基于不同误差函数的判决反馈盲均衡算法研究
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摘要
由于盲均衡算法不需要训练序列,可有效去除码间干扰(ISI)。在这些算法中,常数模算法(CMA)结构简单,但收敛速度慢、收敛后的均方误差大,尤其对于频响起伏较大的信道,CMA的均衡性能不太好。而判决反馈均衡器(DFE)由于反馈滤波器部件具有非线性特性,因而能更适应不同类型的信道。但是,影响均衡的效果除了与所采用均衡器的结构有关外,还与权系数迭代公式中的误差项有关,误差项不同,算法的均衡性能也不同。
本文在分析CMA性能以及误差函数特性的基础上,研究了基于不同误差函数的判决反馈盲均衡算法,并用频响起伏较大的信道进行了仿真。研究内容主要包括以下几个方面:
1.研究了基于不同误差函数的常模盲均衡算法
从随机梯度下降法得知,梯度范数越大则收敛越快,而均方误差愈大,反之亦然。因此,定义了一种变系数加权的误差函数,以控制梯度范数的大小。该误差函数曲线特性可随作者所定义的可变因子的取值不同而发生改变,提出了基于变系数加权误差函数的CMA(VCMA)。
2.研究了基于不同误差函数的判决反馈盲均衡算法
针对频响起伏较大的信道,常模判决反馈盲均衡算法(CMDFE)能够很好地克服CMA的缺点,既加快了收敛速度,又减小了均方误差。另外,为了进一步改善CMDFE的均衡性能,把上述定义的变系数加权误差函数应用到此种均衡系统中,提出了基于变系数加权误差函数的DFE(VCMDFE)。
3.研究了基于不同误差函数的判决反馈双模式盲均衡算法
为了充分利用Bussgang类算法中各独立算法的优点,以及克服各算法所存在的缺陷,并结合改进的误差函数,提出了3类判决反馈双模式盲均衡算法:
1)将VCMDFE与判决引导(DD)算法相结合,提出了基于变系数加权误差函数的判决反馈双模式盲均衡算法(VCMDFE-DD)。
2)利用CMDFE算法较强的收敛能力,在迭代起始阶段一直采用CMDFE均衡,当均衡一段时间后,再根据判决圆环进行两种算法之间的切换,提出了基于引入迭代阈值的常模判决反馈双模式盲均衡算法(LCMDFE-DD)。
3)VCMDFE算法的收敛能力较CMDFE强,同样应用上述迭代阈值的思想,提出了基于引入迭代阈值的VCMDFE-DD的判决反馈盲均衡算法(LVCMDFE-DD)。
4.设计了不同结构以及采用不同算法的盲均衡器模块
利用Simulink库中的一些模块,设计了基于不同结构和不同算法的均衡器:
1)利用库中采用CMA的线性均衡器(LE)模块,设计了基于几种常用误差函数和作者改进的误差函数的LE;
2)利用库中的判决器模块和级联模块,设计了基于不同误差函数和作者改进的误差函数的DFE;
3)针对非常模信号,设计了CMA与DD相结合的双模式判决反馈均衡器,以及可以加快收敛速度的变系数加权误差函数的双模式判决反馈均衡器和引入迭代阈值的双模式判决反馈均衡器。
ISI can be eliminated with blind equalization algorithms that need no training sequence. Of all blind equalization algorithms, the Constant Modulus Algorithm (CMA) has simple structure, but it has slow convergence and large mean square error. Especially to channel of frequency response with obvious fluctuation, CMA has worse equalization performance. But Decision Feedback Filter (DFE) with nonlinear feedback filter is more suitable to channels with different type. Besides the structure of equalizer, influence factor of equalization effectiveness is related to error term of iteration formula for computing weight coefficient. DFE algorithm has different equalization performance when error terms are different.
Decision feedback blind equalization algorithms are studied based on the analyse of different error functions and Constant Modulus Algorithm (CMA). Simulation results with channel of frequency response with obvious fluctuation. The research consists of several aspects of as follows:
1. Analyzing constant modulus blind equalization algorithms based on different error functions
From gradient descent method, the bigger the value of gradient norm of algorithm, the better convergence rate and the larger mean square error is, and vice versa. Hence, an error function with variable weighted coefficient is defined to control value of gradient norm. The characteristic of the proposed algorithm can be changed according with different values of weighted coefficient defined by the author. Thus, a CMA based on the error function of variable weighted coefficient (VCMA) is proposed.
