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Multiple Antenna Secret Broadcast over Multiple Antenna Secret Broadcast over Wireless Networks Wireless Networks Ruoheng Liu and H. Vincent Poor Ruoheng Liu and H. Vincent Poor Princeton University Princeton University IAB IAB

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SLIDE 1

1

Multiple Antenna Secret Broadcast over Multiple Antenna Secret Broadcast over Wireless Networks Wireless Networks

Ruoheng Liu and H. Vincent Poor Ruoheng Liu and H. Vincent Poor

Princeton University Princeton University

IAB IAB – – May, 2007 May, 2007

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SLIDE 2

ACKNOWLEDGEMENTS ACKNOWLEDGEMENTS Ivana Ivana Marvic Marvic, , Zang Zang Li, Li, Predrag Predrag Spasojevic Spasojevic, Roy Yates, and Wade Trappe , Roy Yates, and Wade Trappe

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SLIDE 3

Outline of the Talk Outline of the Talk

  • motivation

motivation

  • physical

physical-

  • layer secret system

layer secret system

  • secret broadcast over wireless networks

secret broadcast over wireless networks

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SLIDE 4

Reliable and Secret Communication over Wireless Network Reliable and Secret Communication over Wireless Network

reliability confidentiality

confidential message W

  • can be successfully decoded by the desired receiver (user 1)
  • cannot be understood by anyone else (e.g. user 2)
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SLIDE 5

Secret Communication Secret Communication

  • Alice

Alice sends a message to sends a message to Bob Bob

  • Eve

Eve accesses the channel and eavesdrops the information accesses the channel and eavesdrops the information

crypto-system (secret key) information-theoretic security (physical-layer)

Alice Bob Eve

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SLIDE 6

Traditional Crypto Traditional Crypto-

  • System

System

encryptor encoder decoder decrypter Alice Bob Eve disadvantage:

  • it is very difficult to distribute initial key in a large wireless network
  • Eve becomes smarter with time and lifetime of secret key is shorter
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SLIDE 7

Physical Physical-

  • Layer Secret System

Layer Secret System

secure encoder secure decoder Alice Bob Eve advantage:

  • secret communication can be achieved without a key
  • perfect communication secrecy can be ensured
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SLIDE 8

How How Physical Physical-

  • Layer Secret System Works

Layer Secret System Works

Alice Bob Eve Bob has a “better” channel than Eve

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SLIDE 9

How How Physical Physical-

  • Layer Secret System Works

Layer Secret System Works

Alice Bob Eve

  • Bob can get the message (y=w)
  • Eve is kept ignorant with respect to the message (w and z are independent)

1 1 1 1

0.5 0.5 0.5

w=[0000000000] y=[0000000000] z=[0110011100]

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SLIDE 10

How to Measure Secrecy Level How to Measure Secrecy Level

Alice Bob: Eve physical-layer secret system can achieve: both reliability and confidentiality

  • reliability is evaluated in terms of error probability
  • secrecy level is measured by the equivocation rate:

H(W | Z )/n

  • perfect secrecy: H(W | Z )/n H(W)/n

W Y Z X Y W ^ H(W | Z )

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SLIDE 11

Wire Wire-

  • Tap Channel

Tap Channel

W

[ [Wyner Wyner, 1975] , 1975]

  • user 1 is a

user 1 is a desired desired receiver receiver

  • user 2 is an

user 2 is an eavesdropper eavesdropper

  • c

confidential

  • nfidential m

message essage W W to User 1 to User 1

  • degraded

degraded b broadcast roadcast c channel hannel

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SLIDE 12

Broadcast Channel with Single CM Set Broadcast Channel with Single CM Set

[ [Csisz Csiszá ár r & & K Kö örner rner, 1978] , 1978]

  • W

W1

1 is a confidential message to user 1

is a confidential message to user 1

  • W

W0

0 is a common message

is a common message to both users to both users

  • non

non-

  • degraded

degraded b broadcast roadcast c channel hannel

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SLIDE 13

Communication of Confidential Messages Communication of Confidential Messages

[ [Csisz Csiszá ár r & & K Kö örner rner, 1978] , 1978] [ [Wyner Wyner, 1975] , 1975] Can we send confidential messages to both users instantaneously?

