一族新Bussgang类盲均衡算法

该文提出了一族新Bussgang类盲均衡算法统一形式的代价函数,该代价函数具有明确的数学意义,包括了经典的Decision-Directed算法,Sato算法,CMA算法及其变种。根据该代价函数,可以设计出新类型的Bussgang盲均衡算法,该文据此设计了两种新型的Bussgang盲均衡算法,仿真实验验证了这两种新算法的收敛性能。     

基于变步长自然梯度算法的盲源分离

相比标准梯度而言，自然梯度算法以其更快的收敛速度和更好的分离性能在盲源分离中占据着重要地位。由于常用的自然梯度算法是基于固定步长的，因此无法真正解决收敛速度和稳态误差之间的矛盾。通过建立步长因子与分离矩阵相互差异之间的非线性关系，提出了一种新的自然梯度算法。由于该算法采用的步长是时变的，加快了收敛速度，减小了稳态误差，从而很好地解决了固定步长的内在矛盾。计算机仿真结果证实了理论分析，并说明了该算法明显优于通常的自然梯度算法。     

CMA算法盲均衡性能分析

由于受多径传输和有限带宽的影响,无线信道不可避免地存在码间干扰和信道间干扰.盲均衡技术是一种不需要训练序列就能补偿信道畸变的新兴自适应均衡技术.文中从Bussgang类盲均衡原理出发,讨论了属于Bussgang类的CMA盲均衡算法,并利用Simulink对算法进行了仿真.从仿真结果可看出步长对算法收敛性能和精度的影响,步长越小,收敛速度越慢,但稳态误差越小;反之亦然.     

源信号数目未知正交投影自然梯度盲分离算法

分析了源信号数目未知的盲信号分离算法中分离矩阵范数趋于无穷进而导致算法发散的原因。利用正交投影自然梯度方法消去了自然梯度中引起冗余移动的冗余分量,推导出源信号数目未知的正交投影自然梯度算法。新算法具有与自然梯度算法相同的收敛速度,且克服了已有算法不能稳定收敛的缺点。仿真验证了新算法的分离性能和收敛稳定性。     

基于萤火虫算法的变步长语音信号盲源分离

针对传统的自然梯度算法对语音信号进行盲源分离时,算法存在收敛速度和稳态误差的矛盾。文中提出一种新的变步长自然梯度算法,利用荧火虫算法对自然梯度算法的步长调整,使算法的步长随信号的分离度变化,并通过计算机仿真验证了该算法的有效性,算法的分离效果更好,收敛速度更快,且稳态误差更小。     

数据复用在Bussgang类盲均衡算法中的应用

为解决突发通信或非合作通信中接收数据短、直接均衡迭代难于收敛问题,该文将数据复用的思想引入Shalvi算法中。通过分析数据复用均衡后序列与原始码元序列峰度的关系,得出了数据复用方法有效收敛的原因。以此为基础,将该结论推广到整类Bussgang盲均衡算法,并分析了影响数据复用盲均衡效果的几个因素。仿真实验表明,数据复用方法大大减少了Bussgang算法收敛所需要的码元数目,有一定的工程实用价值。     

基于Bussgang技术的盲均衡算法

为了减小码间干扰,常常采用均衡技术,基于Bussgang技术的盲均衡算法实现容易,特别是对其进行取符号简化后可大大减少其资源占用量,运算量小,收敛速度快。分析了基于Bussgang技术的盲均衡技术原理,对提出的几种算法的收敛速度进行了研究和比较,研究了算法的特性,提出了盲均衡的发展方向,对于通信质量的提高具有十分重要的工程意义。     

一族新的Bussgang类指数拓展多模盲均衡算法

该文提出一类新的Bussgang指数拓展多模算法,进一步降低传统Bussgang类盲均衡算法收敛时的稳态误差的效果。分析了新代价函数和误差函数等对算法性能的影响,并给出了算法复杂度分析,展示了如何利用作图法求得星座特征常数R的过程。为了削弱该算法对于高阶统计量信息的依赖,提出一种星座特征常量R的近似计算方法,使得星座特征常数不再成为新算法良好工作所必须的先验知识。最后以星座点甚密集方形QAM和非方形QAM系统为例,通过仿真验证该算法对密集QAM系统的盲均衡能力。     

自适应步长加权正交约束自然梯度ICA算法

针对传统自然梯度ICA算法的不稳定和分离结果不准确,提出一种自适应步长加权正交约束自然梯度ICA算法。首先,基于分离矩阵所满足的正交性约束,引入一种单步正交性修正方法。然后,根据相邻迭代结果之差可用于平滑构造每步迭代结果与最优值的距离,设计出一种单步误差估计函数。最后,据此误差估计函数引入一种自适应调整的步长。仿真实验表明,自适应步长加权正交约束自然梯度ICA算法,相比于传统的自然梯度ICA算法具有更快的收敛速度,且算法的稳定性和分离结果的准确性都得到了较大提高。     

同伦BP网络理论与算法

ＢＰ网络和算法是使用最广泛的神经网络模型之一，但由于它使用梯度算法，因而存在有固有的局域极小及收敛速度慢等问题。本文首先把一ＢＰ网络的优化问题变换为一非线性方程的求解，然后将同伦思想引入到神经网络学习训练之中，提出了相应的同伦ＢＰ网络理论与算法，它具有全局收敛的优点，同时具有比传统梯度法收敛速度快一个数量级以上和克服病态的能力，在ＢＰ梯度法不收敛时它也能给出正确解答。本文的理论证明和计算机仿真实验     

Analysis of modified "Bussgang" algorithms (MBAs) for channel equalization

In previous papers, we introduced two modified "Bussgang" algorithms (MBAs) for blind-channel equalization based on Bayesian iterative estimation of the source sequence. They were developed in order to reduce the computational complexity of the original "Bussgang" algorithm as well as to make it more flexible by introducing a kind of source adaptivity. However, the previous work relied on some heuristic findings, validated by a series of computer-based experiments. The aim of this paper is to present a theoretical investigation of some particular aspects of the adapting equations, namely, the steady-state conditions, in order to ameliorate the performances of the MBAs and to better explain their numerical behavior.     

