用于波束形成的最小二乘广义模值算法研究

对用于波束形成的最小二乘广义模值算法(LSGMA)在多种信号环境下的收敛性能进行了分析;在此基础上提出一种新的多用户盲波束形成算法--迭代最小二乘广义模投影(ILSP-GMA)算法,克服LSGMA算法当恒模干扰信号强于所需信号时会错误收敛的缺陷.仿真结果表明该算法可有效适用于多用户情况,并可获得较原迭代最小二乘投影算法(ILSP)更快的收敛速度.     

Total least mean squares algorithm

Widrow (1971) proposed the least mean squares (LMS) algorithm, which has been extensively applied in adaptive signal processing and adaptive control. The LMS algorithm is based on the minimum mean squares error. On the basis of the total least mean squares error or the minimum Raleigh quotient, we propose the total least mean squares (TLMS) algorithm. The paper gives the statistical analysis for this algorithm, studies the global asymptotic convergence of this algorithm by an equivalent energy function, and evaluates the performances of this algorithm via computer simulations     

Adaptive linearly constrained inverse QRD-RLS beamforming algorithm for moving jammers suppression

A general, linearly constrained (LC) recursive least squares (RLS) array-beamforming algorithm, based on an inverse QR decomposition, is developed for suppressing moving jammers efficiently. In fact, by using the inverse QR decomposition-recursive least squares (QRD-RLS) algorithm approach, the least-squares (LS) weight vector can be computed without back substitution and is suitable for implementation using a systolic array to achieve fast convergence and good numerical properties. The merits of this new constrained algorithm are verified by evaluating the performance, in terms of the learning curve, to investigate the convergence property and numerical efficiency, and the output signal-to-interference-and-noise ratio. We show that our proposed algorithm outperforms the conventional linearly constrained LMS (LCLMS) algorithm, and the one using the fast linear constrained RLS algorithm and its modified version.     

基于平行因子分解的大规模MIMO盲信道估计

针对单小区大规模多输入多输出（Multiple-Input Multiple-Output,MIMO）系统上行链路,提出了一种基于平行因子（Parallel Factor,PARAFAC）模型的信道估计方法。在基站端,将接收信号构造成PARAFAC模型,利用大规模MIMO系统中信道的渐近正交的性质,提出了一种基于约束二线性迭代最小二乘算法(Constrained Blinear Alternating Least Squares,CBALS),从而实现了盲信道估计。理论分析及仿真结果表明,所提方法与传统最小二乘方法相比,不仅提高了频带利用率而且具有更高的估计精度;与已有的二线性交替最小二乘方法(BALS)相比,所提算法有更快的收敛速度。     

MIMO系统中应用张量分解进行半盲信道估计的算法分析

针对多输入多输出系统半盲信道估计问题,提出一种基于张量分解的半盲联合信号检测和信道估计算法。其思想是利用张量分解的唯一性,对接收信号构造基于张量分解的平行因子模型,并利用正则交替最小二乘算法对信道和发送信号进行联合迭代估计。仿真结果表明:与传统基于导频信道估计方法相比,所提算法只需少量的导频序列即可获得较高的信道估计精度;与已有的交替最小二乘算法相比,所提算法消除了矩阵求伪逆时可能带来的病态问题,收敛速度较快。文章还详细的分析了正则系数和收敛条件等参数对正则交替最小二乘算法性能的影响。      

基于相关函数的递推最小二乘算法及其在回波消除中的应用

本文给出一种新的类似于RLS（recursive least squares)算法的递推最小二乘算法，该算法直接对输入信号的相关函数进行处理而不是对输入信号本身进行处理，理论分析表明了该算法的收敛性。该算法应用于回波消除问题中，克服了常规自适应滤波算法在出现双方对讲的情况下需停止调节自适应滤波器系数这一不足。计算机模拟仿真表明该算法在双方对讲的情况下有良好的收敛性能。     

A new system identification method for fast echo cancelerinitialization

Proposes a new recursive version of an earlier technique for fast initialization of data-driven echo cancelers (DDECs). The speed of convergence and the covariance of the estimate of the proposed technique are comparable to the recursive least squares (RLS) algorithm, however, the computational complexity is no greater than the least mean square (LMS) algorithm. Analysis of computational complexity and the estimation error is also provided. Simulation results based on both floating-point and fixed-point arithmetic illustrate a remarkable improvement in terms of speed of convergence and steady-state error over the computationally comparable LMS algorithm     

