Bayesian compressive sensing for ultra-wideband channel estimation: algorithm and performance analysis
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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.
KeywordsBayesian compressive sensing (BCS) IEEE 802.15.4a channel models \(\ell _1\)-norm minimization Mean-square error (MSE) lower bound Ultra-wideband (UWB) channel estimation
- 3.Ragoubi, K., Jin, M., Saha, G., & Yang, Y. (2011). Recent advances in UWB systems: Theory and applications. Journal of Telecommunication Systems. doi: 10.1007/s11235-011-9628-8.
- 4.IEEE. (2007). Standart 802.15.4a-2007: Part 15.4: Wireless medium access control (MAC) and physical layer (PHY) specifications for low-rate wireless personal area networks (WPANs).Google Scholar
- 5.De Nardis, L., Fiorina, J., Panaitopol, D., & Di Benedetto, M. G. (2011). Combining UWB with time reversal for improved communication and positioning. Journal of Telecommunication Systems. doi: 10.1007/s11235-011-9630-1.
- 6.Islam, S. M. R., & Kwak, K. S. (2011). Preamble-based improved channel estimation for multiband UWB systems in presence of interferences. Journal of Telecommunication Systems. doi: 10.1007/s11235-011-9440-5.
- 10.Başaran, M., Erküçük, S., & Çırpan, H.A. (2011). The effect of channel models on compressed sensing based UWB channel estimation. In IEEE international conference on ultra-wideband (ICUWB) (pp. 375–379).Google Scholar
- 11.Tipping, M.E., & Faul, A.C. (2003). Fast marginal likelihood maximization for sparse Bayesian models. In Proceedings of 9th international workshop on artificial intelligence and statistics (pp. 1–13).Google Scholar
- 13.Babacan, S.D., Molina, R., & Katsaggelos, A.K. (2009). Fast Bayesian compressive sensing using Laplace priors. In IEEE international conference on acoustics, speech and signal processing (ICASSP) (pp. 2873–2876).Google Scholar
- 14.Yang, D., Li, H., & Peterson, G.D. (2011). Decentralized Turbo Bayesian compressed sensing with application to UWB systems. EURASIP Journal on Advances in Signal Processing, 2011, article ID 817947.Google Scholar
- 16.Shi, L., Zhou, Z., Tang, L., Yao, H., & Zhang, J. (2010). Ultra-wideband channel estimation based on Bayesian compressive sensing. In Proceedings of 10th international symposium on communications and information technologies (ISCIT) (pp. 779–782).Google Scholar
- 17.Özgör, M., Erküçük, S., & Çırpan, H.A. (2012). Bayesian compressive sensing for ultra-wideband channel models. In 35th international conference on telecommunications and signal processing (TSP) (pp. 320–324).Google Scholar
- 18.Zayyani, H., Babaie-Zadeh, M., & Jutten, C. (2009). Compressed sensing block MAP-LMS adaptive filter for sparse channel estimation and a Bayesian Cramér-Rao bound. In IEEE international workshop on machine learning and signal processing (MLSP) (pp. 1–6).Google Scholar
- 19.Kay, S. M. (1993). Fundamentals of statistical signal processing: Estimation theory. Upper Saddle River, NJ: Prentice Hall.Google Scholar
- 21.Erküçük, S., Kim, D.I., & Kwak, K.S. (2007). Effects of channel models and Rake receiving process on UWB-IR system performance. In IEEE international conference on communications (ICC) (pp. 4896–4901).Google Scholar
- 24.Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2003). Bayesian data analysis (2nd ed.). Boca Raton, FL: CRC Press.Google Scholar
- 26.Van Tress, H. L. (1968). Detection, estimation and modulation theory (Part I). New York: Wiley.Google Scholar