Amplify-and-Forward in Wireless Relay Networks

Samar Agnihotri, Sidharth Jaggi, Minghua Chen

Institute of Network Coding

The Chinese University of Hong Kong

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In the Beginning …

… there was

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Analog network coding in the high-SNR regime

- Marić, Goldsmith, Médard. WiNC 2010

- Layered networks

- High SNR

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Relay Channel

s t

Capacity is known only for some special cases

Capacity of the general relay channel is not known

s t

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Achievability Schemes

• Decode-and-Forward (Cover/El Gamal 1979)• Compress-and-Forward (Cover/El Gamal 1979)• Amplify-and-Forward (Laneman/Tse 2002)• Compute-and-Forward (Nazer/Gastpar 2006)• Quantize-map-and-Forward (ADT 2010)

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Achievability Schemes

• Decode-and-Forward (Cover/El Gamal 1979)• Compress-and-Forward (Cover/El Gamal 1979)• Amplify-and-Forward (Laneman/Tse 2002)• Compute-and-Forward (Nazer/Gastpar 2006)• Quantize-map-and-Forward (ADT 2010)

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Amplify-and-Forward Relaying

ii PEX 2

),0(~ 2NZ i

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Amplify-and-Forward Relaying

• Cooperative communication• Capacity estimation• ANC

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General Wireless Networks

Any• Size• Topology• Received SNR

s t

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Network Model

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-Bidirectional links

-Single antenna

-Full-duplex

-Fixed channel gains, known throughout

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Amplify-and-Forward in Wireless Networks

s t

“Intersymbol Interference Channel with Colored Gaussian Noise”

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Achievable Rate for AF Relay Network

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Lemma (Achievable rate for AF relay network):For an AF-relay network with M nodes, the rate achievable with a given amplification vector β is

Maximum Achievable rate:

W. Hirt, J. L. Massey, Capacity of the discrete-time Gaussian channel with intersymbol interference, Trans. IT, vol IT-34, 1988.

Proof technique: circular convolution, DFT

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“Shout Only If You Make Sense”

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s t

R2

R1

1

1

1

0.1

Ps = P1 = P2 = 101.02

99.02max,1 502

max,2

99.02,1 opt 2.02

,2 opt

Scale-and-Forward

Amplify-and-Forward

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Approximating IAF(Ps)

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Computing IAF(Ps) is ``hard’’

Relay without Delay Approximation

S. Katti, I. Marić, A. Goldsmith, D. Katabi, M. Médard, Joint relaying and network coding in wireless networks, Proc. IEEE ISIT 2007, Nice, France, June 2007.

*

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Lower Bound Computation-I

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βi = β, 1≤ i ≤ MNo Attenuation

Constant Total Relay Power

Type-A Network

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Lower Bound Computation-II

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βi = β, 1≤ i ≤ MNo Attenuation

Constant Total Relay Power

Type-B Network

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Cut-set Upper Bounds

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C ≤ min(CBC , CMAC)

M Relays

BC

Cu

tM

AC

Cu

t

s t

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Asymptotic Capacity

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No Attenuation, Constant Total Relay Power

(Type-A Network)

(Type-B Network)

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Conclusions

A unified framework for AF relay networks

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Tighter lower bounds for AF relay networks

AF relaying can be capacity achieving for a broader class of networks

ANC in a class of general networks

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Current and Future Work

Half-duplex networks, multiple-antennas/node, …

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Distributed schemes

Resource-Performance trade-off– rates beyond AF

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Thank You!

Samar Agnihotri

Email: samar@ie.cuhk.edu.hkWeb: http://personal.ie.cuhk.edu.hk/~samar/ https://sites.google.com/site/samaragnihotri/