Power control under best response
dynamics for interference mitigation in
a two-tier femtocell network
Vaggelis G. Douros
Stavros Toumpis
George C. Polyzos
@ RAWNET 2012
Paderborn, Germany,
18 May 2012
1
29/7/2017
[email protected]
Motivation (1)
This
Deadline
is is urgent!
The food
is Fantastic
today!
delicious
shirt!
The problem: Some couples
may not communicate efficiently

2
Motivation (2)
 N couples of friends
discuss in the same cafeteria
 Each couple aims at
achieving a (different)
“minimum quality of
discussion”
 Discussions of other
couples may prevent an
efficient communication
 N pairs of wireless nodes
(e.g., BSs-MNs, FBSs-FMNs)
transmit their data sharing the
same wireless medium
 Each pair aims at achieving
a (different) QoS target
 Interference among
wireless devices may prevent
an efficient communication
Competition for resources among players≡ Non-Cooperative Game
Interference mitigation through power control
3
Which is the wireless network?
A two-tier femtocell network
Chandrasekhar et al., IEEE Comm. Mag., 2008
4
Why Femtocells? (1)

Femtocells:
–
–
–
–
5
low-power access
points
connect to the service
provider’s network via
broadband
provide voice and
broadband services
allow a small number
of simultaneous calls
and data sessions
http://www.smallcellforum.org
Why Femtocells? (2)






6
(+) dense deployment
increase spectrum reuse
(+) better indoor
coverage superior
indoor reception
(+) low(er) cost (than
macrocell deployment)
(+) plug and play
installation
…
(-) interference: This is
the challenge!
Source: Informa Telecoms &
Media, October 2011
A two-tier femtocell network power
control game (1)

Players N transmitters share the same portion of
the spectrum (CDMA Network)
–
–


7
N1 Macrocell Mobile Nodes (MNs)
N2 Femtocell Mobile Nodes (FMNs)
Strategy Selection of the transmission power
–
MN: Pi  [0,Pmax]
–
FMN: Pi  [0,FPmax]
Utility (Payoff)…
A two-tier femtocell network power
control game (2)

N1 MNs
–
–
–

N2 FMNs
–
–
–

8
will be mostly used for voice, inelastic traffic
high(er) priority to be served by the operators
low(er) QoS demands (than FMNs)
are deployed by indoor users for their self interest
should not create high interference to MNs
focus on data serviceshigh(er) QoS demands
Conclusion: Difficult to describe their needs and
restrictions with the same utility function
A two-tier femtocell network power
control game (3)

… Our choices…
MN Utility Function:

FMN Utility Function:

9
A two-tier femtocell network power
control game (4)

N1 MNs
–
–
–
–
–

N2 FMNs
–
–
–
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will be mostly used for voice, inelastic traffic
high(er) priority to be served by the operators
use any transmission power up to Pmax without pricing
low(er) QoS demands (than femtocells)
SINRmax
–
FMNs should not create high interference to MNs
pricing is used to discourage them from creating high
interference to the macrocell users
focus on data serviceshigh(er) QoS demands
No SINRmax
Nash Equilibrium Existence



11
Q1: Has the game G at least one NE?
Yes!
Debreu-Fan-Glicksberg (1952)
Best Response Dynamics Power
Control (1)


Q2: How can we devise an algorithm that
converges to a NE?
The two-tier femtocell game G is a collection
of N parallel optimization problems
–

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each (F)MN aims at maximizing its own utility
function Ui
Best Response Dynamics Scheme…
Best Response Dynamics Power
Control (2)

MN Optimization problem

which leads to:
–

13
(1)
See also [Foschini & Miljanic, TVT’93] [Grandhi et al., WPC’94]
So, the best response dynamics scheme is:
(2)
Best Response Dynamics Power
Control (3)

FMN Optimization problem

which leads to:
–

(3)
See also [Alpcan, Basar, Srikant, Altman, Wireless Netw.‘02]
So, the best response dynamics scheme is:
(4)
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Best Response Dynamics Power
Control (4)



15
Equations (2) and (4)
form a best response
dynamics power control
scheme
(+) simple scheme
(+) distributed algorithm
Uniqueness of the Nash Equilibrium (1)


Q3: Does the best response dynamics power
control scheme based on equations (2) and
(4) converge to the NE that is defined by
equations (1) and (3) respectively?
In general, there are games where the best
response dynamics do not always* lead to a
NE
–
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*from every initial strategy
Uniqueness of the Nash Equilibrium (2)



Q4: Is this the unique NE of the game G?
Answers: Yes & Yes!
Theorem: Let L be the spread factor of the system
and  max  max{ i } be the maximum SINR target
among all the MNs. If N  max  L  1, L  1, then:
  max
–
–

The two-tier femtocell network game has a unique NE
The power control scheme under best response dynamics
for FMNs and MNs converges to this NE
Topology/Scenarios


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Topology parameters are based on an extensive
study by the smallcellforum
Symmetric topologies, vary (F)MN-(F)BS positions
and/or SINR targets
Some Results (1)


Fixed positions
The target SINR of each MN increases with a step
equal to 0.5 dB
Voice is feasible
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Some Results (2)

20
Each FMN gradually moves away from its associated
FBS. All other parameters are fixed
Some Results (3)

Each FMN gradually moves away from its associated
FBS. All other parameters are fixed
Voice is feasible
21
“The Meat”

Two-tier femtocell networks
–
–
–

We show the existence and uniqueness of a NE and
devise an algorithm based on best response dynamics
that converges to it
–

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heterogeneous needs
heterogeneous targets
interference remains a big challenge
Interference mitigation in various scenarios is achieved
Things to do: Stackelberg game formulation, maximize
total revenue, maximize social welfare…
 Danke schön! 
Vaggelis G. Douros
Mobile Multimedia Laboratory
Department of Informatics
Athens University of Economics and Business
[email protected]
http://mm.aueb.gr/~douros
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