Samar Agnihotri Sidharth Jaggi Minghua Chen Institute of Network Coding The Chinese University of Hong Kong In the Beginning there was ITW 2011 Analog network coding in the highSNR ID: 590081
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Slide1
Amplify-and-Forward in Wireless Relay Networks
Samar Agnihotri, Sidharth Jaggi, Minghua Chen
Institute of Network Coding
The Chinese University of Hong KongSlide2
In the Beginning …
… there wasITW 2011Analog network coding in the high-SNR regime
- Marić
, Goldsmith, Médard. WiNC 2010
- Layered networks
- High SNR
2Slide3
ITW 2011
Relay Channel
s
t
Capacity is known only for some special cases
Capacity of the general relay channel is not known
s
t
3Slide4
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)
ITW 2011
4Slide5
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)
ITW 2011
5Slide6
Amplify-and-Forward Relaying
ITW 2011
6Slide7
Amplify-and-Forward Relaying
Cooperative communicationCapacity estimationANCITW 20117Slide8
General Wireless Networks
AnySizeTopologyReceived SNR
s
t
ITW 2011
8Slide9
Network Model
ITW 2011-Bidirectional links-Single antenna
-Full-duplex
9
-Fixed channel gains, known throughoutSlide10
Amplify-and-Forward in Wireless Networks
s
t
“
Intersymbol
Interference Channel with Colored Gaussian Noise”
ITW 2011
10Slide11
Achievable Rate for AF Relay Network
ITW 2011Lemma (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.
11
Proof technique:
circular convolution, DFT Slide12
“Shout Only If You Make Sense”
ITW 2011
s
t
R2
R1
1
1
1
0.1
Ps = P1 = P2 = 10
Scale-and-Forward
Amplify-and-Forward
12Slide13
Approximating I
AF(Ps)ITW 2011Computing IAF(P
s) is ``hard’’
Relay without Delay Approximation
13
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.
*Slide14
Lower Bound Computation-I
ITW 2011βi = β
, 1≤ i
≤ MNo AttenuationConstant Total Relay Power
Type-A Network
14Slide15
Lower Bound Computation-II
ITW 2011βi = β
, 1≤ i
≤ MNo AttenuationConstant Total Relay Power
Type-B Network
15Slide16
Cut-set Upper Bounds
ITW 2011
C ≤
min(CBC
, C
MAC
)
16
M Relays
BC Cut
MAC Cut
s
tSlide17
Asymptotic Capacity
ITW 2011No Attenuation, Constant Total Relay Power
(Type-A Network)
(Type-B Network)
17Slide18
Conclusions
A unified framework for AF relay networksITW 2011Tighter lower bounds for AF relay networksAF relaying can be capacity achieving for a broader class of
networksANC in a class of general networks
18Slide19
Current and Future Work
Half-duplex networks, multiple-antennas/node, …ITW 2011
Distributed schemes
Resource-Performance trade-off
rates beyond AF
19Slide20
ITW 2011
Thank You!20Samar Agnihotri
Email:
samar@ie.cuhk.edu.hkWeb:
http://personal.ie.cuhk.edu.hk/~samar
/
https
://sites.google.com/site/samaragnihotri/