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Adaptation, coordination and distributed resource allocationin interference-limited wireless networks
Keynote speechISWCS’07 Conference, Trondheim
17 October 2007
Prof. David Gesbert
Mobile Communications Dept., Eurecom [email protected]
www.eurecom.fr/∼ gesbert
Thanks to my collaborators!
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Wireless research a la Carte
SYSTEM ARCHITECTURE
PROTOCOLS
Transport (TCP/IP)Cross Layer 1/2
scheduling, multi−user MIMO,cooperative coding. relaying,multicell MIMO, resource alloc.,..
NETWORK OPTIMIZATION
Bits/Sec/Hz/NOK
point−to−pointCoding/Sig Processing
TRANSMISSION
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Outline
• Cooperation vs. coordination
• Cellular vs. adhoc networks
• User vs. infrastructure cooperation
• Coding-based vs. resource allocation-based cooperation
• Some interesting cases
• Open problems
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Cooperation vs. coordination
Two fundamental limitations:
• Fading limits the communication rate of any point to point link.
• Interference limits the reusability of spectral resource in space.
Cooperation schemes:
• Pooling Degrees of Freedom of many transceivers into a single basket.
• Optimizing the degrees of freedom to maximize rates, reliability and reuse.
• Several performance metrics. We choose Network’s sum throughput.
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Non-cooperating network
R3
R1
T1
R2
T3
T2
T4
R4
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Cooperating network
R3
R1
T1
R2
T3
T2
T4
R4
Degrees of freedom for cooperation:
Power
Delay
Bandwidth
Antennas
Users (scheduling)
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Cellular vs. Adhoc
R3
R1
T1
R2
T3
T2
T4
R4
T4
R4
R1
R2
T3
R3
T1
T2
(a) (b)
• "cellular": Users connect to an infrastructure point, close-by.
• "Adhoc": Destinations are other abitrary located users.
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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User-based cooperation (conventional)• Conventional source-relay-destination framework emphasizes diversity gain
for the source user.
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Mutual cooperation• Mutual cooperation balances benefit of relaying vs. overhead.
• Goal is to maximize Rate user1 + Rate user2.
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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A mutual cooperation protocolAssumptions:
• Non-orthogonal Amplify-Forward protocol (NAF) [1]
• Each mobile divides its power across relay and own transmission tasksover time
• User 1 allocates α Watts for relaying user 2’s data, keeps 1 − α for owntransmission.
• User 2 allocates β Watts for relaying user 1’s data, keeps 1 − β for owntransmission.
[1] [Azarian, El Gamal, Schniter] Trans IT 05.
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Expression of sum rate (mobile 1 + mobile 2)Lemma: For the Gaussian memoryless multiple-access channel, the sum-rate is such that R1 + R2 ≤ Iα,β where [2]
Iα,β=log2
[
1 + γ01 + (1 − α)K1
l1(β)+ f(βγ02, γ21)
]
+log2
[
1 + γ02 + (1 − β)K2
l2(α)+ f(αγ01, γ12)
]
whereK1 =
[
γ201 + γ01
]
[γ21 + 1]K2 =
[
γ202 + γ02
]
[γ12 + 1]l1(β) = 1 + γ21 + βγ02
l2(α) = 1 + γ12 + αγ01
f(x, y) = xyx+y+1
[2] [Tourki, Gesbert, Deneire] ISIT’07
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Mutual cooperation is selfish!Lemma: Optimal power allocation is given by either [2]
1. α = α∗ 6= 0 and β = 0 if
γ > γ202 + γ02
γ01 > (1+γ02)2(1+γ)
γ−(γ202+γ02)
− 1
2. α = 0 and β = β∗ 6= 0 if
γ > γ201 + γ01
γ02 > (1+γ01)2(1+γ)
γ−(γ201+γ01)
− 1
3. α = 0 and β = 0 if neither condition above is met.
At most one user cooperates with the other one:
(⇒ opportunistically selfish behavior!)
[2] [Tourki, Gesbert, Deneire] ISIT’07
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Infrastructure-based cooperation
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Levels of infrastructure cooperationSeveral levels:
• Coding, signal processing level
– Data routed to multiple access points
– Optimum use of the available radio links
– Centralized control required
• Resource allocation level
– Data routed to a single access point
– Interference is a problem but reduced coordinated power control andscheduling
– Scalable with network size
– Distributed solutions?
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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coding, signal processing-based cooperationInterference ⇒ Energy ⇒ Additional data pipe ⇒ good for you!
