【作者】 王洋；

【导师】 杨凌；

【作者基本信息】 兰州大学 ， 信息与通信工程·通信与信息系统， 2017， 硕士

【摘要】 Bussgang类盲均衡算法因其原理简单、易于实现、稳健性好、对于不同系统的适用性强等优点成为目前最常被采用的一类盲均衡算法。但由于其非理想的有限长滤波器使得代价函数是非凸的,因此会导致求解的系数为局部最优解,进一步产生误收敛现象。此外,Bussgang类算法在适当步长收敛到稳态所需的符号数很大,收敛速度慢。为此,有学者提出利用支持向量回归机(Support Vector Regression,SVR)的全局最优化特点解决Bussgang类算法非凸代价函数造成的误收敛问题,并利用SVR优秀的小样本学习能力实现小数据包下的快速均衡。经典的支持向量回归机采用迭代重加权二次规划(Iterative Re-Weighted Quadratic Programming,IRWQP)方法确定均衡器系数,使得计算复杂度过高而不适于实际应用。于是近年来提出了基于迭代重加权最小二乘(Iterative Re-Weighted Least Square,IRWLS)的支持向量回归机算法,此算法减小了计算复杂度,缩短了计算时间。传统的基于IRWLS的SVR盲均衡算法的代价函数中的误差函数一般采用Godard代价函数或Sato代价函数。本文将多模算法(Multi Modulus Algorithm,MMA)的代价函数带入到基于IRWLS的SVR盲均衡算法中作为误差函数,提出了基于SVR框架的多模盲均衡算法—SVR-MMA,此算法修正了SVR-CMA的相位旋转问题,更适合多模信号的盲均衡。近年来,一种新的基于信息理论标准和估计传输数据的概率密度函数(Probability Density Function,PDF)的盲均衡算法被提出。这种算法旨在使均衡后数据的概率密度与已知星座图的概率密度相匹配,它比经典的常模算法(Constant Modulus Algorithm,CMA)收敛快,同时在多模情况下取得比CMA更少的剩余残差。本文首次提出以PDF代价函数为误差函数的SVR-PDF盲均衡算法,并分别与CMA、SQD以及SVR-CMA算法作对比。仿真实验表明,从码间干扰(ISI)的角度来看,SVR-PDF盲均衡算法的性能明显优于CMA以及SQD算法,并略优于SVR-CMA。支持向量回归机的损失函数可以有多种不同形式,使用不同的损失函数得到的均衡效果不同。在以往的SVR盲均衡算法中,常常采用ε-不敏感损失函数。本文首次将鲁棒损失函数(Huber损失函数)和ε-Huber损失函数引入到SVR盲均衡算法中,并将其与传统的基于ε-不敏感损失函数的盲均衡算法进行比较。仿真结果表明,基于ε-Huber损失函数的SVR盲均衡器相比基于其余两种损失函数的盲均衡器而言,在ISI精度方面具有一定的优势。更多还原

【Abstract】 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 ε-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 ε-Huber loss function into the SVR blind equalization algorithm and compare them with the SVR blind equalization algorithm based on the traditional ε-insensitive loss function.The simulation results show that the SVR blind equalization using ε-Huber loss function has some advantages compared with the SVR blind equalization using other two loss function in terms of accuracy of ISI.更多还原