Border Games in Cellular Networks
Márk Félegyházi*, Mario Čagalj†, Diego Dufour*, JeanPierre Hubaux*
* Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland
† University of Split, Croatia
Infocom 2007
Problem
►
►
spectrum licenses do not
regulate access over
national borders
adjust pilot power to
attract more users
Is there an incentive for operators to apply competitive
pilot power control?
Infocom 2007
Márk Félegyházi (EPFL)
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Related Work
►
Power control in cellular networks
–
–
–
►
up/downlink power control in CDMA [Hanly and Tse 1999,
Baccelli et al. 2003, Catrein et al. 2004]
pilot power control in CDMA [Kim et al. 1999, Värbrand and
Yuan 2003]
using game theory [Alpcan et al. 2002, Goodman and
Mandayam 2001, Ji and Huang 1998, Meshkati et al. 2005, Lee
et al. 2002]
Coexistence of service providers
–
–
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wired [Shakkottai and Srikant 2005, He and Walrand 2006]
wireless [Shakkottai et al. 2006, Zemlianov and de Veciana
2005]
Márk Félegyházi (EPFL)
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System model (1/2)
Network:
► cellular networks using CDMA
–
channels defined by orthogonal
codes
two operators: A and B
► one base station each
► pilot signal power control
Users:
► roaming users
► users uniformly distributed
► select the best quality BS
► selection based signal-tointerference-plus-noise ratio
(SINR)
►
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Márk Félegyházi (EPFL)
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System model (2/2)
pilot signal SINR:
SINRivpilot 
pilot
I own
TAw
G ppilot  Pi  giv
N0  W  I
pilot
own
I
A


   giv   Pi   Tiw 
w  v , wM i


tr
pilot
I other
 I other
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PB
PA


   giv    Tiw 
 wM i 


I
    g jv   Pj   Tiw 
j i
wM i


traffic signal SINR:
tr
G
p  Tiv  g iv
tr
SINRiv 
tr
tr
N 0  W  I own
 I other
I
TAv
pilot
other
pilot
other
pilot
own
TBw
Pi
v
B
– pilot power of i
Gppilot – processing gain for the pilot signal
giv – channel gain between BS i and user v
N0
W
– noise energy per symbol
– available bandwidth
pilot
– own-cell interference affecting the pilot signal
I own

Tiv
– own-cell interference factor
– traffic power between BS i and user v
Mi
– set of users attached to BS i

– other-to-own-cell interference factor
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Game-theoretic model
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Power Control Game, GPC
players → networks operators (BSs), A and B
– strategy → pilot signal power, 0W < Pi < 10W, i = {A, B}
– standard power, PS = 2W
– payoff → profit, ui   v where v is the expected income
vM i
serving user v
– normalized payoff difference:
–
i 
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
max ui  si , P S   ui  P S , P S 
si
ui  P S , P S 
Márk Félegyházi (EPFL)

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Simulation
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Is there a game?
►
►
►
only A is strategic (B uses PB = PS)
10 data users
path loss exponent, α = 2
Δi
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Strategic advantage
►
normalized payoff difference:
i 
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
max ui  si , P S   ui  P S , P S 
si
ui  P S , P S 
Márk Félegyházi (EPFL)

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Payoff of A
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►
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Both operators are strategic
path loss exponent, α = 4
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Nash equilibrium
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unique NE
NE power P* is higher than PS
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Márk Félegyházi (EPFL)
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Efficiency
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zero-sum game
10 data users
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Convergence to NE (1/2)
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►
convergence based on better-response dynamics
convergence step: 2 W
PA = 6.5 W
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Convergence to NE (2/2)
►
convergence step: 0.1 W
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Summary
►
►
►
►
►
two operators on a national border
single-cell model
pilot power control
roaming users
power control game, GPC
–
operators have an incentive to be strategic
– NE are efficient, but they use high power
►
►
simple convergence algorithm
extended game with power cost
–
Prisoner’s Dilemma
http://people.epfl.ch/mark.felegyhazi
Infocom 2007
Márk Félegyházi (EPFL)
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Future work
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►
►
►
Infocom 2007
multiple base stations
repeated game with power cost
strategic modeling of users
cooperative game of operators
Márk Félegyházi (EPFL)
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