Fγ is the set of all QoS values that can be achieved by means ofpower control with all links being active concurrently.
ω2
feasible point
ω1
Fγ
infeasible point
QoS link 1
QoS
link
2
Assumption: ωk ↑ ⇔ QoS ↑Downward-comprehensiveUpper-bounded
may be non-convex.
depends on power constraints P.
Fγ depends on the physical-layer realization: Key properties of manymultiuser systems are captured by interference functions.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI11/43
Signal-to-Interference(+noise) Ratio (SIR)
Strictly monotonic QoS-SIR map: γ : R→ R+
For any ω ∈ Fγ , there is a power vector p ∈ P such that
γ(ωk) = SIRk(p) =pk
Ik(p)
← transmit power
← interference function
e.g. Gaussian capacity (in nats/channel use): γ(x) = ex − 1, x ≥ 0.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI12/43
Axiomatic Interference Function
Standard Interference Functions (SIF), Yates’95
A1 Positivity: Ik(p) > 0 for all p ≥ 0.
A2 Scalability: Ik(µp) < µIk(p) for any p ≥ 0 and for all µ > 1.
A3 Monotonicity: Ik(p(1)) ≥ Ik(p(2)) if p(1) ≥ p(2).
It models many practical interference scenarios.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
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Interference Function: Examples
Linear interference function
Ik(p) = (Vp + z)k
Matched-filter receiverSIC receiver
Minimum interference function
Ik(p) = minuk∈Uk(V(u)p + z(u))k
MMSE receiver
QoS 3
QoS 1
2
1
2 3
3
1
interference
QoS 2
V1,1
V1,2 u(3)u(2)
u(1)
u(4)
SIR
user
2SIR user 1
G
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI14/43
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
MCI15/43
Problem Statement
Problem (QoS-based power control under SIFs)
p(ω) = arg minp∈P(ω)
wT pw > 0
P(ω) :={p ∈ RK
+ : ∀k SIRk(p) ≥ γ(ωk)}.
Minimum total power
QoS link 1
ω2
ω1
QoS link 2
Feasible QoS region
p2
p1
p2 = γ2I2(p)
p(ω) is the minimum point of P(ω)
p1 = γ1I1(p)
Valid power set
Zander’92, Foschini’94, Yates’95, Ulukus’98, Bambos’00, Boche&Schubert ...
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI16/43
Fixed-Point Iteration, Yates’95
If ω is feasible, then the concurrent iterations
∀k pk(n + 1) = γk Ik(p(n))
converge to p(ω), where γk ≡ γ(ωk).
Component-wise increasing (decreasing) if p(0) = 0 (p(0) ∈ P(ω)).
Amenable to distributed implementation, scalable, works for any SIF
But how should new users join the network without disrupting theconnections of active users?
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI17/43
Fixed-Point Iteration, Yates’95
If ω is feasible, then the concurrent iterations
∀k pk(n + 1) = γk Ik(p(n))
converge to p(ω), where γk ≡ γ(ωk).
Component-wise increasing (decreasing) if p(0) = 0 (p(0) ∈ P(ω)).
Amenable to distributed implementation, scalable, works for any SIF
But how should new users join the network without disrupting theconnections of active users?
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI17/43
Admission Control Scheme
User k is called active at time n if SIRk(p(n)) ≥ γk .
Define An to be the set of all active users at time n and Bn := K \ An.
Power control with active link protection (δ > 1)
pk(n + 1) =
{δ γk Ik(p(n)) k ∈ An (active users)
δ pk(n) = δn+1pk(0) k ∈ Bn (inactive users)
δ > 1 can be interpreted as protection margin.
the larger δ, the faster power-up of the inactive users.δ cannot be too large for all users to be fully admissible.
Bambos’00, Chee Wei Tan’09 (only Ik (p) = (Vp + z)k )
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI18/43
Properties of the admission control scheme
TheoremLet Ik be any standard interference function. Then,
All SIRs converge to some values.
All users are admitted in finite time if γ = (γ1, . . . , γK ) is feasible.
Transmit powers are bounded if and only if δ · γ is feasible.
Active users (k ∈ An):
Preservation of active users: An ⊆ An+1.Bounded power overshoot: pk(n + 1) < δpk(n).
Inactive users (k ∈ Bn):
SIRs of inactive users are increasing SIRk(p(n)) < SIRk(p(n + 1)).
