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Crime and Punishment for Cognitive Radios
Anant Sahaipresenting joint work with:
Kristen Woyach George Atia Venkatesh Saligrama
BWRC and Wireless Foundations CenterU.C. Berkeley
Major support from the National Science Foundation
Allerton Conference
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 1 / 11
Motivation: recovering spectrum holes
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 2 / 11
Motivation: recovering spectrum holes
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 2 / 11
Motivation: recovering spectrum holes
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 2 / 11
Motivation: cooperation
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 3 / 11
Motivation: cooperation
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 3 / 11
Outline
MotivationCrime and punishment
I Prior work:F Rose, Ulukus, Yates ’01F Popescu and Rose ’04F Etkin and Tse ’05F Huang, Berry, Honig ’04F Xu, Kamat, Trappe ’06
I Single-band modelI Multi-band model
Identity (preview of DySpAN ’08)
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 4 / 11
Single-band model
False Alarm
Legal TX
SecondaryTX No TX
No Cheat
Cheat
False Alarm
Legal TX
Primary
Cognitive
Jail
Pcatch
Ppen
p1
q1
Ptx = q/(q+p)
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 5 / 11
Single-band model
00.25
0.50.75
1
00.25
0.50.7510
0.25
0.5
0.75
1
pPtx
Pcheat
Always cheat
Never cheat
Pcatch = 1Ppen = 0.6
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 5 / 11
Single-band model
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
4
5
6
7
8
9
10
Ppen
β =
pai
n of
jail
Pcatch = 0.1
0.2
0.4
0.60.8
1
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 5 / 11
Multi-band model
TX No TX
No Cheat
Cheat
False Alarm
Legal TX
q
SecondaryTX No TX
No Cheat
Cheat
False Alarm
Legal TX
Primary
Cognitive
Band 1Band 2
Band 3
Band B
Global Jail
Pcatch
Pcatch
Primary
Ppen
p1
q1
pN
qN
Ptx = q/(q+p)
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 6 / 11
Multi-band model
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
4
5
6
7
8
9
10
β =
hom
e ba
nds
requ
ired
to in
cent
iviz
e no
che
atin
g
Ppen
B = 1
B = 3
B = 5
B = 7
B = 9
Pcatch = 1
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 6 / 11
Multi-band model with false convictions
TX No TX
No Cheat
Cheat
False Alarm
Legal TX
q
SecondaryTX No TX
No Cheat
Cheat
False Alarm
Legal TX
Primary
Cognitive
Band 1Band 2
Band 3
Band B
Global Jail
Pcatch
Pcatch
Primary
Pwrong
Pwrong
Ppen
p1
q1
pN
qN
Ptx = q/(q+p)
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 7 / 11
Multi-band model with false convictions
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
20
25
30
35
40β
= h
ome
band
s re
quire
d to
ince
ntiv
ize
no c
heat
ing
Pwrong
1
3
5
7
B = 9
Pcatch = 1Ppen = 0.6
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 7 / 11
Multi-band model with false convictions
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
20
25
30
35
40β
= h
ome
band
s re
quire
d to
ince
ntiv
ize
no c
heat
ing
Pwrong
Pcatch = 0.1
0.2
0.4
0.6
0.8
1
B = 3Ppen = 0.6
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 7 / 11
Multi-band model with false convictions
Pcatch = 1Pcatch = 0.5
Pcatch = 0.1Ppe
n
0
1
0.5Pwrong0.1 0.2 0.3 0.4
0.5
B = 3
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 7 / 11
Multi-band model with false convictions
Pcatch = 1Pcatch = 0.5
Pcatch = 0.1Ppe
n
0
1
0.5Pwrong0.1 0.2 0.3 0.4
0.5
B = 3
Ppe
n
0.5
10
1
01 2 6 84
Expansion
Pcatch = 0.1
Pcatch = 0.5
Pcatch = 1
Pwrong = 0.03
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 7 / 11
The cognitive user’s perspective
30
1
2
10 20
3
Expansion
0
0
1
0
0.5
Utility
Fraction of time in jail Ptx = 0.55Pcatch = 1
Pwrong = 0.03
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 8 / 11
The cognitive user’s perspective
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 8 / 11
The “overhead” needed for bandwidth expansion
Exp
ansi
on
0
40
20
30
10
Overhead0.1 0.2 0.3 0.4 0.5
Pwrong = 0.01
Pwrong = 0.06
Pwrong = 0.1
Pwrong = 0.035
Pwrong = .02
Pwrong = 0.001
MaximalExpansion
Ptx = 0.55Pcatch = 1
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 9 / 11
The “overhead” needed for bandwidth expansion
0 0.1 0.2 0.3 0.4 0.50
10
20
30
40
Overhead
Expansion
Pcatch = 1
0.8
0.6
0.4
0.2
0.1
Ptx = 0.55Pwrong = 0.02
MaximalExpansion
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 9 / 11
Outline
Motivation
Crime and punishmentIdentity (preview of DySpAN ’08)
I Prior work:F Faulhaber ’05F Hall, Barbeau, Kranakis ’03F Brik, Banerjee, Gruteser, Oh ’08F Rasmussen and Capkun ’07F Rozovsky and Kumar ’01
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 10 / 11
Identity through taboos
Network IDUser ID
× Device IDTX Identity: Band 1
TX Identity: Band 2
TX Identity: Band 3
. . .Cannot transmit
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 11 / 11
Identity through taboos
1000
800
600
400
200
02000 4000 6000 8000 100000
Time steps until conviction
Per
cent
age
incr
ease
in P
rimar
y er
rors 5% background error in Primary link
Pcatch = 0.9Pwrong = 0.005
Overhead = 5%
Overhead = 10%
Overhead = 25%
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 11 / 11
Identity through taboos
Enf
orce
men
t ove
rhea
d
2000 4000 6000 8000 100000
0.1
0.2
0.3
0.4
0.5
0
Time steps until conviction
200% increase in primary errors
100%
50%
65%
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 11 / 11
Identity through taboos
Min
imum
enf
orce
men
t ove
rhea
d
Number of users
Catch coalition of 4
Catch coalition of 3
Catch coalition of 2
0.1
0.2
0.3
0.4
0.5
02 73 65410 1010 101010
Time steps until conviction = 3000
Anant Sahai (UC Berkeley) Crime and Punishment 9/24/2008 11 / 11