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Cooperative Diversity Using Distributed Turbo Codes

Cooperative Diversity Using Distributed Turbo Codes. Bin Zhao and Matthew C. Valenti mvalenti@wvu.edu 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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  1. Cooperative Diversity Using Distributed Turbo Codes Bin Zhao and Matthew C. Valenti mvalenti@wvu.edu 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

  2. 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.

  3. Conventional Antenna Arrays • With a conventional array, elements are closely spaced (/2) and connected through high bandwidth cabling. • Microdiversity. Receiver Transmitter

  4. 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

  5. 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

  6. 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

  7. 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).

  8. 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)

  9. 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

  10. 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.

  11. 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.

  12. 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

  13. 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.

  14. 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

  15. 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

  16. 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

  17. 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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