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Transcript of Shao Tandra.slides
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Cooperative Diversity inWireless Broadcast
Channels
Jingyi Shao
Rahul Tandra
May 13, 2004, EE224B Project
Dr. Tse, UC Berkeley
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Overview
Problem and motivation
Case 1: slow fading Network model Outage probability and diversity Diversity and rate tradeoff Extension
Case 2: AWGN wireless channels Network model Rate region without cooperation Rate region with cooperation in Scheme 1
Rate region with cooperation in Scheme 2 Extension
Conclusion
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Problem and Motivation
Wireless broadcast channel
One source sends the samemessage to multiple destinations
Multipath fading
Goal: to use cooperation to
exploit spatial diversity Decrease outage probabilty in
slow fading
Increase achievable rate region
in AWGN wireless channels
Applications: sensor networks.
Source
D_1
D_2
D_n
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Slow Fading: Network Model
One source and two
destinations
Assumptions:
Slow fading
Channels independentRayleigh,
Half-duplex
i.i.d. Channel noise ~
)1,0(~CNhi
),0( 0NCN
1h
2h
3h
1D
2D
S
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Slow Fading: Cooperation
Scheme
Divide n channel uses (assuming the n channel uses is less than
the coherence time of the channel) into two equal slots. During Slot 1, the source transmits at a fixed rate, R, and both of
the destinations listen.
The destinations also tracks the channel SNR through trainingsymbols.
Each of the destination decodes at the end of Slot 1, and if itschannel SNR is bigger than some threshold, b, the destinationwill repeat the source signal in Slot 2; otherwise, it will listen.
Slot 1, n/2 channel uses Slot 2, n/2 channel uses
S Tx, D1 and D2 Rx D_i Tx iff SNR_i>b
n channel uses
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Slow Fading: Outage
Probability Calculation
Similar to the selcetion decode in [Laneman et al]
))12
|(|)12
|(|)12
|Pr((|
))12
|(|)12
|Pr((|
2
3
2
2
2
1
2
2
2
1
SNRh
SNRh
SNRh
SNRh
SNRh
RRR
RR
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Slow Fading: Diversity Rate
Tradeoff
Diversity = 2
Rate =
Can we do get a higher rate?
No!1h
2h
3h
1D
2D
S
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Slow Fading: Extention to n
Desitinations
Similar scheme to achieve Diversity = n, rate = 1/(n+1).
1h
2h
1D
2D
S
3
h
3D
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AWGN: Network Model
Assume no fading, and all nodes
knows the channel gains. Without loss of Generality, assume
Assume i.i.d. channel noise ~
S wants to send the samemessage to both D1 and D2.
Half-duplex operations at allnodes.
Each nodes has transmit powerconstraint, P.
|||| 12 hh >
1h
2h
3h
1D
2D
S
),0( 0NCN
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AWGN: Achievable Rate
Region without Cooperation
The common rate is limited by the worse channel.
dBSNR
dBSNR
20
0
2
1
=
=
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AWGN: Cooperation Scheme 1
Divide n channel uses into two slots, and let tbe the
fraction of time for Slot 1, (1-t) be the fraction of timefor Slot 2.
During Slot 1, S allocates a fraction of its power for
the signal to D1, and (1-a) fraction of the power forthe signal to D2 using superposition coding with rateR1 and R2.
)}
)1(||
||1log()
)1(||1{log(
)})1(||
||1{log(
0
2
1
2
1
0
2
22
0
2
1
2
11
NPah
aPh
N
PahtR
NPahaPhtR
+++
+
++
1h
2h
3h
1D
2D
S
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AWGN: Cooperation Scheme 1
cont.
Both destinations can decode its portion of the
message. Note: D2 has a better channel, andreceives more bits than D1.
During Slot 2, S and D2 jointly transmit additional bits
to D1, so that D1 gets the same message as D2.This is a multiple access channel, and the optimalrate D1 gets in Slot 2 is
))|||(|
1log()1(0
2
3
2
1
N
Phht
++
1h
2h
3h
1D
2D
S
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AWGN: Cooperation Scheme 1
cont.
Overall rate for D1 and D2
)))1(||
||1log())1(||1(log(
))|||(|
1log()1())1(||
||1log(
0
2
1
2
1
0
2
22
0
2
3
2
1
0
2
1
2
11
NPahaPh
NPahtR
N
Phht
NPah
aPhtR
+++
+
+++
++
Want R1(t,a) = R2(t,a).
Solve tin terms of a.
Maximize R1 over 0
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AWGN: Cooperation Scheme 1
cont.
t = 0.5
SNR1 = 0dB
SNR2 = 20dB
SNR3 = 17dB
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AWGN: Cooperation Scheme 2
Divide n channel uses into two slots.
During the first slot, S transmits at
Note D2 can decode perfectly, but D1 cannotdecode perfectly. D1 will decode to a list of possible
codewords. During the second time slot, D2 sends D1 some
additional information to help D1 fully decode.
)||1log(0
2
2
NPhR +=
The coding technique used here is similar to [Cover and Gamal 79],which involves random coding and Slepian-Wolf partitioning.
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AWGN: Cooperation Scheme 2
cont.
S, D1, and D2 forms a relay channel with D2 being
the relay. Capacity (full duplex) is known [Cover and Gamal
79]
)}|;(),;,(min{sup 2212),( 2
DDSDDSXXp
XYXIYXXICDS
=
S D1
N1 N-N1D2
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AWGN: Cooperation Scheme 2
cont.
For AWGN degraded relay channels
)}(),)1(2
(min{max1
12121
10 N
aPC
N
PPaPPCC
a
++=
SWith P1
D2
With P2
D1
N1 N-N1
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AWGN: Cooperation Scheme 2
cont.
In our case,
)]}||
()||
([),||
(min{max2/10
2
3
0
2
1
0
2
2
10 N
PhC
N
PhaC
N
PhaCR
a+=
1h
2h3
h
1D
2D
S
With Power P
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AWGN: Cooperation Scheme 2
cont.
Comparing the achievable rate for the two schemes.
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Conclusion
Use cooperation scheme to achieve full
diversity in slow fading wireless broadcastnetwork.
Diversity and rate tradeoff in slow fading
case. Use two cooperation schemes to achieve
higher common rate region in AWGN
wireless broadcast network. Future work.