?

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SLIDE 14

Single Antenna Gaussian Broadcast Channel (GBC) Single Antenna Gaussian Broadcast Channel (GBC)

  • Channel 1 is

Channel 1 is “ “better better” ” than Channel 2 (degraded BC) than Channel 2 (degraded BC)

  • this case reduces to Gaussian wire

this case reduces to Gaussian wire-

  • tap channel

tap channel

)] ; ( ) ; ( [ max

2 1 ) (

= − ≤

2 x p 1

R Y X I Y X I R

Channel 1 Channel 2

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SLIDE 15

M Multi ulti-

  • Antenna

Antenna G Gaussian aussian B Broadcast roadcast C Channel ( hannel (MGBC MGBC) )

  • (W

(W1

1, W

, W2

2): independent,

): independent, confidential confidential messages messages

  • how to achieve reliable,

how to achieve reliable, secret secret communication over the communication over the MGBC MGBC-

  • CM

CM? ?

  • what is the capacity region for the

what is the capacity region for the MGBC MGBC-

  • CM

CM? ?

User 1 User 2 Transmitter A B

1, 2 1 2 2 1

non-degraded BC

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SLIDE 16

A Computable Outer Bound for MGBC A Computable Outer Bound for MGBC-

  • CM

CM ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ≤ ≤ ⊆ ) ~ | ~ ; ( ) ~ | ~ ; (

1 2 2 2 1 1 ) ( ) | ~ , ~ ( BCC

2 1

Y Y I R Y Y I R

p y y p

X X

x x ∪

∩ C

  • basic ideas:

decode the message in a cooperative manner evaluate the secrecy level in a individual manner

  • for GBC, Gaussian input can optimize this outer bound
  • MGBC can be transferred to an equivalent 2-dimension “Z-broadcast” channel model

X h1 g1 g2 Ỹ1 Ỹ2 X1 X2 h2=0

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SLIDE 17

0.5 1 1.5 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R1 R2 time-sharing DPC

  • uter bound
  • uter bound

A Computable Outer Bound for MGBC A Computable Outer Bound for MGBC-

  • CM

CM ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ≤ ≤ ⊆ ) ~ | ~ ; ( ) ~ | ~ ; (

1 2 2 2 1 1 ) ( ) | ~ , ~ ( BCC

2 1

Y Y I R Y Y I R

p y y p

X X

x x ∪

∩ C

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 R1 R2 time-sharing DPC

  • uter bound
  • uter bound

P=10, h=[1, 0]T, g=0.3·[0.20, 0.98]T P=10, h=[1, 0]T, g=2·[0.90, 0.43]T

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SLIDE 18

Transmission Strategy 1: Time Sharing Transmission Strategy 1: Time Sharing

basic ideas:

  • transmission period is divided into two slots of durations t1 and t2
  • transmitter sends W1 during time t1 with power P1,
  • transmitter sends W2 during time t2 with power P2,
  • in each slot, the channel reduces to a Gaussian MISO wiretap channel
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SLIDE 19

Transmission Strategy 1: Time Sharing Transmission Strategy 1: Time Sharing

achievable region: achievable region:

(R1, R2): { t (R1, R2): { t1

1C

Cs,MISO

s,MISO (P

(P1

1), t

), t2

2C

Cs,MISO

s,MISO(P

(P2

2) } for all t

) } for all t1

1P

P1

1+t

+t2

2P

P2

2=P t

=P t1

1+t

+t2

2=1

=1 C Cs,MISO

s,MISO is the secrecy capacity of

is the secrecy capacity of Gaussian MISO wiretap channel Gaussian MISO wiretap channel [Li, [Li, et. al.

