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Sparse adaptive channel estimation based on mixed controlled \(l_2\) and \(l_p\)-norm error criterion. (English) Zbl 1373.93333
Summary: In this paper, we propose sparse adaptive channel estimation algorithms based on a mixed controlled \(l_2\) and \(l_p\)-norm error criterion and zero attracting theory. In the proposed algorithms, a controlling parameter within the range of \([0,1]\) is adopted to control the mixture of the \(l_2\) and \(l_p\) norms which are exerted on the estimation error. The sparsity-aware characteristic is implemented by an \(l_1\)-norm penalty, a correntropy-induced metric penalty and a log-sum function constraint which are to exploit the in-nature sparseness of the channels. The proposed sparsity-aware algorithms give desired zero attractors in their iterations to speed up the convergence. The derivation of the proposed algorithms is presented in detail. We can find that the previously proposed sparsity-aware algorithms can be regarded as a special case of the proposed sparse adaptive algorithms. Also, the behaviors of the proposed algorithms are well verified over a multi-path wireless communication channel. As a result, our proposed algorithms are superior to the previously reported sparse mixed adaptive filters with respect to both the convergence and steady-state error for handling sparse signals.

MSC:
93E10 Estimation and detection in stochastic control theory
93C40 Adaptive control/observation systems
93E03 Stochastic systems in control theory (general)
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[1] Cotter, S. F.; Rao, B. D., Sparse channel estimation via matching pursuit with application to equalization, IEEE Trans. Commun., 50, 3, 374-377, (2002)
[2] Widrow, B.; Stearns, S. D., Adaptive signal processing, (1985), Prentice Hall New Jersey · Zbl 0593.93063
[3] Haykin, S., Adaptive filter theory, (1991), Prentice Hall Englewood Cliffs, NJ · Zbl 0723.93070
[4] Vaz, C. A.; Thakor, N. V., Adaptive Fourier estimation of time-varying evoked potentials, IEEE Trans. Biomed. Eng., 35, 4, 448-550, (1989)
[5] Diniz, P. S.R., Adaptive filtering algorithms and practical implementation, (2013), Spring · Zbl 1257.93001
[6] Haykin, S.; Widrow, B., Least-mean-square adaptive filters, (2003), Wiley New Jersey, USA
[7] Macchi, O., Adaptive processing: the least mean squares approach with applications in transmission, (1995), Wiley · Zbl 0854.94001
[8] Y. Chen, Y. Gu, A.O. Hero, Sparse LMS for system identification, in: Proceedings of the IEEE International conference on Acoustic Speech and Signal Processing, (ICASSP’09), pp:3125-3128, Taipei, 2009.
[9] Chen, B.; Zhao, S.; Zhu, P., Quantized kernel least mean square algorithm, IEEE Trans. Neural Netw. Learn. Syst., 23, 1, 22-32, (2012)
[10] Sethares, W. A.; Mareels, I. M.Y.; Anderson, B. D.O.; Johnson, C. R.; Bitmead, R. R., Excitation conditions for signed regressor least mean squares adaptation, IEEE Trans. Circ. Syst., 35, 6, 613-624, (1988)
[11] F. Albu, C. Paleologu, J. Benesty, A low complexity proportionate affine projection algorithm for echo cancellation, in: Proceedings of the IEEE 2010 Eighteenth European Signal Processing Conference (2010) 6-10.
[12] Kalluri, S.; Arce, G. R., A general class of nonlinear normalized adaptive filtering algorithms, IEEE Trans. Signal Process., 47, 8, 2262-2272, (1999) · Zbl 1003.93054
[13] Aboulnasr, T.; Mayyas, K., A robust variable step-size LMS-type algorithm: analysis and simulations, IEEE Trans. Signal Process., 45, 3, 631-639, (1995)
[14] Li, Y.; Hamamura, M., Zero-attracting variable-step-size least mean square algorithms for adaptive sparse channel estimation, Int. J. Adapt. Control Signal Process., 29, 9, 1189-1206, (2015) · Zbl 1330.93248
[15] Li, Y.; Li, W.; Yu, W., Sparse adaptive channel estimation based on l_{p}-norm-penalized affine projection algorithm, Int. J. Antennas Propag., 2014, 1-9, (2014)
[16] Walach, E.; Widrow, B., The least mean fourth (LMF) adaptive algorithm and its family, IEEE Trans. Inf. Theory, 30, 2, 275-283, (1984)
[17] Gui, G.; Adachi, F., Sparse least mean fourth algorithm for adaptive channel estimation in low signal-to-noise ratio region, Int. J. Commun. Syst., 27, 11, 3147-3157, (2014)
[18] Y. Li, Y. Wang, T. Jiang, Sparse channel estimation based on a p-norm-like constrained least mean fourth algorithm, in: Proceedings of the Seventh International Conference on Wireless Communications and Signal Processing (WCSP 2015), Nanjing, China, 2015.
[19] Lim, S. J.; Haris, J. G., Combined LMS/F algorithm, Electron. Lett., 33, 6, 467-468, (1997)
[20] Y. Li, Y. Wang, F. Albu, Sparse channel estimation based on a reweighted least-mean mixed-norm adaptive filter algorithm, in: Proceedings of the Twenty-fourth European Signal Processing Conference (EUSIPCO’16). (2016) pp. 2380-2384.
