Cooperative Diversity Using Distributed Turbo Codes Bin Zhao and Matthew C. Valenti Lane Dept. of Comp. Sci. & Elect. Eng. West Virginia University Morgantown, WV This work was supported by the Office of Naval Research under grant N

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 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 Receiver #1 Backbone Network

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 Receiver #1 Virtual Connection

6 Related Work Several options for exploiting the broadcast nature of radio have been proposed. –Require maximal-ratio-combining. SourceDestination Relay The relay channel (Cover/El Gamal 1979) Cooperative diversity (Sendonaris/Erkip/Aazhang & Laneman/Wornell 1998) Cooperative coding (Hunter & Nosratinia) Source #2 Source #1 Destination #2 Destination #1 Multihop diversity (Boyer/Falconer/Yanikomeroglu & Gupta/Kumar 2001) Parallel relay channel (Gatspar/Kramer/Gupta 2002) SourceDestination SourceDestination

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 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: 1.Both source-relay and source-destination link in outage: 2.Source-relay link not in outage but parallel link from relay and source to destination is in an outage: SourceDestination Relay  r,d  s,r  s,d

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 P r at distance d m is related to transmitted power P t by Where f c = 2.4 GHz, d o = 1 m, and path loss coefficient n = 3. –Define the “transmit” SNR as P t /(WN o ) 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 The Outage Event Probability (OEP) Average Transmit SNR of the Relay in dB Average Transmit SNR of the Source in dB SourceDestinationRelay 5 m SourceDestinationRelay 1 m9 m SourceDestinationRelay 9 m1 m

13 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. D Source-Relay Channel (& Decoder) Interleaver Relay- Destination Channel D Source- Destination Channel Source = RSC #1 Relay = RSC #2 Turbo Decoder

14 Performance of Distributed Turbo Coding frame size = 512 data bits BPSK modulation SourceDestinationRelay 5 m

15 Performance of Distributed Turbo Coding Average Transmitted SNR of the Relay in dB Average Transmitted SNR of the Source in dB PCCC code (K=2) SCCC code (K=2) SCCC stronger code (K=5,2) PCCC stronger code (K=4) theoretic bound frame size = 512 data bits BPSK modulation SourceDestinationRelay 1 m9 m

16 Multiple Relay Channel E b /N o in dB FER 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 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.