Optimal Design of the Gaussian-Tailed Zero Memory Nonlinearity Function for Impulsive Noise Suppression
ZHANG Yang-yong1, LUO Zhong-tao2, NIE Ya-qin1, ZHANG Gang2
1. Laboratory of Low-frequency Electro-magnetic Communication Technology with the 722 Research Institute, CSIC, Wuhan, Hubei 430019, China;
2. School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
Abstract：Impulsive noise can greatly degrade the performance of long wave communications.This paper proposes the optimal design of the Gaussian-tailed zero memory nonlinearity (GZMNL) function to suppress impulsive noise.The GZMNL function which was proposed for the symmetric α-stable (SαS) noise is not robust in applications,because of the lack of adaptive parameters.This paper proposes to design the GZMNL parameters adaptively to control the linear range and the tails,so that the GZMNL can be effective for various noise distributions.In the GZMNL design,the efficiency is employed as the objective function which is maximized over the GZMNL parameters.To solve this optimization problem,we develop a derivative-free optimization algorithm which searches the maximum efficacy adaptively.Considering practical applications,we propose two fast algorithms for the GZMNL design in the SαS noise,as well as a robust method for the GZMNL design in unknown noise distributions.Simulation results based on the SαS noise and real atmospheric noise show that the GZMNL design achieves almost the best nonlinearity in known noise distributions.The GZMNL design is effective and robust for unknown noise distributions.
[1] KAY S M.Fundamentals of Statistical Signal Processing,Volume II:Detection Theory[M].Englewood Cliffs,NJ,US:Prentice-Hall,1993.626-645.
[2] OH H,NAM H.Design and performance analysis of nonlinearity preprocessors in an impulsive noise environment[J].IEEE Transactions on Vehicular Technology,2017,66(1):364-376.
[3] NIKIAS C L,SHAO M.Signal Processing with Alpha Stable Distribution and Applications[M].New York:Wiley,1995.67-73.
[4] 罗忠涛,卢鹏,等.大气噪声幅度分布与抑制处理分析[J].系统工程与电子技术,2018,40(7):157-162. LUO Zhong-tao,LU Peng,et al.Analysis on amplitude distribution and suppression techniques of atmospheric noise[J].Systems Engineering and Electronics,2018,40(7):157-162.(in Chinese)
[5] LUO Zhong-tao,LU Peng,et al.Locally Optimal detector design in impulsive noise with unknown distribution[J].EURASIP Journal on Advances in Signal Processing,2018,2018(1):34.
[6] 张杨勇,刘勇.低频段大气噪声及处理技术[J].舰船科学技术,2008,30(S1):85-88. ZHANG Yang-yong,LIU Yong.Atmospheric-noise at low frequency and its processing technique[J].Ship Science and Technology,2008,30(S1):85-88.(in Chinese)
[7] ZHANG Guo-yong,WANG Jun,et al.Nonlinear processing for correlation detection in symmetric alpha-stable noise[J],IEEE Signal Processing Letters,2018,25(1):120-124.
[8] LI Xu-tao,SUN Jun,et al.Near-optimal detection with constant false alarm ratio in varying impulsive interference[J].IET Signal Processing,2013,7(9):824-832.
[9] SWAMI A,SADLER B M.On some detection and estimation problems in heavy-tailed noise[J].Signal Processing,2002,82(12):1829-1846.
[10] MIDDLETON D.Procedures for determining the parameters of the first-order canonical models of class A and class B electromagnetic interference[J].IEEE Transactions on Electromagnetic Compatibility,2007,21(3):190-208.
[11] VASTOLA K.Threshold detection in narrow-band non-Gaussian noise[J].IEEE Transactions on Communications,1984,32(2):134-139.
[12] LI Xu-tao,SUN Jun,et al.Bi-parameter CGM model for approximation of α-stable PDF[J].Electronics Letters,2008,44(18):1096-1097.
[13] CHONG E K D and ZAK S H.An Introduction to Optimization[M].4th Edition.Hoboken,New Jersey:John Wiley and Sons,2014.105-108.
[14] NOCEDAL J,WRIGHT S J.Numerical Optimization[M].NY,US:Springer-Verlag New York,Inc,1999.34-62.
[15] 郭莹,邱天爽.基于分数低阶统计量的盲多用户检测算法[J].电子学报,2007,35(9):1670-1674. GUO Ying,QIU Tian-shuang.Blind multiuser detector based on FLOS in impulse noise environment[J].Acta Electronica Sinica,2007,35(9):1670-1674.(in Chinese)
[16] SAMIUDDIN M,EL-SAYYAD G M.On nonparametric kernel density estimates[J].Biometrika,1990,77(4):865-874.
[17] SILVERMAN B W.Density Estimation for Statistics and Data Analysis[M].London,UK:Chapman and Hall,1986.45-48.
[18] 邱天爽,张旭秀,等.统计信号处理:非高斯信号处理及其应用[M].北京:中国水利水电出版社,2004.165-166. QIU Tian-shuang,ZHANG Xu-xiu,et al.Statistical Signal Processing:Non-Gaussian Signal Processing and Its Application[M].Beijing:China Water and Power Press,2004.165-166.(in Chinese)
2019, Vol. 47 
