amplify-and-forward in wireless relay networks samar agnihotri, sidharth jaggi, minghua chen...
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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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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
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“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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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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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: [email protected]: http://personal.ie.cuhk.edu.hk/~samar/ https://sites.google.com/site/samaragnihotri/