Noise-constrained least mean squares algorithm

We consider the design of an adaptive algorithm for finite impulse response channel estimation, which incorporates partial knowledge of the channel, specifically, the additive noise variance. Although the noise variance is not required for the offline Wiener solution, there are potential benefits (and limitations) for the learning behavior of an adaptive solution. In our approach, a Robbins-Monro algorithm is used to minimize the conventional mean square error criterion subject to a noise variance constraint and a penalty term necessary to guarantee uniqueness of the combined weight/multiplier solution. The resulting noise-constrained LMS (NCLMS) algorithm is a type of variable step-size LMS algorithm where the step-size rule arises naturally from the constraints. A convergence and performance analysis is carried out, and extensive simulations are conducted that compare NCLMS with several adaptive algorithms. This work also provides an appropriate framework for the derivation and analysis of other adaptive algorithms that incorporate partial knowledge of the channel     

The performance of the least mean squares algorithm combined withspatial smoothing

Many practical signal environments involve correlation between desired and undesired signals, causing narrowband adaptive array beamformers to exhibit signal cancellation. Spatial smoothing is a technique that can perform beamforming in such environments. This method can be incorporated into an adaptive algorithm, such as least mean squares (LMS), possibly altering the well-known performance characteristics of the algorithm. We discuss methods for combining spatial smoothing with the LMS algorithm in an array with a generalized side-lobe canceler (GSC) structure. The first of these methods is an electronic version of mechanically dithering the array. We show that this well-known method obeys a set of nonhomogeneous dynamical equations, resulting in a limit cycle that increases the misadjustment of the algorithm. The previously reported parallel spatial processing algorithm is also shown to have this increased misadjustment. We then introduce two methods that do not suffer from this misadjustment increase. We compare the methods' computational complexity and performance, in terms of stability and steady-state behavior, including weight misadjustment, GSC output power, and signal-to-noise ratio (SNR). In conclusion, we find that the limit cycle of the first method can be avoided without any increase in complexity by using one of the new methods     

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 robust recursive least squares algorithm

A new algorithm is developed, which guarantees the normalized bias in the weight vector due to persistent and bounded data perturbations to be bounded. Robustness analysis for this algorithm has been presented. An approximate recursive implementation is also proposed. It is termed as the robust recursive least squares (RRLS) algorithm since it resembles the RLS algorithm in its structure and is robust with respect to persistent bounded data perturbation. Simulation results are presented to illustrate the efficacy of the RRLS algorithm     

Reformulating least mean squares in the data domain

It is often the case that an idea is clearly obvious once it becomes ubiquitous. This is why it is so difficult to judge the innovation content of a new idea or concept. A creative, but familiar, idea invariably seems less brilliant than something new and esoteric. A theoretically complex notion first heard may stimulate the mind but generally cannot compare in innovation with, say, something as simple, but ultimately culture transforming, as the wheel. Only the test of time can separate the truly great ideas from the merely clever ones. By this measure, Widrow's work on adaptive processing is unambiguously seminal. Though Dr. Widrow initiated data adaptive least squares processing, the initial optimal noise filtering concept was conceived by Norbert Wiener (1949) and Andrey Kolmogorov (1941) (independently), both whom developed stochastic least squares theory. These prior efforts, while a tour de force of mathematics-one that provided essential insight and analytical tools-suffered from an assumption of the presence of prior knowledge of time series statistics.     

Orthogonal-transformed variable-gain least mean squares (OVLMS)algorithm for fractional tap-spaced adaptive MLSE equalizers

A fast channel-estimation scheme for adaptive maximum-likelihood sequence-estimation (MLSE) equalizers called the orthogonal-transformed variable-gain least mean squares (OVLMS) algorithm is proposed. This algorithm requires only as many operations as the least mean squares algorithm in spite of its excellent performance. Furthermore, an operational complexity reduction method is proposed in which the orthogonal matrix is reconfigured as eigenvectors with valid eigenvalues. The OVLMS algorithm is theoretically analyzed and is shown to have both a fast acquisition and a good tracking performance. An equalizer using OVLMS (OVLMS-MLSE) experimentally attains a 5-dB improvement in bit-error rate (BER) performance at BER of 1.0×10 ^-4 over coherent detection. The OVLMS-MLSE is found to be free of the degradation caused by sampling phase error. Finally, the OVLMS-MLSE equalizer is experimentally verified to synchronize within five symbols     