[21] Li, Y.; Wang, Y.; Jiang, T., Sparse least mean mixed-norm adaptive filtering algorithms for sparse channel estimation applications, Int. J. Commun. Syst., 30, 1-14, (2017)
[22] G. Gui, A. Mehbodniya, F. Adachi, Least mean square/fourth algorithm for adaptive sparse channel estimation, in: Proceedings of the 2013 IEEE Twenty-fourth International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), 2013.
[23] Gui, G.; Adachi, F., Sparse least mean fourth algorithm for adaptive channel estimation in low signal-to-noise ratio region, Int. J. Commun. Syst., 27, 3147-3157, (2014)
[24] Chambers, J. A.; Tanrikulu, O.; Constantinides, A. G., Least mean mixed-norm adaptive filtering, Electron. Lett., 30, 19, 1574-1575, (1994)
[25] Tanrikulu, O.; Chambers, J. A., Convergence and steady-state properties of the least-mean mixed-norm (LMMN) adaptive algorithm, IEEE Proceed. Vis. Image Signal Process., 143, 3, 137-142, (1996)
[26] Li, Y.; Wang, Y.; Jiang, T., Norm-adaption penalized least mean square/fourth algorithm for sparse channel estimation, Signal Process., 128, 243-251, (2016)
[27] Zidouri, A., Convergence analysis of a mixed controlled l_{2}-l_{p} adaptive algorithm, J. Adv. Signal Process., 2010, 1, 1-10, (2010) · Zbl 1204.93115
[28] G. Gui, W. Peng, F. Adachi, Improved adaptive sparse channel estimation based on the least mean square algorithm, in: Proceedings of the 2013 IEEE Wireless Communication and Networking Conference. 2013, pp. 3105-3109.
[29] Li, Y.; Li, W.; Yu, W., Sparse adaptive channel estimation based on l_{p}-norm-penalized affine projection algorithm, Int. J. Antennas Propag., 2014, 1-9, (2014)
[30] R. Meng, R.C. De Lamare, V.H. Nascimento, Sparsity-aware affine projection adaptive algorithms for system identification, in: Proceedings of the Sensor Signal Processing for Defence (2011), p. 7.
[31] Y. Li, Y. Wang, Z. Jin, An improved reweighted zero-attracting NLMS algorithm for broadband sparse channel estimation, in: Proceedings of the IEEE International Conference on Electronic Information and Communication Technology, Harbin, China, August 20-22, 2016.
[32] Gui, G.; Peng, W.; Adachi, F., Improved least mean square algorithm with application to adaptive sparse channel estimation, Eurasip J. Wireless Commun. Netw., 2013, 1, 1-18, (2013)
[33] Gollamudi, S.; Nagaraj, S.; Kapoor, S., Set-membership filtering and a set-membership normalized LMS algorithm with an adaptive step size, IEEE Signal Process. Lett., 5, 5, 111-114, (1998)
[34] Li, Y.; Wang, Y.; Jiang, T., Sparse-aware set-membership NLMS algorithms and their application for sparse channel estimation and echo cancellation, AEU - Int. J. Electron. Commun., 70, 7, 895-902, (2016)
[35] Y. Wang, Y. Li, Set-membership NLSM with reweighted l_{1}-norm penalty for sparse system identification, in: Proceedings of the 2016 International Conference on Digital Signal Processing (DSP). 2016.
[36] Mayyas, K.; Aboulnasr, T., Leaky LMS algorithm: MSE analysis for Gaussian data, IEEE Trans. Signal Process., 45, 4, 927-934, (1997)
[37] Ma, W.; Hua, Q.; Gui, G., Maximum correntropy criterion based sparse adaptive filtering algorithms for robust channel estimation under non-Gaussian environments, J. Frankl. Inst., 352, 7, 2708-2727, (2015) · Zbl 1395.93544
[38] Li, Y.; Wang, Y., Sparse SM-NLMS algorithm based on correntyopy criterion, Electron. Lett., 52, 17, 1461-1463, (2016)
[39] He, R.; Zheng, W. S.; Hu, B. G., Maximum correntropy criterion for robust face recognition, IEEE Trans. Pattern Anal. Mach. Intell., 33, 8, 1561-1576, (2011)
[40] Candes, E. J.; Wakin, M. B.; Boyd, S. P., Enhancing sparsity by reweighted l_{1} minimization, J. Fourier Anal. Appl., 14, 5, 877-905, (2007) · Zbl 1176.94014
[41] Donoho, D. L., Compressed sensing, IEEE Trans. Inf. Theory., 52, 4, 1289-1306, (2006) · Zbl 1288.94016
[42] Mazo, J. E., On the independence theory of equalizer convergence, Bell Syst. Tech. J., 58, 5, 963-993, (1979) · Zbl 0405.94009
[43] Price, R., A useful theorem for non-linear devices having Gaussian inputs, IEEE Trans. Inf. Theory, 4, 69-72, (1958) · Zbl 0108.30605
[44] Sayed, A. H., Fundamentals of adaptive filtering, (2003), Wiley-Interscience New York, NY, USA
[45] Tempo, R.; Calafiore, G.; Fabbene, F., Monte Carlo methods, Randomized Algorithms for Analysis and Control of Uncertain Systems, Communications and Control Engineering, 91-106, (2005), Springer London, United Kingdom
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