Telecommunication Systems

, Volume 59, Issue 4, pp 417–427 | Cite as

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

  • Mehmet Özgör
  • Serhat Erküçük
  • Hakan Ali Çırpan


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.


Bayesian compressive sensing (BCS)  IEEE 802.15.4a channel models \(\ell _1\)-norm minimization Mean-square error (MSE) lower bound Ultra-wideband (UWB) channel estimation 


  1. 1.
    Win, M. Z., & Scholtz, R. A. (2000). Ultra-widebandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications. IEEE Transactions on Communications, 48, 679–691.CrossRefGoogle Scholar
  2. 2.
    Porcino, D., & Hirt, W. (2003). Ultra-wideband radio technology: Potential and challenges ahead. IEEE Communications Magazine, 41(7), 66–74.CrossRefGoogle Scholar
  3. 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. 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. 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. 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.
  7. 7.
    Candès, E. J., Romberg, J., & Tao, T. (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52, 489–509.CrossRefGoogle Scholar
  8. 8.
    Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52, 1289–1306.CrossRefGoogle Scholar
  9. 9.
    Parades, J., Arce, G. R., & Wang, Z. (2007). Ultra-wideband compressed sensing: Channel estimation. IEEE Journal on Selected Topics in Signal Processing, 1, 383–395.CrossRefGoogle Scholar
  10. 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. 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
  12. 12.
    Ji, S., Xue, Y., & Carin, L. (2008). Bayesian compressive sensing. IEEE Transactions on Signal Processing, 56(6), 2346–2355.CrossRefGoogle Scholar
  13. 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. 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
  15. 15.
    Tang, L., Zhou, Z., & Shi, L. (2011). Ultra-wideband channel estimation based on distributed Bayesian compressive sensing. International Journal of Digital Content Technology and its Applications (JDCTA), 5(2), 1–8.CrossRefGoogle Scholar
  16. 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. 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. 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. 19.
    Kay, S. M. (1993). Fundamentals of statistical signal processing: Estimation theory. Upper Saddle River, NJ: Prentice Hall.Google Scholar
  20. 20.
    Eldar, Y. C. (2006). Uniformly improving the Cramér-Rao bound and maximum likelihood estimation. IEEE Transactions on Signal Processing, 54(8), 2943–2956.CrossRefGoogle Scholar
  21. 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
  22. 22.
    Molisch, A. F., et al. (2006). A comprehensive standardized model for ultrawideband propagation channels. IEEE Transactions on Antennas and Propagation, 54, 3151–3166.CrossRefGoogle Scholar
  23. 23.
    Candès, E. J., & Wakin, M. B. (2008). An introduction to compressive sampling. IEEE Signal Processing Magazine, 25, 21–30.CrossRefGoogle Scholar
  24. 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
  25. 25.
    Berger, J. O. (1985). Statistical decision theory and Bayesian analysis (2nd ed.). New York: Springer.CrossRefGoogle Scholar
  26. 26.
    Van Tress, H. L. (1968). Detection, estimation and modulation theory (Part I). New York: Wiley.Google Scholar
  27. 27.
    Baraniuk, R. G. (2007). Compressive sensing. IEEE Signal Processing Magazine, 24(4), 118–121.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Mehmet Özgör
    • 1
  • Serhat Erküçük
    • 2
  • Hakan Ali Çırpan
    • 1
  1. 1.Department of Electronics and Communications Engineeringİstanbul Technical UniversityIstanbulTurkey
  2. 2.Department of Electrical and Electronics EngineeringKadir Has UniversityIstanbulTurkey

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