一种快速递归全局最小二乘算法

针对FIR系统输入和输出信号均被噪声干扰的情况,提出一种快速递归全局最小二乘(XS-RTLS)算法用于迭代计算全局最小二乘解,算法沿着输入数据的符号方向并采用著名的快速增益矢量,搜索约束瑞利商(c-RQ)的最小值得到系统参数估计。算法关于方向更新矢量的内积运算可通过加减运算实现,有效降低了计算复杂度;另外XS-RTLS算法没有进行相关矩阵求逆递归运算,因而具有长期稳定性,算法的全局收敛性通过Laslle不变性原理得到证明。最后通过仿真比较了XS-RTLS算法和递归最小二乘(RLS)算法在非时变系统和时变系统中的性能,验证了XS-RTLS算法的长期稳定性。     

A least mean squares blind equalization techniques for OFDM systems

Classical multicarrier systems based on the discrete Fourier transform(dft) make use of aguard interval (gi) in order to enable a low complexity equalization scheme. Thisguard interval consists of a redundant prefix cyclically appended to each block of modulated symbols so as to exploit the cyclic convolution property of thedft. Therefore, besides decreasing the useful transmitted symbol rate, this technique is very specific todft-basedofdm systems. In order to implement a digital modulator, an oversampled version of the continuous signal that would be produced by the all-analog ideal modulator is often computed. This amounts to appending null symbols to the block of symbols to be modulated. This work shows that forcing the presence of these null symbols at the appropriate places on the receiver side is sufficient to equalize the channel. Here, a linear equalizer is adapted by minimizing a quadratic criterion based on the energy of the subband signals that should be zero. Since no knowledge about theuseful data is required, this method performs blind equalization. Moreover, it requires neither a guard interval nor any reference symbol. As a result, for a given channel bitrate budget, the data rate is increased     

A two-dimensional fast lattice recursive least squares algorithm

This paper is mainly devoted to the derivation of a new two-dimensional fast lattice recursive least squares (2D FLRLS) algorithm. This algorithm updates the filter coefficients in growing-order form with linear computational complexity. After appropriately defining the “order” of 2D data and exploiting the relation with 1D multichannel, “order” recursion relations and shift invariance property are derived. The geometrical approaches of the vector space and the orthogonal projection then can be used for solving this 2D prediction problem. We examine the performances of this new algorithm in comparison with other fast algorithms     

Logarithmic reweighting nonnegative least mean square algorithm

System identification based on least mean square (LMS) adaptive filters is effective due to their simplicity and robustness. Inherent physical characteristic of intended system usually make nonnegativity constraint desirable. In other words, imposing nonnegativity constraint on optimization problem leads to more feasible unknown parameter estimation. Hence, nonnegative least mean square (NNLMS) and its variants were proposed to adaptively solve the Wiener filtering problem considering constraint that makes filter weights nonnegative. In this paper, we propose a new variant of nonnegative least mean square for which its performance is analyzed both theoretically and experimentally. The proposed algorithm behavior is investigated in sparse system identification by Monte Carlo simulations in order to show validation of analysis and theory models. We compare our method with IP-NNLMS and NNLMS in order to prove the advantage of our proposed algorithm. Our proposed algorithm is also used in classification problem, and it is compared with entropy function-based online adaptive decision fusion (EADF) algorithm.     

Recursive total least squares algorithm for single-user blindchannel equalisation

The problem of blind channel identification/equalisation using second-order statistics or equivalent deterministic properties of the oversampled channel output has attracted considerable attention. Deterministic blind subspace algorithms are particularly attractive because of their finite sample convergence property and because their solution can be obtained in closed form. Most subspace algorithms developed up until now, however, are based on block processing and have high computational and memory requirements. In the paper, adaptive techniques are used to lower the computational burden. A single-user direct symbol estimation algorithm is presented. The first step in the algorithm consists of an adaptive matrix singular value decomposition for a (virtual) channel identification-type operation. A recursive total least squares algorithm is then used to recover the input symbols. The algorithm is able to track time-varying channels     

Performance analysis of the total least squares ESPRIT algorithm

The asymptotic distribution of the estimation error for the total least squares (TLS) version of ESPRIT is derived. The application to a uniform linear array is treated in some detail, and a generalization of ESPRIT to include row weighting is discussed. The Cramer-Rao bound (CRB) for the ESPRIT problem formulation is derived and found to coincide with the asymptotic variance of the TLS ESPRIT estimates through numerical examples. A comparison of this method to least squares ESPRIT, MUSIC, and Root-MUSIC as well as to the CRB for a calibrated array is also presented. TLS ESPRIT is found to be competitive with the other methods, and the performance is close to the calibrated CRB for many cases of practical interest. For highly correlated signals, however, the performance deviates significantly from the calibrated CRB. Simulations are included to illustrate the applicability of the theoretical results to a finite number of data     

