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Bayesian compressive sensing for ultra-wideband channel estimation: algorithm and performance analysis

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Abstract

Due to the sparse structure of ultra-wideband (UWB) channels, compressive sensing (CS) is suitable for UWB channel estimation. Among various implementations of CS, the inclusion of Bayesian framework has shown potential to improve signal recovery as statistical information related to signal parameters is considered. In this paper, we study the channel estimation performance of Bayesian CS (BCS) for various UWB channel models and noise conditions. Specifically, we investigate the effects of (i) sparse structure of standardized IEEE 802.15.4a channel models, (ii) signal-to-noise ratio (SNR) regions, and (iii) number of measurements on the BCS channel estimation performance, and compare them to the results of \(\ell _1\)-norm minimization based estimation, which is widely used for sparse channel estimation. We also provide a lower bound on mean-square error (MSE) for the biased BCS estimator and compare it with the MSE performance of implemented BCS estimator. Moreover, we study the computation efficiencies of BCS and \(\ell _1\)-norm minimization in terms of computation time by making use of the big-\(O\) notation. The study shows that BCS exhibits superior performance at higher SNR regions for adequate number of measurements and sparser channel models (e.g., CM-1 and CM-2). Based on the results of this study, the BCS method or the \(\ell _1\)-norm minimization method can be preferred over the other one for different system implementation conditions.

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Notes

  1. For the implementation of (10), the codes provided by Romberg and Candes publicly availble at http://users.ece.gatech.edu/~justin/l1magic/ are used.

  2. For the implementation of BCS, the codes provided by Shihao Ji publicly available at http://people.ee.duke.edu/~lcarin/BCS.html are used.

  3. In Bayesian probability theory, if the resulting posterior distributions \(p(\left. {\mathbf{h}} \right| \mathbf{y})\) are in the same class as prior probability distributions \(p(\mathbf{h})\), then that class of \(p(\mathbf{h})\) is said to be conjugate to the class of likelihood functions \(p(\left. \mathbf{y} \right| {\mathbf{h}})\) [12].

  4. Uniform or flat hyperpriors are known as noninformative hyperpriors [24] which have a minimum effect on the hyperparameter posterior and they can be ignored.

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Authors and Affiliations

  1. Department of Electronics and Communications Engineering, İstanbul Technical University, Maslak, 34469, Istanbul, Turkey

    Mehmet Özgör & Hakan Ali Çırpan

  2. Department of Electrical and Electronics Engineering, Kadir Has University, Fatih, 34083, Istanbul, Turkey

    Serhat Erküçük

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  1. Mehmet Özgör
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  2. Serhat Erküçük
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  3. Hakan Ali Çırpan
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Correspondence to Serhat Erküçük.

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Özgör, M., Erküçük, S. & Çırpan, H.A. Bayesian compressive sensing for ultra-wideband channel estimation: algorithm and performance analysis. Telecommun Syst 59, 417–427 (2015). https://doi.org/10.1007/s11235-014-9902-7

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