Post on 14-Dec-2015
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]
Infocom 2007
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
Infocom 2007
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:
Infocom 2007
Márk Félegyházi (EPFL) 10
Payoff of A
► Both operators are strategic► path loss exponent, α = 4
Infocom 2007
Márk Félegyházi (EPFL) 11
Nash equilibrium
► unique NE► NE power P* is higher than PS
Infocom 2007
Márk Félegyházi (EPFL) 12
Efficiency
► 10 data users zero-sum game
Infocom 2007
Márk Félegyházi (EPFL) 13
► convergence based on better-response dynamics► convergence step: 2 W
Convergence to NE (1/2)
PA = 6.5 W
Infocom 2007
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