Chapter 11: Wireless operators in shared spectrum

© 2007 Levente Buttyán and Jean-Pierre Hubaux

Security and Cooperation in Wireless Networks

http://secowinet.epfl.ch/

Chapter 11: Wireless operators in shared spectrum

multi-domain sensor networks;border games in cellular networks;

2/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum

Chapter outline

11.1 Multi-domain sensor networks11.2 Border games in cellular networks


Typical cooperation: help in packet forwarding Can cooperation emerge spontaneously in multi-

domain sensor networks based solely on the self-interest of the sensor operators?

Multi-domain sensor networks

11.1 Multi-domain sensor networks


Simplified model

C: Cooperation D: Defection

4 possible moves: CC – the sensor asks for help (cost 1) and helps if asked (cost 1) CD – the sensor asks for help (cost 1) and does not help (cost 0) DC – the sensor sends directly (cost 2) and helps if asked (cost 1) DD – the sensor sends directly (cost 2) and does not help (cost 0)

2α

11

1 1 1

11.1 Multi-domain sensor networks11.1.1 Simplified model


Example : CC – CD (1/6)

CC – the sensor tries to get help from the other sensor and helps if the other sensor requests it

CD – the sensor tries to get help but it refuses to help

CC CD






CC CD




CCfailure

CD






CC CD






CC CDsuccess




CC CD

Black player

Cost: 2

• 1 for asking

• 1 for helping

Benefit: 0

(packet dropped)

Gray player

Cost: 1

• 1 for asking

Benefit: 1

(packet arrived)



2α

11

Cost for black Cost for grey

Outcome for black (0 = failure)

Outcome for grey (1 = success)

The simplified model in strategic form



Reception threshold

time

success / failure of packet reception

Sliding window of history

Success(= 1)

Failure(= 0)

Receptionthreshold ρ

Average of the packet reception

Risk of going below threshold adapt strategy (move to theconstrained state: only DC or DDare eligible)

Reception threshold: computed and stored at each sensor node The battery (B) level of the sensors decreases with the moves If the battery is empty, the sensor dies



Game Theoretic Approach

The mentioned concepts describe a game Players: network operators Moves (unconstrained state): CC, CD, DC, DD Moves (constrained state): DC, DD Information sets: histories Strategy: function that assigns a move to every

possible history considering the weight threshold Payoff = lifetime We are searching for Nash equilibria with the highest

lifetimes



Two-step Strategies

B – initial battery

ρ – reception threshold

– path loss exponent (2)

ε1,2 – payoff of transient states

Cooperative Nash equilibrium

Non-cooperative Nash equilibrium

If ρ > 1/3, then (CC/DD, CC/DD) is more desirable



Generalized Model

11.1 Multi-domain sensor networks11.1.2 Generalized model

Simplified model with the following extensions:– many sensors, random placing– minimum energy path routing– common sink / separate sink scenarios– classification of equilibria

• Class 0: no cooperation (no packet is relayed)• Class 1: semi cooperation (some packets are relayed)• Class 2: full cooperation (all packets are relayed)


Main simulation parameters

Parameter Value

Number of sensors per domain 20

Area size 100 x 100 m

Reception threshold ρ 0.6

History length 5

Path loss exponent 2–3–4 (3)



Impact of the path loss exponentPerc

enta

ge o

f si

mula

tion

s

Equilibrium classes ( 0 – no cooperation, 1 – semi cooperation, 2 – full cooperation)

Value of the path loss exponent

– 2

– 3

– 4



Conclusion on multi-domain sensor networks

We examined whether cooperation is possible without the usage of incentives in multi-domain sensor networks

In the simplified model, the best Nash equilibria consist of cooperative strategies

In the generalized model, the best Nash equilibria belong to the cooperative classes in most of the cases

11.1 Multi-domain sensor networks


Chapter outline

11.1 Multi-domain sensor networks11.2 Border games in cellular networks


Motivating example

11.2 Border games in cellular networks


Introduction

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?



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-to-

interference-plus-noise ratio (SINR)

11.2 Border games in cellular networks11.2.1 Model


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

M

tr 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

11.2 Border games in cellular networks11.2.1 Model


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

11.2 Border games in cellular networks11.2.2 Power control game


Simulation settings



Is there a game?

only A is strategic (B uses PB = PS) 10 data users path loss exponent, α = 2

Δi



When both operators are strategic

10 data users path loss exponent, α = 4



Nash equilibria

10 data users 100 data users



Efficiency (1/2)

10 data users



Efficiency (2/2)

100 data users



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

Convergence to NE (1/2)

PA = 6.5 W

11.2 Border games in cellular networks11.2.3 Convergence to a Nash Equilibrium


Convergence to NE (2/2)

convergence step: 0.1 W

11.2 Border games in cellular networks11.2.3 Convergence to a Nash Equilibrium


Conclusion on border games

not only individual nodes may exhibit selfish behavior, but operators can be selfish too

example: adjusting pilot power to attract more users at national borders

the problem can be modeled as a game between the operators– the game has an efficient Nash equilibrium– there’s a simple convergence algorithm that drives the

system into the Nash equilibrium


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Chapter 11: Wireless operators in shared spectrum