Selfperturbing recursive least squares algorithm with fast tracking capability

A novel recursive least squares (RLS) type algorithm with a selfperturbing action is devised. The algorithm possesses a fast tracking capability in itself because its adaptation gain is automatically revitalised through perturbation of the covariance update dynamics by the filter output error square when it encounters sudden parameter changes. Furthermore, the algorithm converges to the true parameter values in stationary environments.<>     

A delta least squares lattice algorithm for fast sampling

Most shift operator-based adaptive algorithms exhibit poor numerical behavior when the input discrete time process is obtained from a continuous time process by fast sampling. This includes the shift operator based least squares lattice algorithm. We develop a delta least squares lattice algorithm. This algorithm has a low computational complexity compared with the delta Levinson RLS algorithm and shows better numerical properties compared with the shift least squares lattice algorithm under fast sampling. Computer simulations show that the new algorithm also outperforms an existing delta least squares lattice algorithm     

Fast orthogonal least squares algorithm for efficient subset modelselection

An efficient implementation of the orthogonal least squares algorithm for subset model selection is derived. Computational complexity of the algorithm is examined and the result shows that this new fast orthogonal least squares algorithm significantly reduces computational requirements     

Robust least mean square adaptive FIR filter algorithm

The authors propose a new robust adaptive FIR filter algorithm for system identification applications based on a statistical approach named the M estimation. The proposed robust least mean square algorithm differs from the conventional one by the insertion of a suitably chosen nonlinear transformation of the prediction residuals. The effect of nonlinearity is to assign less weight to a small portion of large residuals so that the impulsive noise in the desired filter response will not greatly influence the final parameter estimates. The convergence of the parameter estimates is established theoretically using the ordinary differential equation approach. The feasibility of the approach is demonstrated with simulations     

Adaptive echo cancellation using least mean mixed-norm algorithm

A novel algorithm for echo cancellation is presented in this work. The algorithm consists of simultaneously applying the least mean square (LMS) algorithm to the near-end section of the echo canceller and the least mean fourth (LMF) algorithm to the far-end section. This new scheme results in a substantial performance improvement over the LMS algorithm and other algorithms     

A fast exact least mean square adaptive algorithm

A general block formulation of the least-mean-square (LMS) algorithm for adaptive filtering is presented. This formulation has an exact equivalence with the original LMS algorithm; hence it retains its convergence properties, while allowing a reduction in arithmetic complexity, even for very small block lengths. Working with small block lengths is interesting from an implementation point of view (large blocks result in large memory and large system delay) and allows a significant reduction in the number of operations. Tradeoffs between a number of operations and a convergence rate are obtainable by applying certain approximations to a matrix involved in the algorithm. Hence, the usual block LMS appears as a special case, which explains its convergence behavior according to the type of input signal (correlated or uncorrelated)     

Least mean squares algorithm for fractionally spaced blind channelestimation

The authors consider the problem of blind estimation and equalisation of digital communication finite impulse response (FIR) channels using fractionally spaced samples. The system input is assumed to be a deterministic but unknown data sequence. Exploiting the periodicity of the transmitted data sequence in the frequency domain in the noise free case, it is shown that it is possible to form a linear system in terms of the unknown channel impulse response. In the presence of noise, a least mean squares (LMS) criterion is used to resolve the channel. The resulting algorithm has an appealing interpretation and can be considered as a single channel counterpart of the multi-channel cross-relation (CR) method. Finally, it is shown that the latter can be derived from the proposed algorithm     

An efficient recursive total least squares algorithm for FIRadaptive filtering

An algorithm for recursively computing the total least squares (TLS) solution to the adaptive filtering problem is described. This algorithm requires O(N) multiplications per iteration to effectively track the N-dimensional eigenvector associated with the minimum eigenvalue of an augmented sample covariance matrix. It is shown that the recursive least squares (RLS) algorithm generates biased adaptive filter coefficients when the filter input vector contains additive noise. The TLS solution on the other hand, is seen to produce unbiased solutions. Examples of standard adaptive filtering applications that result in noise being added to the adaptive filter input vector are cited. Computer simulations comparing the relative performance of RLS and recursive TLS are described