Shao Tandra.slides

8/10/2019 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


2/20

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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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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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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cont.

t = 0.5

SNR1 = 0dB

SNR2 = 20dB

SNR3 = 17dB


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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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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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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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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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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.

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