一种基于拟牛顿法的递归最小二乘方法

基于拟牛顿优化方法,提出了一种稳健的自适应FIR滤波算法。新算法用最小二乘误差(LSE)代替了均方误差(MSE)作为代价函数,它具有和常规递归最小二乘(CRLS)算法相近似的追踪能力,且不存在数值计算不稳定性的问题,在收敛速度以及稳态效果方面也要优于De Campos的拟牛顿(QN)算法。通过计算机仿真比较了有关算法的性能。     

变遗忘因子递推最小二乘Hammerstein系统辨识算法

摘.要:本论文研究了单输入单输出非线性Hammerstein系统的辨识问题,提出了一种具有变遗忘因子的递推最小二乘算法.由于Hammerstein系统模型的非线性特征,传统的递推最小二乘算法无法直接用来解决该系统的辨识问题.为此,论文将Hammerstein系统参数进行了映射变换,使得变换后的系统参数与Hammerst...     

A fast learning algorithm for Gabor transformation

An adaptive learning approach for the computation of the coefficients of the generalized nonorthogonal 2-D Gabor (1946) transform representation is introduced. The algorithm uses a recursive least squares (RLS) type algorithm. The aim is to achieve minimum mean squared error for the reconstructed image from the set of the Gabor coefficients. The proposed RLS learning offers better accuracy and faster convergence behavior when compared with the least mean squares (LMS)-based algorithms. Applications of this scheme in image data reduction are also demonstrated.     

Convergence Analysis of the Hierarchical Least Squares Algorithm for Bilinear-in-Parameter Systems

This paper studies the convergence of the hierarchical identification algorithm for bilinear-in-parameter systems. By replacing the unknown variables in the information vector with their estimates, a hierarchical least squares algorithm is derived based on the model decomposition. The proposed algorithm has higher computational efficiency than the over-parameterization model-based recursive least squares algorithm. The performance analysis shows that the parameter estimation errors converge to zero under persistent excitation conditions. The effectiveness of the proposed algorithm is verified by simulation examples.     

A set of algorithms linking NLMS and block RLS algorithms

This paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares (NLMS) and the block recursive least squares (BRLS) algorithms. All these algorithms use small block lengths, thus allowing easy implementation and small input-output delay. It is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares (LMS) algorithm, while converging much faster. A precise evaluation of the arithmetic complexity is provided, and the adaptive behavior of the algorithm is analyzed. Simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the NLMS algorithm. The conclusions of the theoretical analysis are checked by simulations, illustrating that, even in the case where noise is added to the reference signal, the proposed algorithm allows altogether a faster convergence and a lower residual error than the NLMS algorithm. Finally, a sample-by-sample version of this algorithm is outlined, which is the link between the NLMS and recursive least squares (RLS) algorithms     

卫星通信中快速非线性信道RLS均衡算法

幅度相位联合调制(Amplitude Phase Shift Keying, APSK)信号经过卫星信道时容易引起非线性失真,产生码间串扰。为此,本文将Wiener均衡应用于APSK卫星通信中,并提出了一种快速非线性信道递归最小二乘(Nonlinear Channel Recursive Least Squares, NCRLS)均衡算法,在传统NCRLS算法的基础上,建立了遗忘因子与步长因子的关系,推出了变遗忘因子的非线性信道递归最小二乘(Variable Forgetting Factor Nonlinear Channel Recursive Least Squares, VFFNCRLS)均衡算法,有效地提高了收敛速度。仿真结果表明,VFFNCRLS算法有效地纠正了非线性失真信号的星座扭曲和频谱再生,解决了卫星通信系统中有记忆非线性信道失真的问题,相比传统算法,具有较快的收敛速度和较好的稳定性。      

Robust M-estimate adaptive filtering

An M-estimate adaptive filter for robust adaptive filtering in impulse noise is proposed. Instead of using the conventional least-square cost function, a new cost function based on an M-estimator is used to suppress the effect of impulse noise on the filter weights. The resulting optimal weight vector is governed by an M-estimate normal equation. A recursive least M-estimate (RLM) adaptive algorithm and a robust threshold estimation method are derived for solving this equation. The mean convergence performance of the proposed algorithm is also analysed using the modified Huber (1981) function (a simple but good approximation to the Hampel's three-parts-redescending M-estimate function) and the contaminated Gaussian noise model. Simulation results show that the proposed RLM algorithm has better performance than other recursive least squares (RLS) like algorithms under either a contaminated Gaussian or alpha-stable noise environment. The initial convergence, steady-state error, robustness to system change and computational complexity are also found to be comparable to the conventional RLS algorithm under Gaussian noise alone     

