Open Access

Application of the Evidence Procedure to the Estimation of Wireless Channels

EURASIP Journal on Advances in Signal Processing20072007:079821

DOI: 10.1155/2007/79821

Received: 5 November 2006

Accepted: 8 March 2007

Published: 15 May 2007


We address the application of the Bayesian evidence procedure to the estimation of wireless channels. The proposed scheme is based on relevance vector machines (RVM) originally proposed by M. Tipping. RVMs allow to estimate channel parameters as well as to assess the number of multipath components constituting the channel within the Bayesian framework by locally maximizing the evidence integral. We show that, in the case of channel sounding using pulse-compression techniques, it is possible to cast the channel model as a general linear model, thus allowing RVM methods to be applied. We extend the original RVM algorithm to the multiple-observation/multiple-sensor scenario by proposing a new graphical model to represent multipath components. Through the analysis of the evidence procedure we develop a thresholding algorithm that is used in estimating the number of components. We also discuss the relationship of the evidence procedure to the standard minimum description length (MDL) criterion. We show that the maximum of the evidence corresponds to the minimum of the MDL criterion. The applicability of the proposed scheme is demonstrated with synthetic as well as real-world channel measurements, and a performance increase over the conventional MDL criterion applied to maximum-likelihood estimates of the channel parameters is observed.


Authors’ Affiliations

Signal Processing and Speech Communication Laboratory, Graz University of Technology
Institute of Electronic Systems, Aalborg University
Forschungszentrum Telekommunikation Wien (ftw.)


  1. Krim H, Viberg M: Two decades of array signal processing research: the parametric approach. IEEE Signal Processing Magazine 1996,13(4):67-94. 10.1109/79.526899View ArticleGoogle Scholar
  2. Fleury BH, Tschudin M, Heddergott R, Dahlhaus D, Pedersen KI: Channel parameter estimation in mobile radio environments using the SAGE algorithm. IEEE Journal on Selected Areas in Communications 1999,17(3):434-450. 10.1109/49.753729View ArticleGoogle Scholar
  3. Duda RO, Hart PE, Stork DG: Pattern Classification. 2nd edition. John Wiley & Sons, New York, NY, USA; 2000.MATHGoogle Scholar
  4. Wax M, Kailath T: Detection of signals by information theoretic criteria. IEEE Transactions on Acoustics, Speech, and Signal Processing 1985,33(2):387-392. 10.1109/TASSP.1985.1164557MathSciNetView ArticleGoogle Scholar
  5. Rissanen J: Modelling by the shortest data description. Automatica 1978,14(5):465-471. 10.1016/0005-1098(78)90005-5View ArticleMATHGoogle Scholar
  6. Haykin S (Ed): Kalman Filtering and Neural Networks. John Wiley & Sons, New York, NY, USA; 2001.Google Scholar
  7. Feder M, Weinstein E: Parameter estimation of superimposed signals using the EM algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing 1988,36(4):477-489. 10.1109/29.1552View ArticleMATHGoogle Scholar
  8. MacKay DJ: Information Theory, Inference, and Learning Algorithms. Cambridge University Press, Cambridge, UK; 2003.MATHGoogle Scholar
  9. Fitzgerald WJ: The Bayesian approach to signal modelling. IEE Colloquium on Non-Linear Signal and Image Processing (Ref. No. 1998/284), May 1998, London, UK 9/1-9/5.Google Scholar
  10. Schwarz G: Estimating the dimension of a model. Annals of Statistics 1978,6(2):461-464. 10.1214/aos/1176344136MathSciNetView ArticleMATHGoogle Scholar
  11. Rissanen JJ: Fisher information and stochastic complexity. IEEE Transactions on Information Theory 1996,42(1):40-47. 10.1109/18.481776MathSciNetView ArticleMATHGoogle Scholar
  12. Lanterman AD: Schwarz, Wallace, and Rissanen: intertwining themes in theories of model selection. International Statistical Review 2001,69(2):185-212.View ArticleMATHGoogle Scholar
  13. MacKay DJC: Bayesian interpolation. Neural Computation 1992,4(3):415-447. 10.1162/neco.1992.4.3.415View ArticleMATHGoogle Scholar
  14. MacKay DJC: Bayesian methods for backpropagation networks. In Models of Neural Networks III. Edited by: Domany E, van Hemmen JL, Schulten K. Springer, New York, NY, USA; 1994:211-254. chapter 6Google Scholar
  15. Tipping ME: Sparse Bayesian learning and the relevance vector machine. Journal of Machine Learning Research 2001,1(3):211-244.MathSciNetMATHGoogle Scholar
  16. Rappaport TS: Wireless Communications: Principles and Practice. Prentice Hall PTR, Saddle River, NJ, USA; 2002.MATHGoogle Scholar
  17. Heckerman D: A tutorial on learning with Bayesian networks. In Tech. Rep. MSR-TR-95-06. Microsoft Research, Advanced Technology Division, One Microsoft Way, Redmond, Wash, USA; 1995.Google Scholar
  18. Neal R: Bayesian Learning for Neural Networks, Lecture Notes in Statistics. Volume 118. Springer, New York, NY, USA; 1996.View ArticleGoogle Scholar
  19. Berger O: Statistical Decision Theory and Bayesian Analysis. 2nd edition. Springer, New York, NY, USA; 1985.View ArticleMATHGoogle Scholar
  20. Grünwald P: A tutorial introduction to the minimum description length principle. In Advances in Minimum Description Length: Theory and Applications, 2005, Cambridge, Mass, USA. Edited by: Grünwald P, Myung I, Pitt M. MIT Press; 80 pages.Google Scholar
  21. Barron A, Rissanen J, Yu B: The minimum description length principle in coding and modeling. IEEE Transactions on Information Theory 1998,44(6):2743-2760. 10.1109/18.720554MathSciNetView ArticleMATHGoogle Scholar
  22. Faul AC, Tipping ME: Analysis of sparse Bayesian learning. In Advances in Neural Information Processing Systems (NIPS '01), December 2002, Vancouver, British Columbia, Canada. Volume 14. Edited by: Dietterich TG, Becker S, Ghahramani Z. MIT Press; 383-389.Google Scholar
  23. Conradsen K, Nielsen A, Schou J, Skriver H: A test statistic in the complex Wishart distribution and its application to change detection in polarimetric SAR data. IEEE Transactions on Geoscience and Remote Sensing 2003,41(1):4-19. 10.1109/TGRS.2002.808066View ArticleGoogle Scholar
  24. Goodman NR: Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction). The Annals of Mathematical Statistics 1963,34(1):152-177. 10.1214/aoms/1177704250View ArticleMathSciNetMATHGoogle Scholar
  25. Evans M, Hastings N, Peacock B: Statistical Distributions. 3rd edition. John Wiley & Sons, New York, NY, USA; 2000.MATHGoogle Scholar
  26. Abramowitz M, Stegun IA: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York, NY, USA; 1972.MATHGoogle Scholar
  27. Laakso TI, Välimäki V, Karjalainen M, Laine UK: Splitting the unit delay [FIR/all pass filters design]. IEEE Signal Processing Magazine 1996,13(1):30-60. 10.1109/79.482137View ArticleGoogle Scholar
  28. Golub GH, van Loan CF: Matrix Computations. The Johns Hopkins University Press, Baltimore, Md, USA; 1996.MATHGoogle Scholar


© Dmitriy Shutin et al. 2007

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