Application of the Evidence Procedure to the Estimation of Wireless Channels
1 Signal Processing and Speech Communication Laboratory, Graz University of Technology, Graz 8010, Austria
2 Institute of Electronic Systems, Aalborg University, Fredrik Bajers Vej 7A, Aalborg 9220, Denmark
3 Forschungszentrum Telekommunikation Wien (ftw.), Donau City Strasse 1, Wien 1220, Austria
EURASIP Journal on Advances in Signal Processing 2007, 2007:079821 doi:10.1155/2007/79821Published: 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.