Iterative least squares estimators in nonlinear image restoration

The concept of iterative least squares estimation as applied to nonlinear image restoration is considered. Regarding the convergence analysis of nonlinear iterative algorithms, the potential of the global convergence theorem (GCT) is explored. The theoretical analysis is performed on a general class of nonlinear algorithms, which defines a signal-dependent linear mapping of the residual. The descent properties of two normed functions are considered. Furthermore, a procedure for the selection of the iteration parameter is introduced. The steepest descent (SD) iterative approach for the solution of the least squares optimization problem is introduced. The convergence properties of the particular algorithm are readily derived on the basis of the generalized analysis and the GCT. The factors that affect the convergence rate of the SD algorithm are thoroughly studied. In the case of the SD algorithm, structural modifications are proposed, and two hybrid-SD algorithms attain convergence in a more uniform fashion with respect to their entries. In general, the algorithms achieve larger convergence rates than the conventional SD technique     

An adaptive algorithm for differentially coherent detection in the presence of intersymbol interference

An adaptive equalization method is proposed for use with differentially coherent detection of M-ary differential phase-shift keying (DPSK) signals in the presence of unknown carrier frequency offset. A decision-feedback or a linear equalizer is employed, followed by the differentially coherent detector. The equalizer coefficients are adjusted to minimize the post-detection mean squared error. The error, which is a quadratic function of the equalizer vector, is used to design an adaptive algorithm of stochastic gradient type. The approach differs from those proposed previously, which linearize the post-detection error to enable the use of least mean squares (LMS) or recursive least squares (RLS) adaptive equalizers. The proposed quadratic-error (Q) algorithm has complexity comparable to that of LMS, and equal convergence speed. Simulation results demonstrate performance improvement over methods based on linearized-error (L) algorithm. The main advantages of the technique proposed are its simplicity of implementation and robustness to carrier frequency offset, which is maintained for varying modulation level.     

Adaptive blind channel estimation by least squares smoothing

A least squares smoothing (LSS) approach is presented for the blind estimation of single-input multiple-output (SIMO) finite impulse response systems. By exploiting the isomorphic relation between the input and output subspaces, this geometrical approach identifies the channel from a specially formed least squares smoothing error of the channel output. LSS has the finite sample convergence property, i.e., in the absence of noise, the channel is estimated perfectly with only a finite number of data samples. Referred to as the adaptive least squares smoothing (A-LSS) algorithm, the adaptive implementation has a high convergence rate and low computation cost with no matrix operations. A-LSS is order recursive and is implemented in part using a lattice filter. It has the advantage that when the channel order varies, channel estimates can be obtained without structural change of the implementation. For uncorrelated input sequence, the proposed algorithm performs direct deconvolution as a by-product     

Fast Converging Semi-Blind Space-Time Equalisation for Dispersive QAM MIMO Systems

A novel semi-blind space-time equaliser (STE) is proposed for dispersive multiple-input multiple-output systems that employ high-throughput quadrature amplitude modulation signalling. A minimum number of training symbols, approximately equal to the dimension of the STE, are first utilised to provide a rough initial least squares estimate of the STE?s weight vector. A concurrent gradient-Newton constant modulus algorithm and soft decision-directed scheme is then applied to adapt the STE. The proposed semi-blind adaptive STE is capable of converging fast to the minimum mean square error STE solution. Simulation results confirms that the convergence speed of this semi-blind adaptive algorithm is very close to that of the training-based recursive least squares algorithm.     

一种抗飞行器衰落的快速均衡算法

对流层散射通信信道为时变多径信道,当飞行器飞越散射通信链路会导致飞行器衰落。针对飞行器衰落,提出了一种收敛速度快、跟踪能力强、数值稳定性高、复杂度低的快速自适应均衡算法——基于选择更新的累积误差递归最小二乘自适应均衡算法。根据指数加权最小二乘准则,推导出累积误差递归最小二乘算法,依据共轭斜量算法提出抽头系数选择更新准则。均衡算法的复杂度分析和仿真实验表明提出的快速自适应均衡算法不仅复杂度低,而且有效地提高了均衡器克服信道时间衰落的能力。     

Combined RLS-LMS initialization for per tone equalizers in DMT-receivers

In discrete multitone receivers, the classical equalizer structure consists of a (real) time domain equalizer (TEQ) combined with complex one-tap frequency domain equalizers. An alternative receiver is based on a per tone equalization (PTEQ), which optimizes the signal-to-noise ratio (SNR) on each tone separately and, hence, the total bitrate. In this paper, a new initialization scheme for the PTEQ is introduced, based on a combination of least mean squares (LMS) and recursive least squares (RLS) adaptive filtering. It is shown that the proposed method has only slightly slower convergence than full square-root RLS (SR-RLS) while complexity as well as memory cost are reduced considerably. Hence, in terms of complexity and convergence speed, the proposed algorithm is in between LMS and RLS.