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Code-Aided Estimation and Detection on Time-Varying Correlated Mimo Channels: A Factor Graph Approach

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This paper concerns channel tracking in a multiantenna context for correlated flat-fading channels obeying a Gauss-Markov model. It is known that data-aided tracking of fast-fading channels requires a lot of pilot symbols in order to achieve sufficient accuracy, and hence decreases the spectral efficiency. To overcome this problem, we design a code-aided estimation scheme which exploits information from both the pilot symbols and the unknown coded data symbols. The algorithm is derived based on a factor graph representation of the system and application of the sum-product algorithm. The sum-product algorithm reveals how soft information from the decoder should be exploited for the purpose of estimation and how the information bits can be detected. Simulation results illustrate the effectiveness of our approach.


  1. 1.

    Biglieri E, Proakis J, Shamai S: Fading channels: information-theoretic and communications aspects. IEEE Transactions on Information Theory 1998, 44(6):2619–2692. 10.1109/18.720551

  2. 2.

    Caire G, Taricco G, Biglieri E: Bit-interleaved coded modulation. IEEE Transactions on Information Theory 1998, 44(3):927–946. 10.1109/18.669123

  3. 3.

    Hall EK, Wilson SG: Design and analysis of turbo codes on Rayleigh fading channels. IEEE Journal on Selected Areas in Communications 1998, 16(2):160–174. 10.1109/49.661105

  4. 4.

    Li X, Ritcey JA: Trellis-coded modulation with bit interleaving and iterative decoding. IEEE Journal on Selected Areas in Communications 1999, 17(4):715–724. 10.1109/49.761047

  5. 5.

    Valenti MC, Woerner BD: Iterative channel estimation and decoding of pilot symbol assisted turbo codes over flat-fading channels. IEEE Journal on Selected Areas in Communications 2001, 19(9):1697–1705. 10.1109/49.947034

  6. 6.

    Komninakis C, Wesel RD: Joint iterative channel estimation and decoding in flat correlated Rayleigh fading. IEEE Journal on Selected Areas in Communications 2001, 19(9):1706–1717. 10.1109/49.947035

  7. 7.

    Komninakis C, Fragouli C, Sayed AH, Wesel RD: Multi-input multi-output fading channel tracking and equalization using Kalman estimation. IEEE Transactions on Signal Processing 2002, 50(5):1065–1076. 10.1109/78.995063

  8. 8.

    Dong M, Tong L, Sadler BM: Optimal insertion of pilot symbols for transmissions over time-varying flat fading channels. IEEE Transactions on Signal Processing 2004, 52(5):1403–1418. 10.1109/TSP.2004.826182

  9. 9.

    Schafhuber D, Matz G, Hlawatsch F: Kalman tracking of time-varying channels in wireless MIMO-OFDM systems. Proceedings of the 37th IEEE Asilomar Conference on Signals, Systems and Computers, November 2003, Pacific Grove, Calif, USA 2: 1261–1265.

  10. 10.

    Baccarelli E, Cusani R, Galli S: A novel adaptive receiver with enhanced channel tracking capability for TDMA-based mobile radio communications. IEEE Journal on Selected Areas in Communications 1998, 16(9):1630–1639. 10.1109/49.737632

  11. 11.

    Liu Z, Ma X, Giannakis GB: Space-time coding and Kalman filtering for time-selective fading channels. IEEE Transactions on Communications 2002, 50(2):183–186. 10.1109/26.983312

  12. 12.

    Anderson BDO, Moore JB: Optimal Filtering. Prentice-Hall, Englewood Cliffs, NJ, USA; 1979.

  13. 13.

    Kschischang FR, Frey BJ, Loeliger H-A: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 2001, 47(2):498–519. 10.1109/18.910572

  14. 14.

    Wadayama T: An iterative decoding algorithm for channels with additive linear dynamical noise. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2003, E86-A(10):2452–2460.

  15. 15.

    Shen M, Niu H, Liu H: Iterative receiver design in Rayleigh fading using factor graph. Proceedings of the 57th IEEE Vehicular Technology Conference (VTC '03), April 2003, Jeju, South Korea 4: 2604–2608.

  16. 16.

    Colavolpe G, Barbieri A, Caire G, Bonneau N: Bayesian and nonBayesian methods for iterative joint decoding and detection in the presence of phase noise. Proceedings of IEEE International Symposium on Information Theory (ISIT '04), June–July 2004, Chicago, Ill, USA 131.

  17. 17.

    Dauwels J, Loeliger H-A: Phase estimation by message passing. Proceedings of IEEE International Conference on Communications (ICC '04), June 2004, Paris, France 1: 523–527.

  18. 18.

    Worthen AP, Stark WE: Unified design of iterative receivers using factor graphs. IEEE Transactions on Information Theory 2001, 47(2):843–849. 10.1109/18.910595

  19. 19.

    Wiberg N: Codes and decoding on general graphs, M.S. thesis. Linkoping University, Linkoping, Sweden; 1996.

  20. 20.

    Nguyen VK, White LB, Jaffrot E, Soamiadana M, Fijalkow I: Recursive receivers for diversity channels with correlated flat fading. IEEE Journal on Selected Areas in Communications 2003, 21(5):754–764. 10.1109/JSAC.2003.810332

  21. 21.

    Gesbert D, Bölcskei H, Gore DA, Paulraj AJ: Outdoor MIMO wireless channels: models and performance prediction. IEEE Transactions on Communications 2002, 50(12):1926–1934. 10.1109/TCOMM.2002.806555

  22. 22.

    Kotecha JH, Sayeed AM: Transmit signal design for optimal estimation of correlated MIMO channels. IEEE Transactions on Signal Processing 2004, 52(2):546–557. 10.1109/TSP.2003.821104

  23. 23.

    Loeliger H-A: An introduction to factor graphs. IEEE Signal Processing Magazine 2004, 21(1):28–41. 10.1109/MSP.2004.1267047

  24. 24.

    Simoens F, Wymeersch H, Moeneclaey M: Spatial mapping for MIMO systems. Proceedings of IEEE Information Theory Workshop (ITW '04), October 2004, San Antonio, Tex, USA 187–192.

  25. 25.

    Wang HS, Chang P-C: On verifying the first-order Markovian assumption for a Rayleigh fading channel model. IEEE Transactions on Vehicular Technology 1996, 45(2):353–357. 10.1109/25.492909

  26. 26.

    Jakes WC: Mobile Microwave Communication. John Wiley & Sons, New York, NY, USA; 1974.

  27. 27.

    Bahl LR, Cocke J, Jelinek F, Raviv J: Optimal decoding of linear codes for minimizing symbol error rate. IEEE Transactions on Information Theory 1974, 20(2):284–287.

  28. 28.

    Berrou C, Glavieux A, Thitimajshima P: Near Shannon limit error-correcting coding and decoding: turbo-codes. 1. Proceedings of IEEE International Conference on Communications (ICC '93), May 1993, Geneva, Switzerland 1064–1070.

  29. 29.

    MacKay DJC: Good error-correcting codes based on very sparse matrices. IEEE Transactions on Information Theory 1999, 45(2):399–431. 10.1109/18.748992

  30. 30.

    Simoens F, Wymeersch H, Steendam H, Moeneclaey M: Synchronization for MIMO systems. In Smart Antennas—State of the Art, EURASIP Book Series on Signal Processing and Communications. Hindawi, New York, NY, USA; 2005. chapter 6

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Correspondence to Frederik Simoens.

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  • Graph Representation
  • Quantum Information
  • Estimation Scheme
  • Spectral Efficiency
  • Sufficient Accuracy