Study On The Blind Equalization Algorithm Based On Support Vector Regression

Bussgang's blind equalization algorithm is the most commonly used blind equalization algorithm because of its simple principle,easy implementation,good robustness and applicability to different systems.However,due to its non-ideal finite length filter,the cost function is non-convex which causes the coefficients of the solution are local optimal and further leads to false convergence.In addition,the Bussgang algorithm requires a large number of symbols to convergence to steady state with the appropriate steps,and the convergence rate is slow.Therefore,The global optimization of Support Vector Regression(SVR)is proposed by some scholars to solve the false convergence caused by Bussgang's non-convex cost function,while achieving rapid equalization of a small packet by the use of excellent small sample learning ability of SVR.The classical support vector regression(SVR)method uses the iterative re-weighted quadratic programming(IRWQP)method to determine the equalizer coefficients,which is not suitable for practical application because of the high computational complexity.In recent years,a new support vector regression algorithm based on iterative weighted least square(IRWLS)is proposed.This algorithm reduces the computational complexity and shortens the computation time.The Godard cost function or Sato cost function are used as the error function in the cost function of traditional SVR blind equalization algorithm based on IRWLS.In this paper,we firstly take the MMA cost function into the IRWLS based SVR blind equalization algorithm as error function,and propose a multi-mode blind equalization algorithm which is named SVR-MMA based on SVR framework.This algorithm corrects the phase rotation problem of SVR-CMA blind equalization algorithm,and more suitable for blind equalization of the multi-mode signal.In recent years,a new blind equalization algorithm named probability density function(PDF)blind equalization based on information theory standard and estimating transmission data has been proposed.This algorithm aims to match the probability density of the equalized data with the probability density of the known constellation,which can achieve faster convergence than the classic constant modulus algorithm(CMA),the classic algorithm of the Bussgang's algorithm and better performance than the CMA algorithm in multi-mode situation.In this paper,SVR-PDF blind equalization algorithm via the PDF error function is proposed firstly and compared with the constant modulus algorithm(CMA),the SQD algorithm and the SVR-CMA blind equalization algorithm.Simulation results show that the performance of SVR-PDF blind equalization is better than the CMA algorithm and the SQD algorithm,and slightly better than SVR-CMA blind equalization algorithms from the viewpoint of intersymbol interference(ISI).The loss function of the SVR can have a variety of different forms.There are different equalization results with different forms of the loss functions.The ?-insensitive loss function is often used in the previous SVR blind equalization algorithms.This article firstly introduce the robust loss function(Huber loss function)and the ?-Huber loss function into the SVR blind equalization algorithm and compare them with the SVR blind equalization algorithm based on the traditional ?-insensitive loss function.The simulation results show that the SVR blind equalization using ?-Huber loss function has some advantages compared with the SVR blind equalization using other two loss function in terms of accuracy of ISI.