From competition to cooperation
CO
OP
ER
AT
ION
join
t con
trol
CO
OP
ER
AT
ION
CO
OP
ER
AT
ION
(rel
ay p
roto
col)
(rel
ay p
roto
col)
cell 2
cell 1
INTERFERENCE
Capacity of Multicell MIMO can be reached as regular multi-user MIMO ca-pacity with additional power constraints [3][4]
[3] [Shamai, Zaidel] VTC’01
[4] [Karakayali, Foschini, Valenzuela, Yates] ICC’06
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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MIMO vs. Multicell MIMO
<=>Mk
Pmax
PmaxPmaxPmax
Pmax
Pmax
join
t pro
cess
ing
1 base (with per−antenna power constraint)3 bases (1 antenna each)
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Three cell MIMO network
Rate performance without (left) and with MIMO cooperation (three sectors inhexagon)
−1 −0.5 0 0.5 1−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
1
2
3
4
5
6
7
(a) Without coop
−1 −0.5 0 0.5 1−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
4
4.2
4.4
4.6
4.8
5
5.2
5.4
5.6
5.8
6
(b) With coop
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Multi-cell MIMO in practice
• Gives significant advantage for edge-of-cell users if hard fairness is en-forced.
• Easy to implement for small subnets (2 cells)
• Many cells cooperating may be difficult due to inter-cell CSI overhead
• Routing in backhaul must be optimized
• Dynamic clustering can be a solution
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Multi-cell multiplexing with Dynamic clustering [5]
[5] [Papadogiannis, Gesbert] ICC’08 Submitted
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Resource allocation-based cooperationMotivations:
• Multicell-MIMO is not scalable.
• Distributed MIMO signal processing hard.
• Broadcast routing of data not always desirable.
• Can we achieve cooperation gains without it?
Remaining degrees of freedom:
• Delay (equivalently user scheduling)
• Power
• bandwidth
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Centralized resource allocation
Centralized
Resource Controller
BS
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BS
UT
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Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Optimal scheduling and power controlSearching over all scheduling vectors U and power vectors P :
(U ∗,P ∗) = arg maxU∈ΥP∈Ω
C(U ,P ), (1)
where:
C(U ,P )∆=
1
N
N∑
n=1
log(
1 + Γ([U ]n,P ))
. (2)
and the SINR in cell n is:
Γ([U ]n, P ) =Gun,nPun
σ2 +N∑
i 6=n
Gun,iPui
, (3)
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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A surprising result for two cellsTheorem:
For two cells, the optimum power allocation is ON-OFF:
arg max(P1,P2)∈∆Ω2
C(U , (P1, P2)) = arg max(P1,P2)∈Ω
C(U , (P1, P2)) (4)
where ∆Ω2 = (Pmax, 0), (0, Pmax), (Pmax, Pmax)
[6] [Gjendemsjoe, Gesbert, Oien , Kiani] IEEE Trans. Wireless Comm. toappear.
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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But we want...distributed resource allocation
BS
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BS
UT
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UTUT
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UT
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Paths toward distributed allocation [7]
• Game theoretic approaches
• Stastical optimization approaches
• Optimization under ON-OFF power control model
• Optimization in the large number of user case
[7] [Gesbert, Kiani, Gjendemsjoe, Oien] Proceedings of the IEEE, 2007.
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Game theoretic approachesThe non-cooperative power control game [8][9] writes
max0≤pn≤Pmax
n
fn(pn,p−n) ∀ n.
or with pricing
max0≤pn≤Pmax
n
fn(pn,p−n) − cn(pn) ∀ n.
where fn is selfish utility of user n. Nash equilibrium may not maximize net-work utility.
Cooperative games lead to Nash bargaining equilibrium, socially more opti-mal, but non-distributed.
[8] [Meshkati, Poor, Schwartz] IEEE SP Magazine 2007
[9] [Goodman, Mandayam] IEEE Personal Comm. Mag 2000
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Optimization under ON-OFF power controlLet N is the number of active cells, assumed large.
Cell m weighs its capapcity contribution to the system against the interfer-ence it generates:
Cell m is activated if (Capacity (with cell m) > Capacity (without cell m)), thatis if
Γ([U ]n, P ) ≥
∏
n∈Nn 6=m
∑
i 6=ni∈N
Pi
∏
n∈Nn 6=m
∑
i 6=n 6=mi∈N
Pi
=
(
N − 1
N − 2
)(N−1)
≈ e
Leads to opportunistic reuse patterns.
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Static reuse patterns
Inactive Cell
Active Cell
Cluster size 3 Cluster size 4
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Opportunistic reuse pattern
Active Cell
Inactive Cell
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Opportunistic reuse pattern
Active Cell
Inactive Cell
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Opportunistic reuse pattern
Active Cell
Inactive Cell
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Capacity performance vs. number of users
1 2 3 4 5 6 7 8 9 102
3
4
5
6
7
8
No. of Users
Net
wor
k C
apac
ity (
bits
/sec
/Hz/
cell)
Game Theoretic ApproachIterative Binary Power AllocationFull Resue
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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The large number of users case• We let number of users per cell grow asymptotically
• System capacity will grow with number of users
⇒ (multi-user multi-cell diversity!)
