Cooperative diversity using distributed turbo codes
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Cooperative Diversity Using Distributed Turbo Codes. Bin Zhao and Matthew C. Valenti [email protected] Lane Dept. of Comp. Sci. & Elect. Eng. West Virginia University Morgantown, WV This work was supported by the Office of Naval Research under grant N00014-00-0655. Motivation & Goals.

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Cooperative Diversity Using Distributed Turbo Codes

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Cooperative diversity using distributed turbo codes

Cooperative Diversity Using Distributed Turbo Codes

Bin Zhao and Matthew C. Valenti

[email protected]

Lane Dept. of Comp. Sci. & Elect. Eng.

West Virginia University

Morgantown, WV

This work was supported by the Office of Naval Research

under grant N00014-00-0655


Motivation goals

Motivation & Goals

  • Embedded networks of sensors and actuators:

    • Enabling technology for several revolutionary new applications.

    • Low cost, disposable devices.

      • Single antenna.

      • Simple detection (noncoherent) and decoding (hard-decision).

      • High spatial density, but low node activity cycle.

      • Little or no movement = slow / quasi-static fading.

    • IEEE 802.15 TG 4

  • Spatial diversity:

    • Fading can be mitigated using antenna arrays.

    • However, antenna arrays are too cumbersome for EmNets.

  • Goal is to achieve spatial diversity in a dense network of low-cost devices, each with a single antenna.

    • “virtual” antenna array.

    • Emphasis on low cost solutions.

    • A cross-layer approach.


Conventional antenna arrays

Conventional Antenna Arrays

  • With a conventional array, elements are closely spaced (/2) and connected through high bandwidth cabling.

    • Microdiversity.

Receiver

Transmitter


Distributed antenna array

Distributed Antenna Array

  • With a distributed array, the antennas are widely separated (e.g. different base stations) and connected through a moderate bandwidth backbone.

    • Macrodiversity.

Receiver #2

Transmitter

Backbone

Network

Receiver #1


Virtual antenna array

Virtual Antenna Array

  • With a virtual array, the antenna elements are widely spaced (attached to different receivers) but are not connected by a backbone.

    • Virtual connection achieved by MAC-layer design.

    • Decentralized macrodiversity.

Receiver #2

Transmitter

Virtual Connection

Receiver #1


Related work

Related Work

  • Several options for exploiting the broadcast nature of radio have been proposed.

    • Require maximal-ratio-combining.

Relay

The relay channel (Cover/El Gamal 1979)

Source

Destination

Cooperative diversity

(Sendonaris/Erkip/Aazhang & Laneman/Wornell 1998)

Cooperative coding (Hunter & Nosratinia)

Source #1

Destination #1

Source #2

Destination #2

Parallel relay channel

(Gatspar/Kramer/Gupta 2002)

Source

Destination

Multihop diversity

(Boyer/Falconer/Yanikomeroglu & Gupta/Kumar 2001)

Source

Destination


Information theoretic bounds

Information Theoretic Bounds

  • The capacity of the relay channel has been investigated by Cover and El Gamal (1979)

    • AWGN channel.

    • Assumes relay can simultaneously Rx & Tx.

    • Assumes perfect transmit CSI (beamforming effect).

  • Høst-Madsen extended analysis to TDD (2002)

    • Still assumed source+relay transmit coherently.

  • The coherent transmission requirement is not practical.

    • Difficult to synchronize spatially-separated oscillators.

    • We remove this assumption by requiring the source & relay to transmit orthogonally (for instance by using separate time-slots).


Cooperative coding

Cooperative Coding

  • With cooperative coding:

    • The source creates a rate r code of length N but only transmits a fraction  of the coded symbols as a N bit sequence.

    • The relay receives and decodes the symbols. If the sequence is decoded correctly, it will re-encode with the same rate r code, but will transmit the (1-)N code symbols that were not transmitted by the source.

    • The destination receives and decodes the entire N bit codeword.

  • The “overall” code rate of the relay channel is r.

