amplify-and-forward schemes for wireless communications
DESCRIPTION
Amplify-and-Forward Schemes for Wireless Communications. Wireless Relay Network. Fixed channel. t. t. The network is the channel. s. s. “Tunable” channel. Problem: Design the optimal channel. Relay Networks: Advantages. Enhanced coverage. Increased throughput. Resilient communication. - PowerPoint PPT PresentationTRANSCRIPT
Amplify-and-Forward Schemes for Wireless Communications
2
Wireless Relay Network
s t
s t
Fixed channel
The network is the channel
“Tunable” channel
Problem: Design the optimal channel
3
Relay Networks: Advantages
Enhanced coverage
Increased throughput
Resilient communication
4
Wireless Relay Networks
NoiseInterferenceSynchronizationChannel Parameters
Challenge:Low complexity communication schemes for Wireless relay Networks
SourceReceiver
Three Candidates
A: DNC“Noisy” Network
Coding
B: PNCAmplify-and-forward
C: Quantize-map-and-forward
Alice Bob⁞
⁞
α
β
2mF
111 101 001 …… 110 101 011 ……A single link:
Overall network bit-error ~Ber(p)No more than pEmn 1s (Worst-case)
“Noisy” Network coding
n
“Noisy” Network coding: Bounds
Q. Wang, S. Jaggi, S.-Y. R. Li. Binary error correcting network codes. In Proc. ITW 2011.
TX(1)
2pEmn
TX(2) 2pEmn
TX(3)
2pEmn
)2(1 pHc
ERGV
For both coherent & incoherent NC
pEmnpEmn
pEmn
)(1Hamming pHc
ER
9
ii PEX 2
),0(~ 2NZ i
Amplify-and-Forward Relaying
10
s t
“Intersymbol Interference Channel with Colored Gaussian Noise”
Amplify-and-Forward in Wireless Networks
11
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:
Achievable Rate for AF Relay Networks
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Part I: Approximating IAF(Ps)
Relay without Delay Approximation:
In some scenarios, almost optimal performance
Lower-bound within a constant gap from cutset upper-bound
Computing IAF(Ps) is ``hard’’
S. Agnihotri, S. Jaggi, M. Chen. Amplify-and-forward in wireless relay networks. In Proc. ITW 2011.
13
Layered Wireless Networks
s t
“No Intersymbol Interference, White Gaussian Noise”
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AF Rate in Layered Networks
Previous Work– High SNR– Max. Transmit Power– Few layers
Our Work– Arbitrary SNR– Optimal Transmit Power– Any number of layers
Function of βli
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Part II: Computing
can be computed layer-by-layer
Lemma (Computing Optimal β):
- maximize the sum rate to the next layer
- exponential reduction in the search space: NL L N
The optimal AF rates for
s t
Equal channel gains along all links between two adjacent layers
S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR regime. To appear in ISIT 2012.
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Part III: A Greedy Scheme
s t
- The optimal AF rate for the Diamond Network- First analytical characterization
For general layered networks: better rate approximation
The optimal AF rates fors t
Equal channel gains along all outgoing links from every node
S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR regime: performance of a greedy scheme. To appear in NetCod 2012.
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Part IV: Network SimplificationWhat fraction of the optimal rate can be maintained by using k out of N relays in each layer?
RN – Rk = 2L log(N/k)RN/Rk = (N/k)2L-1
Diamond Network:s t
RN – Rk = log(N/k) RN/Rk = N/k
s tECGAL Network:
S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR regime: performance of network simplification. Submitted to ITW 2012.
18
Project Outcome So Far
New fundamental results for layered AF-networks: many firsts
New insights useful for:• characterization of the optimal rate in general AF networks• design of the optimal relay scheme for layered networks
Communication over a point-to-point channel
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. . .= = = = =
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and we take its binary representation
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122 ,6 Pm
Communication over a point-to-point channel
1X 2X 3X 1nX nX
);(max12
YXICEX
iii NXY
iX iY
iN
)1,0(~ NNi
P 1log2
1
PEX i 2, ,
iX is an integer
. . .
0 00 0 0 1 00 1 0 0 11 0 0 0 00 1 1 1 01 0 1 1 1
. . .
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. . .
. . .
= = = = =
5 42 3 19 9
and we take its binary representation
iN0 1 0
1Y 2Y 3Y 1nY nY. . .
00 0 0 1 11 1 0 0 11 1 0 0 00 0 0 0 10 0 0 1 1
. . .