2. Analyzing decision feedback blind equalization algorithms based on different error functions
For channel of frequency response with obvious fluctuation, the constant modulus decision feedback equalizer (CMDFE) has better convergence and less mean square error than CMA algorithm. In order to improve convergence rate of CMDFE, above mentioned error function based on variable weighted coefficient is applied to this equalization system and a decision feedback blind equalization algorithm based on the error function of variable weighted coefficient (VCMDFE) is proposed.
3. Analyzing dual-mode decision-feedback blind equalization algorithms based on different error functions
For making full use of the advantage of each Bussgang blind algorithm and eliminating the disadvantage, we do research on three kinds of dual-mode decision-feedback blind equalization algorithms.
1) Combining VCMDFE and Decision Directed (DD), a dual-mode blind equalization algorithm based on the error function of variable weighted coefficient is proposed.
2) With the aid of better convergence of CMDFE, an iteration threshold (hereinafter as limit) is introduced to iteration process to modify judging conditions of the dual-mode decision-feedback algorithm based on constant modulus (CMDFE-DD). At the beginning of iteration, iterations adopted CMDFE are equal to iteration threshold, and then switch is carried out based on the decision circle ring. Thus, a dual-mode decision-feedback blind equalization algorithm based on constant modulus and by introducing iteration threshold is proposed.
3) VCMDFE algorithm has better convergence than CMDFE algorithm. Similarly, by using above mentioned idea of iteration threshold, a dual-mode decision-feedback blind equalization algorithm of variable weighted coefficient by introducing iteration threshold is proposed.
4. Designing different equalizer-modules based on different structures and different algorithms
With the aid of Simulink library, equalizer-modules in papers based on different structures and different algorithms are designed under simulation modeling environment of Simulink.
1) With the aid of linear equalizer (LE) modules with CMA in the library, LE-modules based on frequently used error functions and the error functions defined by the author are designed.
2) With the help of decision modules and concatenation modules in the library, DFE-modules based on frequently used error functions and the error functions defined by the author are designed.
3) According to the signal that is not constant modulus, a dual-mode DFE-module combining CMDFE and DD is designed. In order to improve convergence rate of the above dual-mode DFE-module, the author has designed two kinds of different dual-mode DFE-modules, based on error function of variable weighted coefficient and introducing iteration threshold.
本文在分析CMA性能以及误差函数特性的基础上,研究了基于不同误差函数的判决反馈盲均衡算法,并用频响起伏较大的信道进行了仿真。研究内容主要包括以下几个方面:
1.研究了基于不同误差函数的常模盲均衡算法
从随机梯度下降法得知,梯度范数越大则收敛越快,而均方误差愈大,反之亦然。因此,定义了一种变系数加权的误差函数,以控制梯度范数的大小。该误差函数曲线特性可随作者所定义的可变因子的取值不同而发生改变,提出了基于变系数加权误差函数的CMA(VCMA)。
2.研究了基于不同误差函数的判决反馈盲均衡算法
针对频响起伏较大的信道,常模判决反馈盲均衡算法(CMDFE)能够很好地克服CMA的缺点,既加快了收敛速度,又减小了均方误差。另外,为了进一步改善CMDFE的均衡性能,把上述定义的变系数加权误差函数应用到此种均衡系统中,提出了基于变系数加权误差函数的DFE(VCMDFE)。
3.研究了基于不同误差函数的判决反馈双模式盲均衡算法
为了充分利用Bussgang类算法中各独立算法的优点,以及克服各算法所存在的缺陷,并结合改进的误差函数,提出了3类判决反馈双模式盲均衡算法:
1)将VCMDFE与判决引导(DD)算法相结合,提出了基于变系数加权误差函数的判决反馈双模式盲均衡算法(VCMDFE-DD)。
2)利用CMDFE算法较强的收敛能力,在迭代起始阶段一直采用CMDFE均衡,当均衡一段时间后,再根据判决圆环进行两种算法之间的切换,提出了基于引入迭代阈值的常模判决反馈双模式盲均衡算法(LCMDFE-DD)。
3)VCMDFE算法的收敛能力较CMDFE强,同样应用上述迭代阈值的思想,提出了基于引入迭代阈值的VCMDFE-DD的判决反馈盲均衡算法(LVCMDFE-DD)。
4.设计了不同结构以及采用不同算法的盲均衡器模块
利用Simulink库中的一些模块,设计了基于不同结构和不同算法的均衡器:
1)利用库中采用CMA的线性均衡器(LE)模块,设计了基于几种常用误差函数和作者改进的误差函数的LE;
2)利用库中的判决器模块和级联模块,设计了基于不同误差函数和作者改进的误差函数的DFE;
3)针对非常模信号,设计了CMA与DD相结合的双模式判决反馈均衡器,以及可以加快收敛速度的变系数加权误差函数的双模式判决反馈均衡器和引入迭代阈值的双模式判决反馈均衡器。
ISI can be eliminated with blind equalization algorithms that need no training sequence. Of all blind equalization algorithms, the Constant Modulus Algorithm (CMA) has simple structure, but it has slow convergence and large mean square error. Especially to channel of frequency response with obvious fluctuation, CMA has worse equalization performance. But Decision Feedback Filter (DFE) with nonlinear feedback filter is more suitable to channels with different type. Besides the structure of equalizer, influence factor of equalization effectiveness is related to error term of iteration formula for computing weight coefficient. DFE algorithm has different equalization performance when error terms are different.