  • et. al., CISS 07]

, CISS 07]

0.5 1 1.5 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R1 R2 time-sharing DPC

  • uter bound
  • uter bound

time-sharing

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 R1 R2 time-sharing DPC

  • uter bound
  • uter bound

time-sharing

P=10, h=[1, 0]T, g=0.3·[0.20, 0.98]T P=10, h=[1, 0]T, g=2·[0.90, 0.43]T

MISO wiretap MISO wiretap

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SLIDE 20

Transmission Strategy 2: Secret Transmission Strategy 2: Secret D Dirty irty P Paper aper C Coding (DPC)

  • ding (DPC)

0.5 1 1.5 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 R1 R2 time-sharing DPC

  • uter bound
  • uter bound

DPC time-sharing

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 R1 R2 time-sharing DPC

  • uter bound
  • uter bound

time-sharing DPC

P=10, h=[1, 0]T, g=0.3·[0.20, 0.98]T P=10, h=[1, 0]T, g=2·[0.90, 0.43]T

⎪ ⎪ ⎭ ⎪ ⎪ ⎬ ⎫ ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ + + ≤ + + + − + + + ≤ =

≤ +

1 1 log 1 ) ( 1 log 1 ) ( 1 log

2 2 2 2 1 ) ( tr

h h g g h h g g g g h h

V H V H V H V U H V H V U H P K K

K K R K K K K K K R

V U

∪

[DPC]

R

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SLIDE 21

Communication of Confidential Messages Communication of Confidential Messages

[ [Csisz Csiszá ár r & & K Kö örner rner, 1978] , 1978] [ [Wyner Wyner, 1975] , 1975] [Liu et al, 2006 & 2007] [Liu et al, 2006 & 2007]

downlink downlink scenario scenario uplink uplink scenario scenario

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SLIDE 22

Communication of Confidential Messages Communication of Confidential Messages

[ [Csisz Csiszá ár r & & K Kö örner rner, 1978] , 1978] [ [Wyner Wyner, 1975] , 1975]

User 1 Destination W1 User 2 W1 W1 ^ W2 ^ W2 X1 (Y2, X2) Y

[ [Liu et al Liu et al, 2006 & 2007] , 2006 & 2007] [ [Liu et al Liu et al, 2006] , 2006]

downlink downlink scenario scenario uplink uplink scenario scenario

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SLIDE 23

Challenge and Opportunity Challenge and Opportunity

W1 W2 W1 W2 W1 W2 W1 W2 W1 W2 W1 W2 W1 W2 W2 W1 W2 W1

(a) IC -- CM (b) MAC -- CM (c) BC -- CM

(a) (a) I Interference nterference C Channel with hannel with C Confidential

  • nfidential M

Messages ( essages (IC IC-

  • CM)

CM) (b) M (b) Multiple ultiple A Access ccess C Channel with hannel with C Confidential

  • nfidential M

Messages ( essages (MAC MAC-

  • CM)

CM) (c) B (c) Broadcast roadcast C Channel with hannel with C Confidential

  • nfidential M

Messages ( essages (BC BC-

  • CM)

CM)

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SLIDE 24
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SLIDE 25
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SLIDE 26

A Computable Outer Bound for MGBC A Computable Outer Bound for MGBC-

  • CM

CM ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ≤ ≤ ⊆ ) ~ | ~ ; ( ) ~ | ~ ; (

1 2 2 2 1 1 ) ( ) | ~ , ~ ( BCC

2 1

Y Y I R Y Y I R

p y y p

X X

x x ∪

∩ C

  • basic ideas:

decode the message in a cooperative manner evaluate the secrecy level in a individual manner

  • for GBC, Gaussian input can optimize this outer bound
  • MGBC can be transferred to an equivalent 2-dimension “Z-broadcast” channel model

X h1 g1 g2 Ỹ1 Ỹ2 X1 X2 h2=0