Fast Sparse Multipath Channel Estimation with Smooth L0 Algorithm for Broadband Wireless Communication Systems

Guan Gui, Qun Wan, Ni Na Wang, Cong Yu Huang

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DOI: 10.4236/cn.2011.31001                

Abstract

Broadband wireless channels are often time dispersive and become strongly frequency selective in delay spread domain. Commonly, these channels are composed of a few dominant coefficients and a large part of coefficients are approximately zero or under noise floor. To exploit sparsity of multi-path channels (MPCs), there are various methods have been proposed. They are, namely, greedy algorithms, iterative algorithms, and convex program. The former two algorithms are easy to be implemented but not stable; on the other hand, the last method is stable but difficult to be implemented as practical channel estimation problems be-cause of computational complexity. In this paper, we introduce a novel channel estimation strategy using smooth L0 (SL0) algorithm which combines stable and low complexity. Computer simulations confirm the effectiveness of the introduced algorithm. We also give various simulations to verify the sensing training signal method.

Keywords

Smooth L0 Algorithm, Restricted Isometry Property, Sparse Channel Estimation, Compressed Sensing

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Z. Yan, M. Herdin, A. M. Sayeed and E. Bonek, “Experimental Study of MIMO Channel Statistics and Capacity via the Virtual Channel Representation,” February 2007. http://dune.ece.wisc.edu/pdfs/zhoumeas.pdf.
[2]	J. Kivinen, P. Suvikunnas, L. Vuokko and P. Vainikainen, “Experimental Investigations of MIMO Propagation Channels,” Antennas and Propagation Society Interna- tional Symposium, IEEE, 2002.
[3]	W. F. Schreiber, “Advanced Television Systems for Terres-Trial Broadcasting: Some Problems and Some Proposed Solutions,” IEEE Proceedings, Vol. 83, No. 6, June 1995, pp. 958-981. doi:10.1109/5.387095
[4]	R. Steele, “Mobile Radio Communications,” IEEE Press, New York, 1992.
[5]	M. Kocic, D. Brady and M. Stojanovic, “Sparse Equalization for Real Time Digital Underwater Acoustic Communications,” OCEANS’95 MTS/IEEE Challenges of Our Changing Global Environment Conference Proceedings, San Diego, Vol. 3, October 1995, pp. 1417-1422. doi:10. 1109/OCEANS.1995.528671
[6]	C. Carbonelli, S. Vedantam and U. Mitra, “Sparse Channel Estimation with Zero Tap Detection,” IEEE Transactions on Wireless Communications, Vol. 6, No. 5, May 2007, pp. 1743-1753. doi:10.1109/TWC.2007.360376
[7]	Z. G. Karabulut and A. Yongacoglu, “Sparse Channel Estimation Using Orthogonal Matching Pursuit Algorithm,” 2004 IEEE 60th Vehicular Technology Conference, Vol. 60, No. 6, 2004, pp. 3880-3884. doi:10.1109/ VETECF.2004.1404804
[8]	J. A. Tropp and A. C. Gilbert, “Signal Recovery from Random Measurements via Orthogonal Matching Pursuit,” IEEE Transaction on Information Theory, Vol. 53, No. 12, 2007, pp. 4655-4666. doi:10.1109/TIT.2007.909 108
[9]	U. W. Bajwa, J. Haupt, G. Raz and R. Nowak, “Compressed Channel Sensing,” 42nd Annual Conference on Information Sciences and Systems, CISS’08, Princeton, 19-21March 2008. doi:10.1109/CISS.2008.4558485
[10]	D. Needell and J. A. Tropp, “CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples,” Applied and Computational Harmonic Analysis, Vol. 26, No. 3, 2008, pp. 301-321. doi:10.1016/j.acha.2008.07.002
[11]	G. Gui, Q. Wan, W. Peng and F. Adachi, “Sparse Multipath Channel Estimation Using Compressive Sampling Matching Pursuit Algorithm,” IEEE VTS APWCS 2010, 19-22 May 2010.
[12]	E. J. Candès, “The Restricted Isometry Property and Its Implications for Compressed Sensing,” Compte Rendus de l’Academie des Sciences, Vol. 346, No. 9-10, May 2008, pp. 589-592. doi:10.1016/j.crma.2008.03.014
[13]	E. Candès and T. Tao, “The Dantzig Selector: Statistical Estimation When p is Much Larger than n,” Annals of Statistics, Vol. 35, No. 6, 2007, pp. 2313-2351. doi:10. 1214/009053607000000532
[14]	N. H. Nguyen and T. D. Tran, “The Stability of Regularized Orthogonal Matching Pursuit Algorithm,” http:// www.dsp.ece.rice.edu/cs/Stability_of_ROMP.pdf.
[15]	H. Mohimani, M. Babaie-Zadeh and C. Jutten, “Complex-Valued Sparse Representation Based on Smoothed L0 Norm,” Proceedings of ICASSP2008, Las Vegas, April 2008, pp. 3881-3884.
[16]	E. Candès, J. Romberg and T. Tao, “Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information,” IEEE Transaction on Information Theory, Vol. 52, No. 2, February 2006, pp. 489-509. doi:10.1109/TIT.2005.862083
[17]	D. L. Donoho, “Compressed Sensing,” IEEE Transaction on Information Theory, Vol. 52, No. 4, April 2006, pp. 1289-1306. doi:10.1109/TIT.2006.871582
[18]	E. J. Candès, “The Restricted Isometry Property and Its Implications for Compressed Sensing,” Comptes Rendus Mathematique, Vol. 346, No. 9-10, May 2008, pp. 589- 592. doi:10.1016/j.crma.2008.03.014
[19]	D. Needell and J. A. Tropp, “CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples,” Applied and Computational Harmonic Analysis, Vol. 26, No. 3, May 2009, pp. 301-321. doi:10.1016/j.acha.2008.07. 002