Application of the Evidence Procedure to the Estimation of Wireless Channels
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Research Article Application of the Evidence Procedure to the Estimation of Wireless Channels Dmitriy Shutin,1 Gernot Kubin,1 and Bernard H. Fleury2, 3 1 Signal
Processing and Speech Communication Laboratory, Graz University of Technology, 8010 Graz, Austria of Electronic Systems, Aalborg University, Fredrik Bajers Vej 7A, 9220 Aalborg, Denmark 3 Forschungszentrum Telekommunikation Wien (ftw.), Donau City Strasse 1, 1220 Wien, Austria 2 Institute
Received 5 November 2006; Accepted 8 March 2007 Recommended by Sven Nordholm 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. Copyright © 2007 Dmitriy Shutin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Deep understanding of wireless channels is an essential prerequisite to satisfy the ever-growing demand for fast information access over wireless systems. A wireless channel contains explicitly or implicitly all the information about the propagation environment. To ensure reliable communication, the transceiver should be constantly aware of the channel state. In order to make this task feasible, accurate channel models, which reproduce in a realistic manner the channel behavior, are required. However, efficient joint estimation of the channel parameters, for example, number of the multipath components (model order), their relative delays, Doppler frequencies, directions of the impinging wavefronts, and polarizations, is a particularly difficult task. It often leads to analytically intractable and computationally very expensive optimization procedures. The problem is often relaxed by assuming that the numb
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