Abstract
Alpha stable distribution is better for modeling impulsive noises than Gaussian distribution in wireless communication system. This class of process has no close form of probability density function and finite second order moments. In general, Wiener filter theory is not meaningful in α SG environments because the expectations may be unbounded. We proposed a new adaptive recursive least p-norm State space multiuser detection algorithm based on least p-norm of innovation process with infinite variances. The simulation experiments show that the proposed new algorithm is more robust than the conventional state space multiuser detection algorithm.
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References
C.L. Nikias and M. shao, Signal Processing with Alpha-Stable Distributions and Applications, New York John Wiley and Sons Inc., 1995.
M. shao and C.L. Nikias, “Signal Processing with Fractional Lower Order Moments Stable Processes and Their Applications”, Proceedings of IEEE, Vol. 81, No. 7, pp. 986–1010, 1993.
G. Samorodnitsky and M.S. Taqqu, Stable Non-Gaussian Random Process Stochastic Models with Infinite Variance, New York Chapman and Hall, 1994
J. Ilow, D. Hatzinakos, Anastasios, and N. Venetsanopoulos, “Performance of FH SS Radio Networks with Interference Modeled as A Mixture of Gaussian and Alpha-Stable Noise”, IEEE Trans. On Communications, Vol. 46, No. 4, April, 1998
M. Pourahmadi, “On Minimality and Interpolation of Harmonizable Stable Processes”, SIAM J. Appl. Math., Vol. 44, No. 5, October. 1984.
B.W. Stuck, “Minimum Error Dispersion Linear Filtering of Scalar Symmetric Stable Processes”, IEEE Trans. Automat. Contr., Vol. AC–23, pp. 507–509, June 1978.
D.B. Cline and P.J. Brockwell, “Linear Prediction of Arma Processes with Infinite Variance”, Stoch. Process. Applicat., Vol. 19, pp. 281–296, 1985.
R. Yarlagadda, J. Schroeder, and J. Hershey, “Lp Normed Minimization with Applications to Linear Predictive Modeling for Sinusoidal Frequency Estimation”, Signal Process., Vol. 24, No. 2, pp. 193–216, 1991.
H.-Z. An and Z.-G. Chen, “On Convergence of LAD Estimates in Autoregression with Infinite Variance”, J. Multivariate Anal., Vol. 12, pp. 335–345, 1982.
E. Deno'el and J.P. Solvay, “Linear Prediction of Speech with A Least Absolute Error Criterion”, IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-33, pp. 1397–1403, 1985.
S. Gross and W.L. Steiger, “Least Absolute Deviation Estimates in Autoregression with Infinite Variance”, J. Appl. Prob., Vol. 16, pp. 104–116, 1979.
J. Schroeder and R. Yarlagadda, “Linear Predictive Spectral Estimation Via the L1 Norm”, Signal Process., Vol. 17, No. 1, pp. 19–29, 1989.
T. Kailath, “An Innovations Approach to Least-Squares Estimation Part I. Linear Filtering in Additive White Noise”, IEEE Trans. on Autom. Contr., Vol. 13, pp. 646–655, 1968
S.S. Haykin, “Adaptive Filter Theory”, 3rd ed. Englewood Cliffs, N.J. Prentice-Hall, 1996.
Ercan E. Kuruoglu, Peter J.W. Rayner, and William J. Fitzgerald, “Least Lp-Norm Estimation of Autoregressive Model Coefficients of Symmetric α-Stable Processes”, IEEE Signal Processing Letters, Vol. 4, No. 7, 1997.
J.F. Weng and S.H. Leung, “Adaptive Nonlinear RLS Algorithm for Robust Filtering in Impulse Noise”, in Proc. IEEE Int. Symp. Circuits Syst., Vol. 4, pp. 2337–2340, 1997.
S. Verdu, Multiuser Detection, Cambridge, U.K. Cambridge Univ. Press, 1998.
D. Middleton, “Non-Gaussian Noise Models in Signal Processing for Telecommunications New Methods and Results for Class A and Class B Noise Models”, IEEE Trans. Inform. Theory, Vol. 45, pp. 1129–1149, October. 1999.
H.V. Poor and M. Tanda, “Multiuser Detection in Impulsive Channels”, Ann. Telecommun., Vol. 54, pp. 392–400, 1999.
T.C. Chuah, B.S. Sharif, and O.R. Hinton, “Robust Adaptive Spread-Spectrum Receiver with Neural Net Preprocessing in Non-Gaussian Noise”, IEEE Trans. on Neural Networks, Vol. 12, No. 3, 2001
J.G. Gonzalez, “Robust Techniques for Wireless Communications in Non-Gaussian Environments”, Ph.D. Dissertation, Dept. Elect. Comput. Eng., Univ. Delaware, Newark, DE, Dec. 1997.
T.C. Chuah; B.S. Sharif, and Hinton O.R., Robust, “CDMA Multiuser Detection Using A Neural-Network Approach, Neural Networks”, IEEE Transactions on, Vol. 13, Issu. 6, No. 2002, pp 1532–1539.
S. Kapoor, S. Gollamudi, S. Nagaraj, and Y.F. Huang, “Adaptive multiuser Detection and Beamforming for Interference Suppression in CDMA Mobile Radio Systems”, IEEE Trans. Veh. Technol., Vol. 48, pp. 1341–1355, 1999.
T.C. Chuah, B.S. Sharif, and O.R. Hinton, “Nonlinear Decorrelator for Multiuser Detection in Non-Gaussian Impulsive Environments”, Electron. Lett., Vol. 36, No. 10, pp. 920–922, May 2000.
R. Brcich, A. Zoubir, “Estimation and Detection in A Mixture of Symmetric Alpha Stable and Gaussian Interference, Higher-Order Statistics”, Proceedings of the IEEE Signal Processing Workshop on, Vol. 14-16, pp. 219–223, June 1999.
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Daifeng Zha was born in 1971 and received the B.S. degree in electrical engineering from Dalian University of Technology, Dalian, China, in 1995. He was a research engineer at ChineseHelicopter Research and Development Institute, Jingdezhen, China, from 1995 through 2000. He received the Ph.D degree in Dalian University of Technology in 2005. He is currently an associate professor in College of Electronic Engineering from Jiujiang University. His research interests include non-gaussian signal processing, array signal processing, underwater signal processing.
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Zha, D. Robust Multiuser Detection Method Based on Least p-Norm State Space Criterion. Wireless Pers Commun 40, 191–204 (2007). https://doi.org/10.1007/s11277-006-9109-7
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DOI: https://doi.org/10.1007/s11277-006-9109-7