Research On Fractional Order Blind Equalization Algorithm In Impulsive Noise Environment

With the continuous development of wireless communication technology and the substantial increase of user communication services,the communication system is developing towards high-speed,high-precision and high-frequency spectrum utilization.However,the inter symbol interference(ISI)caused by the multipath effect of the transmission channel affects the transmission quality of the signal.As one of the important methods to reduce ISI,channel equalization technology is an indispensable research content in wireless communication system.Channel equalization technology is mainly divided into two categories.One is the equalization method using auxiliary data for training,but this kind of method will occupy large spectrum resources;The other is the blind equalization method without auxiliary data training.This method can recover the transmitted signal only by using the statistical information of the signal.Among them,the most widely used is the constant modulus blind equalization algorithm(CMA).Blind equalization algorithm has good equalization performance in Gaussian noise environment,but when the environmental noise is non Gaussian noise with impulse characteristics,such as atmospheric noise and underwater acoustic noise,the equalization performance of blind equalization algorithm is seriously degraded or even invalid.Therefore,the research on blind equalization technology in impulse noise environment has very important theoretical value and application value.This paper mainly studies the channel blind equalization algorithm under the condition of impulse noise.The main contents are as follows:Firstly,Aiming at the performance degradation of constant modulus algorithm based on maximum correlation criterion(MCC＿CMA)in strong impulse noise environment,This paper proposes a constant modulus blind equalization algorithm based on fractional maximum correlation entropy criterion(FOMCC＿CMA).The algorithm introduces fractional low-order statistics and replaces the second-order statistics in the original cost function with fractional low-order statistics,which improves the ability of the algorithm to suppress impulse noise and makes it more robust.In addition,the fractional step method is used to optimize the weight coefficient of the equalizer to solve the problem that there is no integer derivative of the fractional correlation entropy cost function under some clear conditions,so as to improve the stability of the algorithm.Then,taking the minimum mean square deviation as a mathematical tool,the step size range to ensure the stable convergence of the algorithm is given.The simulation results show that FOMCC＿CMA not only has faster convergence speed,lower residual ISI and lower bit error rate under weak impulse noise,but also has more stable convergence and better robustness under strong impulse noise.Second,When CMA processes multi-mode signal,the phase rotation of equalizer output signal will occur,so additional phase compensation circuit needs to be added for correction,which will improve the complexity of equalization system.In order to solve this problem,this paper proposes a multimode blind equalization algorithm based on fractional maximum correlation entropy criterion(FOMCC＿MMA).Based on the idea of multimode algorithm,the fractional correlation entropy cost function is divided into in-phase component and orthogonal component,which can suppress the strong impulse noise and complete the phase correction at the same time.In addition,by analyzing the stability of the algorithm,the convergence range of step size is given.The simulation results show that FOMCC＿MMA can realize blind equalization and carrier phase recovery at the same time,which is better than FOMCC＿CMA has better pulse suppression ability.