New Algorithms for Blind Equalization: The Constant Norm Algorithm Family

In this paper, a new, efficient class of blind equalization algorithms is proposed for use in high-order, two-dimensional digital communication systems. We have called this family: the Constant Norm Algorithms (CNA). This family is derived in the context of Bussgang techniques. Therefore, the resulting algorithms are very simple. We show that some well-known blind algorithms such as "Sato's algorithm" or the Constant Modulus Algorithm (CMA) are particular cases in our CNA family. In addition, from this class, a new cost function, named Constant sQuare Algorithm (CQA), is derived, which is well designed for QAM. It results in a lower algorithm noise without increasing the complexity. Another advantage of this class lies in the possibility of creating new norms by combining several existing norms in order to benefit from the advantages of each original norm. For example, we present the norm resulting from the combination of the two algorithms, CMA and CQA. Moreover, we highlight that, with regard to the excess mean-square error performance, there is an optimal norm for each constellation, i.e., each modulation, in order to equalize it blindly     

Multichannel blind image deconvolution using the Bussgang algorithm: spatial and multiresolution approaches

This work extends the Bussgang blind equalization algorithm to the multichannel case with application to image deconvolution problems. We address the restoration of images with poor spatial correlation as well as strongly correlated (natural) images. The spatial nonlinearity employed in the final estimation step of the Bussgang algorithm is developed according to the minimum mean square error criterion in the case of spatially uncorrelated images. For spatially correlated images, the nonlinearity design is rather conducted using a particular wavelet decomposition that, detecting lines, edges, and higher order structures, carries out a task analogous to those of the (preattentive) stage of the human visual system. Experimental results pertaining to restoration of motion blurred text images, out-of-focus spiky images, and blurred natural images are reported.     

Fast-convergence filtered regressor algorithms for blindequalisation

The authors present a simple extension of the standard Bussgang blind equalisation algorithms that significantly improves their convergence properties. The technique uses the inverse channel estimate to filter the regressor signal. The modified algorithms provide quasi-Newton convergence in the vicinity of a local minimum of the chosen cost function with only a modest increase in the overall computational complexity of the system. An example of the technique as applied to the constant-modulus algorithm indicates its superior convergence behaviour     

Convergence of exponentiated gradient algorithms

This paper studies three related algorithms: the (traditional) gradient descent (GD) algorithm, the exponentiated gradient algorithm with positive and negative weights (EG± algorithm), and the exponentiated gradient algorithm with unnormalized positive and negative weights (EGU± algorithm). These algorithms have been previously analyzed using the “mistake-bound framework” in the computational learning theory community. We perform a traditional signal processing analysis in terms of the mean square error. A relationship between the learning rate and the mean squared error (MSE) of predictions is found for the family of algorithms. This is used to compare the performance of the algorithms by choosing learning rates such that they converge to the same steady-state MSE. We demonstrate that if the target weight vector is sparse, the EG± algorithm typically converges more quickly than the GD or EGU± algorithms that perform very similarly. A side effect of our analysis is a reparametrization of the algorithms that provides insights into their behavior. The general form of the results we obtain are consistent with those obtained in the mistake-bound framework. The application of the algorithms to acoustic echo cancellation is then studied, and it is shown in some circumstances that the EG± algorithm will converge faster than the other two algorithms     

Adaptive Step-Size Natural Gradient ICA Algorithm with Weighted Orthogonalization

To improve the stability of the traditional natural gradient independent component analysis (ICA) algorithm and the accuracy of its separated results, a adaptive step-size natural gradient ICA algorithm with weighted orthogonalization is proposed. First, to take advantage of the pre-whitening pre-processing and keep the equivariance property of the ICA algorithm, based on the weighted orthogonal constraint on the separating matrix without pre-whitening of observed signals, weighted orthogonalization is introduced after the traditional gradient update. Then, according to the error estimation from the smoothed distance between separated outputs and optimal outputs, we obtain two adaptive step sizes based, respectively, on an unconstrained natural gradient ICA process and a weighted orthogonalization process. Simulation experiment results show that the speed of convergence of the adaptive step-size natural gradient ICA algorithms with weighted orthogonalization are faster than the traditional one; also, the stability of the algorithms and the accuracy of the separated results are improved observably.     

Exploiting sparsity in adaptive filters

This paper studies a class of algorithms called natural gradient (NG) algorithms. The least mean square (LMS) algorithm is derived within the NG framework, and a family of LMS variants that exploit sparsity is derived. This procedure is repeated for other algorithm families, such as the constant modulus algorithm (CMA) and decision-directed (DD) LMS. Mean squared error analysis, stability analysis, and convergence analysis of the family of sparse LMS algorithms are provided, and it is shown that if the system is sparse, then the new algorithms will converge faster for a given total asymptotic MSE. Simulations are provided to confirm the analysis. In addition, Bayesian priors matching the statistics of a database of real channels are given, and algorithms are derived that exploit these priors. Simulations using measured channels are used to show a realistic application of these algorithms