Cooperative Communication Behnaam Aazhang Outline Motivation A - - PDF document

Cooperative Communication

Behnaam Aazhang

Outline

• Motivation
• A new paradigm

– Relay channel – User cooperation

• A few recent results
• Future directions

Motivation

• Wireless communication

– “Better” reliability – “Higher” data rates

RATE OUTAGE

“Better” Reliability

• Probability of error

– Bit – Symbol – Frame

• Simple white Gaussian channels
• Fading channels

SNR

BER

−

∝ exp

SNR BER 1 ∝

“Higher” Data Rates

• Spectral efficiency (bits/seconds/Hertz)
• Achievable rates in AWGN
• Fast fading channels (ergodic)

) 1 log(

2

D SNR R

Trans

+ ∝

)] | | 1 [log(

2 α

D SNR h E R

Trans h

+ ∝

Data Rates

• Ergodic capacity
• Slow varying channels
• A bad realization may last as long as a frame
• Probability of outage

)] | | 1 [log(

2 α

D SNR h E R

Trans h

+ ∝ ] ) | | 1 Pr[log(

2

r D SNR h P

Trans

• ut

< + =

α

Target rate

Outage

• Probability of outage
• Lower bound on frame error rate

] ) | | 1 Pr[log(

2

r D SNR h P

Trans

• ut

< + =

α

SNR FER P

• ut

1 ∝ ≤

Question

Can we improve reliability and data rate without increasing power or bandwidth? Yes

Degrees of Freedom/Dimensions

[Telatar, Zhang & Tse]

• Free dimensions used for diversity
• Free dimensions used for multiplexing (i.e.,

increasing rates)

• Tradeoff between diversity and multiplexing

d

SNR BER 1 ∝

)] | | 1 [log(

2 α

D SNR h mE R

Trans

+ ∝

Diversity versus Multiplexing

Multiplexing Gain Diversity Gain

Additional Dimensions

• Spectral
• Temporal
• Spatial

– Multiple antennas – Cooperation

• Feedback?
• Cross layer optimization?

Fading Relay Channels

• A paradigm shift

S D R

X1 Y1 X2 Y0

Historical Account

• Introduced in 1971 [Van der Meulen]
• Degraded relay channel in 1979

[Cover & El Gamal]

• Isolated work in the 80’s and 90’s
• Recent resurgence

S D R

X1 Y1 X2 Y0

Two Relays

• A broader configuration [Shein & Gallegar]

S R R D

Multi Hop Network

• Large body of recent work

[Gupta & Kumar, Gastpar & Vetterli, Reznik & Verdu & Kulkarni]

R R R S D

User Cooperation

• A multiuser perspective [Sendonaris & Erkip &

Aazhang]

U1 U2 D

A Broader Picture: Network Coding

D U U U U U U

Channel H Channel H

U S

Infor- mation

S

Gaussian Fading Model

• The channel qualities

2 20 2 2 10 1 1 2 12

| | , | | , N h N h N h = = = γ γ γ

X1 X2 Y1 = h12 X1+ Z1

Y 0= h10 X1+ h20 X2+ Z0

Source h10 Z1 Z0 Destination h12 h20 Relay

Relay Operation

• Full Duplex

– Relay can receive and transmit same time and same frequency band

• RF isolation
• Transmit signal may be 100-150 dB above

received signal

Relay Operation

• Half duplex

– Relay will not receive and transmit same time and same frequency band

• Time division duplex
• Frequency division duplex
• Code division duplex

Multiple access Broadcast

R R

2nd time slot 1st time slot

S S D D

Relay Function

• Fixed relaying

– Decode and forward – Estimate and forward – Amplify and forward

• Adaptive relaying

– Selection – Incremental

Amplify and Forward

[Laneman & Tse & Wornell]

n

X X X

, 1 2 , 1 1 , 1

, , L

• The codeword at the source
• The received signal at relay
• The relay transmits

n

Y Y Y

, 1 2 , 1 1 , 1

, , L

i i

Y X

, 1 , 2

β =

Model

• The equivalent channel model for half duplex

⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

1 20 1 20 12 10 , ,

1 1 Z Z Z h X h h h Y Y

MA BC

β β

X1 X2 Source h10 Z1 Z0 h12 h20 Relay Destination

Gaussian Vector Channel

• Mutual information

] | | | | ) ( | | det[ log ) , ; (

1 1 2 20 2 12 20 12 20 * 10 * 12 20 10 2 10 , , 1 −

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ≤ N N h N h h h h h h h h h P I Y Y X I

S MA BC

β β β β

Achievable Rates for AF

• For Gaussian fading
• Outage

)] 2 2 1 4 2 1 [log( 2 1 ) , , (

2 2 1

γ γ γ γ γ

r S r S S r S AF

P P P P P E P P R + + + + = γ

S D R

PS Y0 Pr

γ

2

γ

1

γ

FER r R P

AF

• ut

≤ ≤ = ] Pr[

Diversity Gain in Outage

• 5

5 10 15 20 25 10

• 3

10

• 2

10

• 1

10

SNR (dB) Pout

direct transmission half-duplex multi-hop amplify forward half-duplex decode forward

Achievable Rate

• 5

5 10 15 20 0.5 1 1.5 2 2.5 3 3.5 4 4.5

SNR (dB) Achievable Rate

direct transmission half-duplex multi-hop amplify forward half-duplex decode forward

The Promise

• Diversity gain
• Rate increase

– Scale?

Current Focus

• Information theoretic analysis

– Multiple antennas

• Code construction
• Feedback

U1 U2 D S D R

X1 Y1 X2 Y0

Performance Limit

• 5
• 4
• 3
• 2
• 1

1 2 3 4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Rate Eb/No

min

(dB) d=0.5

Lower Bound Decode and Forward Single User System

Multiple Antennas

• Multiplexing gain?
• Diversity gain?

S D R

LDPC Example

• 5

5 10 15 20 10

• 4

10

• 3

10

• 2

10

• 1

10

Pout Power (dB)

Optimal power control Without feedback 1 bit feedback const Pr 1 bit feedback var Pr Amplify and Forward (R=1, α=3, d=0.5)

Conclusions and Possible Directions

• A new paradigm

– Low to mid SNR’s – Application: handhelds with limited form factors – Implications on larger networks

• Code construction
• Feedback for power and rate control
• Implementation

Research Platform

TAP: A Mesh Network

• Transit Access Point

Channel?

• Network is the channel

Channel Channel

U U

Channel Channel Channel Channel

D

Channel Channel Channel Channel

S U