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 ∝ exp − SNR BER • Fading channels 1 ∝ BER SNR

“Higher” Data Rates • Spectral efficiency (bits/seconds/Hertz) • Achievable rates in AWGN Trans SNR ∝ + log( 1 ) R 2 D • Fast fading channels (ergodic) 2 Trans | | h SNR ∝ + [log( 1 )] R E α h D

Data Rates 2 Trans | | h SNR ∝ + [log( 1 )] • Ergodic capacity R E α h D • Slow varying channels • A bad realization may last as long as a frame • Probability of outage 2 Trans | | h SNR = + < Pr[log( 1 ) ] P r α out D Target rate

Outage • Probability of outage 2 Trans | | h SNR = + < Pr[log( 1 ) ] P r α out D • Lower bound on frame error rate 1 ≤ ∝ P FER out SNR

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 1 ∝ BER d SNR • Free dimensions used for multiplexing (i.e., increasing rates) 2 Trans | | h SNR ∝ + [log( 1 )] R mE α D • Tradeoff between diversity and multiplexing

Diversity versus Multiplexing Multiplexing Gain Diversity Gain

Additional Dimensions • Spectral • Temporal • Spatial – Multiple antennas – Cooperation • Feedback? • Cross layer optimization?

Fading Relay Channels Y 0 D X 2 R Y 1 • A paradigm shift X 1 S

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 X 2 Y 1 R X 1 S D Y 0

Two Relays • A broader configuration [Shein & Gallegar] R D S R

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] U 2 D U 1

A Broader Picture: Network Coding D U U U U Channel H Channel H U U U S Infor- S mation

Gaussian Fading Model • The channel qualities 2 2 2 h | | | | h h γ = γ = γ = 12 10 20 , , 0 1 2 N N N 1 0 0 Z 0 Source Destination h 10 X 1 Y 0 = h 10 X 1 + h 20 X 2 + Z 0 h 12 Z 1 h 20 Y 1 = h 12 X 1 + Z 1 X 2 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 2 nd time slot 1 st 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] L , , X X X • The codeword at the source 1 , 1 1 , 2 1 , n L , , Y Y Y • The received signal at relay 1 , 1 1 , 2 1 , n = β • The relay transmits X Y 2 , 1 , i i

Model • The equivalent channel model for half duplex ⎡ ⎤ Z ⎡ ⎤ 1 ⎡ ⎤ ⎡ ⎤ Y 0 1 0 ⎢ ⎥ h = + 0 , BC 10 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ X Z ⎢ ⎥ β β 1 0 0 1 Y ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ h h h ⎢ ⎥ 0 , MA 12 20 20 ⎣ ⎦ Z 0 Z 0 Source Destination h 10 X 1 h 12 Z 1 h 20 X 2 Relay

Gaussian Vector Channel • Mutual information ≤ + ( ; , ) log det[ I X Y Y I 1 0 , 0 , BC MA ⎛ ⎞ ⎡ ⎤ β 2 * | | ( ) h h h h ⎜ ⎟ 10 10 20 12 ⎢ ⎥ P ⎜ ⎟ β β S * 2 ⎣ | | ⎦ h h h h h ⎝ ⎠ 10 20 12 20 12 − 1 ⎛ ⎞ 0 N ⎜ ⎟ 0 ] ⎜ ⎟ β + 2 0 | | ⎝ ⎠ h N N 20 1 0

Achievable Rates for AF • For Gaussian fading γ γ 4 1 P P = + γ + γ 2 0 S r ( , , ) [log( 1 2 )] R P P E P + γ + γ 1 AF S r S 2 1 2 2 P P 0 2 S r • Outage = ≤ ≤ Pr[ ] P R r FER out AF P r γ R γ 0 2 γ P S S 1 D Y 0

Diversity Gain in Outage 0 10 -1 10 Pout -2 10 direct transmission half-duplex multi-hop amplify forward half-duplex decode forward -3 10 -5 0 5 10 15 20 25 SNR (dB)

Achievable Rate 4.5 direct transmission 4 half-duplex multi-hop amplify forward 3.5 half-duplex decode forward Achievable Rate 3 2.5 2 1.5 1 0.5 0 -5 0 5 10 15 20 SNR (dB)

The Promise • Rate increase • Diversity gain – Scale?

Current Focus • Information theoretic analysis – Multiple antennas • Code construction • Feedback U 2 X 2 D Y 1 R X 1 S U 1 D Y 0

Performance Limit d=0.5 1 0.9 0.8 0.7 0.6 Rate 0.5 0.4 0.3 Lower Bound 0.2 Decode and Forward Single User System 0.1 -5 -4 -3 -2 -1 0 1 2 3 4 Eb/No (dB) min

Multiple Antennas • Multiplexing gain? • Diversity gain? R S D

LDPC Example

Amplify and Forward (R=1, α =3, d=0.5) 0 10 Without feedback -1 10 Optimal power Pout -2 control 10 -3 1 bit feedback 10 const Pr 1 bit feedback var Pr -4 10 -5 0 5 10 15 20 Power (dB)

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 U Channel Channel U Channel Channel Channel Channel D S Channel Channel U Channel Channel