Stanczak&Kaliszan&Bambos’09
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI19/43
No power constraints, TX and RX beamforming
00 50 100 150 20000
10
10 20 30 40
1
2
3
4
5
6
7
8
20
30
40
50
60
70
80
90
T.4 A.6T.5A.4T.3A.3T.2A.2 A.5T.1
SIR
n
user active at n = 0user inactive at n = 0common SIR target
T.x: Transceiver optimization phasesA.x: Admission control phases
A.1
SIR
n
K = 10, nT = nR = 4, γ = 8, δγ = 9.6, An = {1, . . . , 5}The highest feasible SIR (example):
0.88 (fixed beamformers), 1.37 (RX beamforming), 8 (TX/RX beamforming)
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI20/43
Incorporating power constraints
TheoremSuppose that δγ is feasible and
p(m) ≤ βδI(p(m))
holds for some m ∈ N0 and β ∈ [1, βmax]. Then, there exists βmax > 1 such thatAn ⊆ An+1 for all n ≥ m.
Active users send distress signals until the condition is satisfied.
Stanczak&Kaliszan&Bambos’09
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI21/43
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
MCI22/43
Problem Statement
Problem (Utility-based power control)
ω∗ = arg maxω∈Fγ
wTω w > 0 .
w
ω∗ is a maximal point of Fγ
Fγ
ω1
ω2
Feasible QoS regionFγ
ω2
ω1
Maximal point of Fγ
Goodman’00, Saraydar’02, Xiao’03, Neely’03, Chiang’04, Huang’05,Tassiulas’05 ...
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI23/43
Convexity of Feasible QoS Region
q∗ = (q∗1 ,q∗2)
w
q 2
Fγ(P)
q1
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.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI29/43
Some Simulation Results
10 20 30 40 500
5
10
15
20
25
30
35
40
number of users
min
k SIR
k/γ k
Maximum power
PC
PC + RX Beamf.
PC + RX/TX Beamf.
0
0
0.2
0.1
0.4
0.2
0.6
0.3
0.8
0.4
1
0.5
1.2
0.6
1.4
0.7
0
0
10
10
20
20
30
30
40
40
50
50
ave
rag
e d
ela
ya
ve
rag
e d
ela
yarrival rate
StaticPC (Utility−Max.)PC (Queue−Weighted Utility−Max.)
PC+Beamforming (Max−Min−SINR)PC (Utility−Max.)PC (Queue−Weighted Utility−Max.)
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI30/43
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
MCI31/43
Utility-Based Power Control
Equivalent minimization problem: ψ(x) = −Ψ(x)
p∗ = arg minp∈P
F (p) = arg minp∈P
∑k
wkψ(SIRk(p)
).
Positivity of minimizers: p∗ > 0
Even if ψ(ex) is convex, the problem is not convex in general.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI32/43
Convex Statement of the Problem
Theorem
If Ik(es) is log-convex and ψ(ex) convex, the following problem is convex:
s∗ = arg mins∈S
Fe(s)
s := log p,p > 0
S := {log x : x ∈ P+}Fe(s) = F (es)
Ik(es) =∑
l vk,lesl + zk is log-convex (Hoelder inequality).
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI33/43
Gradient-Projection Algorithm
Let τ > 0 be constant step size (small enough), and let
s(n + 1) = ΠS
[s(n)− τ∇Fe(s(n))
]s(0) ∈ S
∇Fe(s) = diag(es1 , . . . , esK )∇F (es):
∇F (p) = (I−VT Γ(p))g(p)
gk(p) = wkψ′(SIRk(p))SIRk(p)/pk (locally available)
Γ(p) = diag(SIR1(p), . . . , SIRK (p))
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI34/43
Min-max reformulation
mins
maxu
∑k
wkψ(esk
uk
)subject to
es − p ≤ 0
u− t ≤ 0
∀k Ik(es)− tk = 0 .
Linear interference function: Ik(es) = (Ves + z)k .
The Hessian is diagonal and its diagonals are given by the gradient.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI35/43
Conditional Newton Algorithm
8><>:
s(n + 1)
µ(n + 1)
!=
s(n)
µ(n)
!− (∇2
(s,µ)L(z(n)))−1∇(s,µ)L(z(n))
∇(u,λu ,λ,t)L(z(n + 1)) = 0 can be solved explicitely
L(z) = L(s,u,µ,λu,λ, t): A modified Lagrangian function.
Quadratic convergence.
Global convergence if ψ(x) = − log(x) andψ(x) = 1/x .
No step size.
Distributed implementation possible!