• What is the loss due to interference ?
• What can we achieve with a distributed scheme (power control + schedul-ing)?
[Gesbert, Kountouris] IEEE Trans. IT 2007, submitted
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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A bounding approachWe study two bounds on capacity:
• Upper bound obtained with no interference
• Lower bound obtained with full powered interference
In three network scenarios:
1. All users have same average received power (located on circle around thebase)
2. Users uniformly located in the cell
3. Users uniformly located but cannot get too close to the base
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Upper bound on capacity: No interference
C(U ∗,P ∗) ≤ Cub =1
N
N∑
n=1
log(
1 + Γubn
)
. (5)
where the upper bound on SINR is given by:
Γubn = max
un=1..UGun,nPmax/σ
2 (6)
The corresponding scheduler is the max SNR scheduler: Fully distributed
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Lower bound on capacity: Full interference
C(U ∗, P ∗) ≥ Clb = C(U ∗FP ,Pmax) (7)
U∗FP is the optimal scheduling vector assuming full interference, defined by
[U ∗FP ]n = arg max
U∈Υ
(
Γlbn =
Gun,nPmax
σ2 +∑N
i 6=n Gun,iPmax
)
(8)
The corresponding scheduler is the max SINR scheduler: Also fully dis-tributed
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Capacity scaling for symmetric network
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Capacity scaling with many users (U → ∞)
In the interference-free case (using extreme value theory):
Lemma: For fixed N and U asymptotically large, the upper bound on theSINR in cell n scales like
Γubn ≈
Pmaxγn
σ2log U (9)
Theorem: For fixed N and U asymptotically large, the average of the upperbound on the network capacity scales like
E(Cub) ≈ log log U (10)
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Capacity scaling with many users (U → ∞)
In the full powered interference case (using extreme value theory):
lemma: For fixed N and U asymptotically large, the lower bound on the SINRin cell n scales like
Γlbn ≈
Pmaxγn
σ2log U (11)
theoremThen for fixed N and U asymptotically large, the average of the lowerbound on the network capacity scales like
E(Clb) ≈ log log U (12)
System with and without interference have same growth rates!
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Interpretations• Interference creates vanishing loss for large number of users
• Physically, the max-rate resource allocator looks for users which are
– shielded from interference and
– with large SNR
• When number of users is large, interference becomes small comparedwith noise.
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Capacity scaling for symmetric network
0 50 100 150 2001
2
3
4
5
6
7
8
9
Num
ber
of B
its/S
ec/H
z/C
ell
number of users per cell
Interference−free optimum capacityOptimum capacity assuming full−powered interference
Scaling of upper and lower bounds of capacity, versus U for a symmetricnetwork (N = 4)
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Capacity scaling for non-symmetric network
Important: Path loss fading has heavy tail behavior while Rayleigh fading hasnot
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Capacity scaling for non-symmetric networkFrom extreme value theory of heavy-tailed random variables:
Theorem: The upper bound on capacity will behave like:
E(Cub) ≈ǫ
2log U for large U (13)
Theorem: The lower bound on capacity will behave like:
E(Clb) ≈ǫ
2log U for large U (14)
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Capacity scaling for non-symmetric network
0 50 100 150 2000
2
4
6
8
10
12
14
16
18
20
Num
ber
of B
its/S
ec/H
z/C
ell
number of users per cell
Interference−free optimum capacityOptimum capacity assuming full−powered interference
Scaling of upper and lower bounds of capacity, versus U for a non-symmetricnetwork (N = 4)
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Capacity scaling for hybrid networkUsers excluded from disk with radius 5 percent of cell radius.
0 50 100 150 2000
2
4
6
8
10
12
14
Num
ber
of B
its/S
ec/H
z/C
ell
number of users per cell
Interference−free optimum capacityOptimum capacity assuming full−powered interference
Scaling of upper and lower bounds of capacity, versus U for a hyrbid network(N = 4)
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Conclusions
• Large number of users reveals simple structure of the resource allocationproblem:
– Fully ditributed solution possible
– Price paid due to interference is small
• QoS-oriented scheduling will give different results
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007
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Open problemsCooperation creates gains and challenges:
• May affect routing
• Easier with infrastructure based cooperation (than user-based)
• In theory, each user receives tiny bits of information through everybodyelse.
• In practice, optimization must be distributed to keep information exchangelocal
• More issues: Synchronization, QoS guarantee issues
• Promising avenue: A two-scale optimization within a single network
– Small scale: coding, signal processing based cooperation (multicellMIMO)
– Large scale: resource allocation-based
Gesbert - ISWCS07 Keynote speech c© Eurecom Oct 2007