    • The code rate of the source is r/

    • The code rate of the relay is r/(1-)

    • Typically, =1/2 and r=1/4 (50% cooperation)


Theoretical limits on outage

Assume quasi-static fading.

For one block of data, each channel is AWGN with instantaneous SNR 

The SNRs change from block-to-block.

The average SNR is .

A single channel is in an outage if:

The overall relay channel is in an outage if either:

Both source-relay and source-destination link in outage:

Source-relay link not in outage but parallel link from relay and source to destination is in an outage:

Theoretical Limits on Outage

Relay

r,d

s,r

s,d

Source

Destination


Calculation of outage event prob

Calculation of Outage Event Prob.

  • The outage event region is the range of instantaneous SNRs such that:

  • The outage event probability (OEP) is:

    • Under the assumption of independent quasi-static Rayleigh fading channels.


Numerical results

Numerical Results

  • Consider the following example:

    • The received power Pr at distance dm is related to transmitted power Pt by

      • Where fc = 2.4 GHz, do = 1 m, and path loss coefficient n = 3.

    • Define the “transmit” SNR as Pt/(WNo)

  • We can visualize performance in two dimensions by plotting contours of source/relay transmit SNRs required to achieve desired OEP.

  • Assume source & destination separated by 10 m

    • Relay lies on line connecting source & destination.


The outage event probability oep

Source

Relay

Destination

9 m

1 m

Source

Relay

Destination

5 m

5 m

Source

Relay

Destination

1 m

9 m

The Outage Event Probability (OEP)

90

85

80

Average Transmit SNR of the Source in dB

75

70

65

60

20

30

40

50

60

70

80

90

100

Average Transmit SNR of the Relay in dB


Distributed turbo coding

Source = RSC #1

Source-Destination

Channel

Turbo

Decoder

D

Relay-

Destination

Channel

Source-Relay

Channel

(& Decoder)

Interleaver

Relay = RSC #2

D

Distributed Turbo Coding

  • Source & relay each have a recursive encoder.

  • If relay interleaves between decoding and re-encoding, then a turbo code has been created.


Performance of distributed turbo coding

BPSK relay

RSC Relay

96

distributed rate 1/3 PCCC

distributed rate 1/4 PCCC

94

distributed rate 1/4 SCCC

92

theoretical bound

90

88

86

Average transmitted SNR of the source in dB

84

Source

Relay

Destination

5 m

5 m

82

80

78

76

40

50

60

70

80

90

100

Average transmitted SNR of the relay in dB

Performance of Distributed Turbo Coding

frame size = 512 data bits

BPSK modulation


Performance of distributed turbo coding1

Source

Relay

Destination

1 m

9 m

Performance of Distributed Turbo Coding

95

PCCC code (K=2)

SCCC code (K=2)

SCCC stronger code (K=5,2)

90

PCCC stronger code (K=4)

theoretic bound

85

80

Average Transmitted SNR of the Source in dB

75

70

frame size = 512 data bits

BPSK modulation

65

60

50

55

60

65

70

75

80

85

90

95

100

Average Transmitted SNR of the Relay in dB


Multiple relay channel

Multiple Relay Channel

0

10

RSC direct link L=0, R=1/2

RSC relay with L=1, R=1/3

RSC relay with L=2, R=1/4

RSC relay with L=4, R=1/6

distributed pccc with L=1, R=1/3

distributed pccc with L=2, R=1/4

distributed pccc with L=4, R=1/6

-1

10

FER

-2

10

0

5

10

15

20

25

Eb/No in dB

L is the number of relays; assume perfect source-relay links


Conclusions

Conclusions

  • Energy efficient signaling is possible by using a relay to assist communications.

    • “Virtual” antenna array.

  • Distributed turbo coding is an effective way to achieve distributed spatial diversity.

    • Comes within 2.5 dB from the capacity bound with reasonable complexity and frame sizes.

  • Idea can be extended to multiple relays.

  • Performance can be further improved by proper design of MAC layer.

    • MAC layer must decide which (if any) relay forwards message.

    • If MAC layer schedules relays, then it is also performing the network-layer mechanism of routing.


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