Border Games in Cellular Networks

Infocom 2007

Márk Félegyházi*, Mario Čagalj†, Diego Dufour*, Jean-Pierre Hubaux*

* Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland

† University of Split, Croatia

Infocom 2007

Márk Félegyházi (EPFL) 2

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) 3

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– wired [Shakkottai and Srikant 2005, He and Walrand 2006]– wireless [Shakkottai et al. 2006, Zemlianov and de Veciana

2005]

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Márk Félegyházi (EPFL) 4

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 controlUsers:► roaming users► users uniformly distributed► select the best quality BS► selection based signal-to-

interference-plus-noise ratio (SINR)

Infocom 2007

Márk Félegyházi (EPFL) 5

System model (2/2)

0

pilotp i ivpilot

iv pilot pilotown other

G P gSINR

N I I

W

i

pilotown iv iw

w

I g T

M

i

pilotother jv j iw

j i w

I g P T

M

A Bv

PAPB

TAv

TBw

TAw

0

trp iv ivtr

iv tr trown other

G T gSINR

N I I

W

, i

pilotown iv i iw

w v w

I g P T

Mtr pilotother otherI I

pilot signal SINR:

traffic signal SINR:

Pi – pilot power of i

– processing gain for the pilot signalpilotpG

ivg

0N – noise energy per symbol

W

ivT

pilotownI

– channel gain between BS i and user v

– available bandwidth

– own-cell interference affecting the pilot signal

– own-cell interference factor

– traffic power between BS i and user v

– other-to-own-cell interference factor

iM – set of users attached to BS i

Infocom 2007

Márk Félegyházi (EPFL) 6

Game-theoretic model

► 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, where is the expected income

serving user v – normalized payoff difference:

i

i vv

u

M

v

max , ,

,i

S S Si i i

si S S

i

u s P u P P

u P P

Infocom 2007

Márk Félegyházi (EPFL) 7

Simulation

Infocom 2007

Márk Félegyházi (EPFL) 8

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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Márk Félegyházi (EPFL) 9

Strategic advantage

max , ,

,i

S S Si i i

si S S

i

u s P u P P

u P P

► normalized payoff difference:

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Márk Félegyházi (EPFL) 10

Payoff of A

► Both operators are strategic► path loss exponent, α = 4

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Márk Félegyházi (EPFL) 11

Nash equilibrium

► unique NE► NE power P* is higher than PS

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Márk Félegyházi (EPFL) 12

Efficiency

► 10 data users zero-sum game

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Márk Félegyházi (EPFL) 13

► convergence based on better-response dynamics► convergence step: 2 W

Convergence to NE (1/2)

PA = 6.5 W

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Márk Félegyházi (EPFL) 14

Convergence to NE (2/2)► convergence step: 0.1 W

Infocom 2007

Márk Félegyházi (EPFL) 15

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) 16

Future work

► multiple base stations► repeated game with power cost► strategic modeling of users► cooperative game of operators