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0 1 0
Bit flips
54321
654321
6
122 ,6 Pm
0
Communication over a point-to-point channel
1X 2X 3X 1nX nX
);(max12
YXICEX
iii NXY
iX iY
iN
)1,0(~ NNi
P 1log2
1
PEX i 2, ,
iX is an integer
. . .
0 00 0 0 1 00 1 0 0 11 0 0 0 00 1 1 1 01 0 1 1 1
. . .
. . .
. . .
. . .
. . .
= = = = =
5 42 3 19 9
and we take its binary representation
0 1 054321
6iN
1Y 2Y 3Y 1nY nY
00 0 0 1 11 1 0 0 11 1 0 0 00 0 0 0 10 0 0 1 1
. . .
. . .
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. . .
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0 1 0
Bit flips
54321
6
. . .
122 ,6 Pm
0
Communication over a point-to-point channel
1X 2X 3X 1nX nX
);(max12
YXICEX
iii NXY
iX iY
iN
)1,0(~ NNi
P 1log2
1
PEX i 2, ,
iX is an integer
. . .
0 00 0 0 1 00 1 0 0 11 0 0 0 00 1 1 1 01 0 1 1 1
. . .
. . .
. . .
. . .
. . .
= = = = =
5 42 3 19 9
and we take its binary representation
iN0 1 0
54321
61Y 2Y 3Y 1nY nY
1 00 0 0 1 11 1 0 0 11 1 0 0 00 0 0 0 10 0 0 1 1
. . .
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. . .
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0 1 0
Bit flips
54321
6
Dependent bit flips
. . .
122 ,6 Pm
Communication over a point-to-point channel
1X 2X 3X 1nX nX
);(max12
YXICEX
iii NXY
iX iY
iN
)1,0(~ NNi
P 1log2
1
PEX i 2, ,
iX is an integer
. . .
0 00 0 0 1 00 1 0 0 11 0 0 0 00 1 1 1 01 0 1 1 1
. . .
. . .
. . .
. . .
. . .
= = = = =
5 42 3 19 9
and we take its binary representation
iN0 1 0
54321
61Y 2Y 3Y 1nY nY
1 00 0 0 1 11 1 0 0 11 1 0 0 00 0 0 0 10 0 0 1 1
. . .
. . .
. . .
. . .
. . .
0 1 0
Bit flips
54321
6
Dependent bit flips
. . .
Less noisy bit levels
Very noisy bit levels
122 ,6 Pm
Communication over a point-to-point channel
1X 2X 3X 1nX nX
);(max12
YXICEX
iii NXY
iX iY
iN
)1,0(~ NNi
P 1log2
1
PEX i 2, ,
iX is an integer
. . .
0 00 0 0 1 00 1 0 0 11 0 0 0 00 1 1 1 01 0 1 1 1
. . .
. . .
. . .
. . .
. . .
= = = = =
5 42 3 19 9
and we take its binary representation
iN0 1 0
54321
61Y 2Y 3Y 1nY nY
1 00 0 0 1 11 1 0 0 11 1 0 0 00 0 0 0 10 0 0 1 1
. . .
. . .
. . .
. . .
. . .
0 1 0
Bit flips
54321
6
. . .
Less noisy bit levels
Very noisy bit levels
Code to correct adversarial errors
122 ,6 Pm
T. Dikaliotis, H. Yao, A. S. Avestimehr, S. Jaggi, T. Ho. Low-Complexity Near-Optimal Codes for Gaussian Relay Networks. In SPCOM 2012.
25
Publications1. S. Agnihotri, S. Jaggi, M. Chen. Amplify-and-forward in wireless relay
networks. In Proc. ITW 2011.2. Q. Wang, S. Jaggi, S.-Y. R. Li. Binary error correcting network codes. In
Proc. ITW 2011.3. S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR
regime. To appear in ISIT 2012.4. S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR
regime: performance of a greedy scheme. To appear in NetCod 2012.5. S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR
regime: performance of network simplification. To appear in ITW 2012.6. T. Dikaliotis, H. Yao, A. S. Avestimehr, S. Jaggi, T. Ho. Low-Complexity
Near-Optimal Codes for Gaussian Relay Networks. To appear in SPCOM 2012.
7. S. Agnihotri, S. Jaggi, M. Chen. Analog network coding in general SNR regime. In preparation for submission to Trans. Info. Theory.
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Current and Future Work
Optimal and efficient relay schemes for layered networks
Distributed relay schemes
“Back to general AF networks”- the optimal rate, distributed schemes
General wireless relay networks- resource-performance tradeoff- optimal relay scheme, capacity
“The capacity of relay channel”
Incorporating “simple” error-correction
27
Thank You