基于优化理论的盲均衡技术研究

发布时间：2018-03-11 04:10

本文选题：盲均衡　切入点：优化理论　出处：《解放军信息工程大学》2014年博士论文　论文类型：学位论文

【摘要】：近年来,工业化的快速发展使得开放的电磁环境更加复杂.,在无线通信中由信道特性不理想所引起的码间干扰更加严重,对信号的接收与恢复带来了新的挑战,也对消除码间干扰的盲均衡器的性能提出了更高要求。.基于此,本课题以提高盲均衡器的性能为目的,利用现代优化方法,如线性规划,半正定规划,向量范数等理论,研究了提高盲均衡器收敛速度的方法,设计了更能反映信号统计特征的代价函数以降低稳态误差,构造了凸代价函数以保证均衡器收敛性。主要工作有以下几方面：1、研究提高盲均衡器收敛速度的方法。研究改进了基于随机梯度下降法寻找代价函数最优值的方式,针对多模盲均衡算法给出了一种新的最速下降优化实现方法,新方法通过将信道输出统计量的估计与均衡器迭代相分离,使得均衡器在每次迭代后不需要对其输出统计量重新计算,避免了对信道输出数据循环重用所导致的较长处理时延,适合并行化实时处理。新的迭代方法具有更快的收敛速度和更小的稳态误差,只要总的处理时间不超过数据缓存时间,就可以实现流水线式的实时处理,尤其适合数据包传输场合。2、针对Bussgang类盲均衡算法大都基于非凸代价函数,对其优化往往会陷入局部极值点因而不能充分消除码间干扰的问题。本文给出了一种针对QAM信号盲均衡的凸代价函数,并将凸优化求解问题转化为一种可快速计算的线性规划,新的代价函数在恒定约束下,具有较少的未知变量和约束方程,复杂度较低。为克服恒定约束条件下,对某些信道的均衡可能存在收敛速度慢,甚至不收敛的问题,本文又给出一种基于自适应约束凸代价函数的盲均衡算法,该算法只需要很少的信号样点,经过多次迭代即可达到更好的收敛性能,可适用于短时信号的盲均衡。相比于传统的MMA算法,新方法采用了凸代价函数,能够保证均衡器收敛至理想值。3、针对Bussgang类算法代价函数对信号所包含信息未充分利用,致使稳态误差大的问题,本文研究并设计了更能反映信号统计特征的代价函数,以降低稳态误差,依据向量范数性质,结合将约束方程转换为无约束方程的方法,给出了一种新的无约束盲均衡准则,证明了无噪声情况下,代价函数的局部最优解即对应理想均衡条件,且能够实现发送信号幅值的恢复。可采用批数据处理和在线自适应迭代两种方法更新均衡器系数,无需自动增益控制,算法实现简单,同时稳态误差更小。4、针对传统的峰度最大化盲均衡算法不能纠正均衡输出的相位偏移,以及功率最大化算法在低信噪比下性能下降较大的问题。本文利用向量范数性质,基于均衡器输出峰度最大化的思想,’给出了一种对加性高斯噪声更加鲁棒的方形QAM信号盲均衡与载波相位恢复准则,证明了无噪声情况下,代价函数的局部最优解即对应理想均衡条件,并采用批数据处理的方法求均衡器权值。相比于传统的Donoho算法、CMA、SW、SFA等峰度最大化算法,新算法能够纠正均衡输出的相位偏移,相比功率最大化的QP-FSE算法以及自适应的迭代求解算法βMMA,新算法受加性高斯噪声的影响更小。5、针对盲均衡中对非凸代价函数的优化存在收敛速度慢,对初始化条件和步长敏感,且容易误收敛的问题,本文采用半正定规划方法对传统的采用随机梯度下降法实现的盲均衡算法进行改进,通过对MSOSA算法代价函数的修正,给出了一种新的基于半正定规划的求解算法,并将其松弛为凸规划,相比采用随机梯度下降法的求解方法,新算法需要的数据样点更少,且收敛后的稳态误差更小,该方法尤其适合于数据量获取较少的场合。
[Abstract]:In recent years, the rapid development of industrialization makes the electromagnetic environment open more complicated. In wireless communication, the non ideal channel characteristics caused by intersymbol interference is more serious, the signal is received and the recovery has brought new challenges, but also put forward higher requirements. Based on the performance of the blind equalizer to eliminate intersymbol interference in this paper, in order to improve the performance of blind equalizer for the purpose of using modern optimization methods, such as linear programming, semidefinite programming, vector norm theory, research methods to improve the convergence rate of blind equalizer, a cost function is designed to better reflect the statistical characteristics of the signal in order to reduce the steady-state error, the convex cost function to construct ensure the equalizer convergence. The main works are as follows: 1. Research on the method of improving the convergence rate of blind equalizer. The improved cost function for the optimal value of the stochastic gradient descent method based on the way, According to the multi modulus blind equalization algorithm is given a new steepest descent optimization method, a new method by the iterative channel estimation and equalizer output statistics of phase separation, the equalizer after each iteration does not need to recalculate the output statistics, avoid long processing delay caused by the channel output cycle of data reuse, suitable for parallel real-time processing. The steady-state error of new iterative method has faster convergence speed and smaller, as long as the total processing time is less than the data cache time, can achieve real-time processing pipeline, especially suitable for packet transmission occasions.2, for the Bussgang blind equalization algorithms are based on non convex cost function for optimization tend to fall into local extremum and cannot fully eliminate the ISI problem. This