Decision feedback blind equalization algorithms are studied based on the analyse of different error functions and Constant Modulus Algorithm (CMA). Simulation results with channel of frequency response with obvious fluctuation. The research consists of several aspects of as follows:
1. Analyzing constant modulus blind equalization algorithms based on different error functions
From gradient descent method, the bigger the value of gradient norm of algorithm, the better convergence rate and the larger mean square error is, and vice versa. Hence, an error function with variable weighted coefficient is defined to control value of gradient norm. The characteristic of the proposed algorithm can be changed according with different values of weighted coefficient defined by the author. Thus, a CMA based on the error function of variable weighted coefficient (VCMA) is proposed.
2. Analyzing decision feedback blind equalization algorithms based on different error functions
For channel of frequency response with obvious fluctuation, the constant modulus decision feedback equalizer (CMDFE) has better convergence and less mean square error than CMA algorithm. In order to improve convergence rate of CMDFE, above mentioned error function based on variable weighted coefficient is applied to this equalization system and a decision feedback blind equalization algorithm based on the error function of variable weighted coefficient (VCMDFE) is proposed.
3. Analyzing dual-mode decision-feedback blind equalization algorithms based on different error functions
For making full use of the advantage of each Bussgang blind algorithm and eliminating the disadvantage, we do research on three kinds of dual-mode decision-feedback blind equalization algorithms.
1) Combining VCMDFE and Decision Directed (DD), a dual-mode blind equalization algorithm based on the error function of variable weighted coefficient is proposed.
2) With the aid of better convergence of CMDFE, an iteration threshold (hereinafter as limit) is introduced to iteration process to modify judging conditions of the dual-mode decision-feedback algorithm based on constant modulus (CMDFE-DD). At the beginning of iteration, iterations adopted CMDFE are equal to iteration threshold, and then switch is carried out based on the decision circle ring. Thus, a dual-mode decision-feedback blind equalization algorithm based on constant modulus and by introducing iteration threshold is proposed.
3) VCMDFE algorithm has better convergence than CMDFE algorithm. Similarly, by using above mentioned idea of iteration threshold, a dual-mode decision-feedback blind equalization algorithm of variable weighted coefficient by introducing iteration threshold is proposed.
4. Designing different equalizer-modules based on different structures and different algorithms
With the aid of Simulink library, equalizer-modules in papers based on different structures and different algorithms are designed under simulation modeling environment of Simulink.
1) With the aid of linear equalizer (LE) modules with CMA in the library, LE-modules based on frequently used error functions and the error functions defined by the author are designed.
2) With the help of decision modules and concatenation modules in the library, DFE-modules based on frequently used error functions and the error functions defined by the author are designed.
3) According to the signal that is not constant modulus, a dual-mode DFE-module combining CMDFE and DD is designed. In order to improve convergence rate of the above dual-mode DFE-module, the author has designed two kinds of different dual-mode DFE-modules, based on error function of variable weighted coefficient and introducing iteration threshold.
引文
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[3]Rontogiannis A A,Berberidis K.Efficient decision feedback equalization for sparse wireless channels[J].IEEE Transactions on Wireless Communications,2003,3(2):570-581
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