25
K = 50
ψ(x) = − log(x)
Conditional Newton
Gradient projection
20151050-1
0
1
2
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI36/43
Adjoint Networks: A Simple Example
Primal network:
Measure SIR at E1 and E2
E1 and E2 compute some messagesbased on localmeasurements/parameters
S1
S2
E2
E1
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI37/43
Adjoint Networks: A Simple Example
Primal network:
Measure SIR at E1 and E2
E1 and E2 compute some messagesbased on localmeasurements/parameters
S1
S2
E2
E1
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI37/43
Adjoint Networks: A Simple Example
Primal network:
Measure SIR at E1 and E2
E1 and E2 compute some messagesbased on localmeasurements/parameters
S1
S2
E2
E1
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI37/43
Adjoint Networks: A Simple Example
Primal network:
Measure SIR at E1 and E2
E1 and E2 compute some messagesbased on localmeasurements/parameters
S1
S2
E2
E1
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI37/43
Adjoint Networks: A Simple Example
Reversed network:
The messages determine thetransmit powers of E1 and E2.
Cooperation by interference
⇒ S1 and S2 estimate the messagesfrom the received powers
S1
S2
E2
E1
Significant gains compared to schemes relying on flooding protocols.Estimation errors are dealt with stochastic approximation.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI37/43
Adjoint Networks: A Simple Example
Reversed network:
The messages determine thetransmit powers of E1 and E2.
Cooperation by interference
⇒ S1 and S2 estimate the messagesfrom the received powers
S1
S2
E2
E1
Significant gains compared to schemes relying on flooding protocols.Estimation errors are dealt with stochastic approximation.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI37/43
Adjoint Networks: A Simple Example
Reversed network:
The messages determine thetransmit powers of E1 and E2.
Cooperation by interference
⇒ S1 and S2 estimate the messagesfrom the received powers
S1
S2
E2
E1
Significant gains compared to schemes relying on flooding protocols.Estimation errors are dealt with stochastic approximation.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI37/43
Adjoint Networks: A Simple Example
Reversed network:
The messages determine thetransmit powers of E1 and E2.
Cooperation by interference
⇒ S1 and S2 estimate the messagesfrom the received powers
S1
S2
E2
E1
Significant gains compared to schemes relying on flooding protocols.Estimation errors are dealt with stochastic approximation.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI37/43
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
MCI38/43
Problem Statement
s∗(ω) := arg mins∈S Fe(s) s.t. ∀k fk(s) := Ik(es)/esk − 1/γk ≤ 0
�����������������������������������������������������������������������������
�����������������������������������������������������������������������������
������������������������������������������������������������������������������������������������
������������������������������������������������������������������������������������������������
FγP◦(ω)
P2
p2
ω1
ω2
P1
p1
The projection is not amenable to distributed implementation.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI39/43
Primal-dual algorithm based on standard Lagrangian
Primal-dual iteration under individual power constraints sk(n + 1) = min{
sk(n)− δesk (n)[hk(s(n)) + Σk
(s(n),µ(n)
)], log(Pk)
}λk(n + 1) = max
{0, λk(n) + δfk(s(n))
}Σk(s,λ) =
∑l vl,k
(λl
esl+ |SIRl(es)gl(s)|
)=∑
l vl,kml(s, µl)
Estimation of Σk using the adjoint network.
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI40/43
Soft QoS Support
Fα(z) =∑k∈A
akψα
(SIRk(p)
γk
)︸ ︷︷ ︸
penalty term
+∑k∈B
bkψ(SIRk(p)
)︸ ︷︷ ︸
aggregate utility
.
A: QoS users need to satisfy SIRk ≥ γk , k ∈ AB: best-effort users
A \ B: pure QoS users (voice)A ∩ B: best-effort users with QoS requirements (video)B \ A: pure best-effort users (data)
Each user, say user k , determines its utility by choosing αk ≥ 1.
Slightly modified algorithms
Amenable to distributed implementation
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI41/43
Soft QoS Support: Example
γ2
QoS
ofP
ure
QoS
Use
r2
QoS of Best Effort User 1
A = 2
B = 1
1
3
2
1 - max-min-fairness
2 - Utility-based power control with α2 = 1
3 - Utility-based power control with soft QoS support, α2 →∞
2 3 as α2 →∞→
No overshoot of user 2.
8
12
4
02 6 10 14 18
A ∩ BSIR Target
α
a = b = 1K = 4SNR=40dBψ(x) = − log(x)
SIR
A \ B
B \ A
B \ A
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Conclusions and Outlook
The power control problem isrelatively well-understood.
Throughput maximization in the lowSINR regime is an open problem.
Outlook
Joint optimization of
transmit powers,schedulers (time+frequency),physical-layer (single- andmulti-mode transmission).
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
Volume 3
W. Utschick · H. Boche · R. Mathar Series Editors
Theory and Algorithms
Second Expanded Edition
Sławomir StańczakMarcin WiczanowskiHolger Boche
2nd Ed.› springer.com
isbn 978-3-540-79385-4
SPCN_Stanczak.indd 1 05.06.2008 17:12:41 Uhr
UCLA, 22.09.2009Fraunhofer German−Sino Lab
Mobile Communications
MCI43/43