paper presents a blind equalization for QAM signals with convex cost function, And the convex optimization problem is transformed into a fast calculation of linear programming, a new cost function under constant constraints, variables and constraint equations with fewer and lower complexity. In order to overcome the constant constraint conditions of some channel equilibrium may exist slow convergence, even no convergence problem in this paper, and presents an adaptive blind equalization algorithm based on constrained convex cost function, the algorithm requires only a few signals, after several iterations to achieve better convergence performance, blind equalization can be applied to the short-time signal. Compared with the traditional MMA algorithm, a new method using a convex cost function, can guarantee the equalizer converge to the ideal value of.3, according to the Bussgang algorithm cost function does not make full use of the information contained in the signal, resulting in the problem of steady-state error, this paper study and design to better reflect the statistical characteristics of the signal The cost function, in order to reduce the steady-state error, based on the vector norm properties, combining constraint equations into unconstrained equations, a new unconstrained blind equalization criterion is given, that the absence of noise, the local optimal solution of the cost function corresponding to the ideal equilibrium conditions, which can realize the amplitude of the transmitted signal the number of recovery. Data processing and online adaptive iterative methods to update two equalizer coefficients, without the automatic gain control algorithm is simple, and smaller steady-state error.4, the phase shift of traditional kurtosis maximization blind equalization algorithm can not correct the equilibrium output, and the maximum power algorithm in the low SNR performance decline the larger problem. Using the properties of vector norm, the equalizer output kurtosis maximization based on the idea of "gives an additive Gauss noise robust square QAM signal Blind equalization and carrier phase recovery, proved the absence of noise, the local optimal solution of the cost function corresponding to the ideal equilibrium condition, and the method of batch data processing for the equalizer weights. Compared with the traditional Donoho algorithm, CMA, SW, SFA, kurtosis maximization algorithm, the new algorithm can correct the phase equilibrium output the maximum power compared to the QP-FSE algorithm and adaptive iterative algorithm of beta MMA, the new algorithm by smaller.5 effects of additive Gauss noise, aiming at the optimization of non convex cost function blind equalization in slow convergence for the initial condition and the step of sensitive and easy convergence problem, this paper adopts semi definite the planning of the traditional method of using stochastic gradient descent method to achieve blind equalization algorithm is improved by modifying the cost function of MSOSA algorithm, a new positive semi definite programming requirements are given based on The algorithm is relaxed to convex programming. Compared with the method of stochastic gradient descent algorithm, the new algorithm needs less data points and smaller steady-state error after convergence. This method is especially suitable for less data acquisition.

【学位授予单位】：解放军信息工程大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN911.5

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