Recursive Least-squares Adaptive Algorithm Research Articles

On the Regularization of Recursive Least-Squares Adaptive Algorithms Using Line Search Methods

Stereophonic acoustic echo cancellation (SAEC) requires the identification of four unknown impulse responses corresponding to four loudspeaker-to-microphone pairs. Recent developments in the field of adaptive filters for SAEC setups have allowed for the handling of a single complex-valued adaptive impulse response, instead of the four classical real-valued adaptive filters. With the simplified framework provided by the widely linear (WL) model, more advanced versions of recursive least-squares (RLS) were employed in order to take advantage of their superior tracking speeds when working with highly correlated input signals (such as speech). Despite the performances and numerical stability provided by using exponentially weighted versions of the RLS family in combination with line search methods (LSMs), the SAEC configurations have limited capabilities in mitigating the negative effects caused by high-level disturbances affecting the two microphone signals. Such is the case of double-talk scenarios, which considerably reduce the update accuracy of the adaptive system. This paper analyzes a regularization technique for the named WL-RLS-LSM adaptive filters by adjusting the correlation matrix associated with the input signals and creating a reaction in the update process. The proposed method is designed to considerably slow (or even freeze) the adaptation process while the disturbance is manifested. Simulation results are discussed in order to validate the theoretical content.

Efficient Algorithms for Linear System Identification with Particular Symmetric Filters

In linear system identification problems, it is important to reveal and exploit any specific intrinsic characteristic of the impulse responses, in order to improve the overall performance, especially in terms of the accuracy and complexity of the solution. In this paper, we focus on the nearest Kronecker product decomposition of the impulse responses, together with low-rank approximations. Such an approach is suitable for the identification of a wide range of real-world systems. Most importantly, we reformulate the system identification problem by using a particular symmetric filter within the development, which allows us to efficiently design two (iterative/recursive) algorithms. First, an iterative Wiener filter is proposed, with improved performance as compared to the conventional Wiener filter, especially in challenging conditions (e.g., small amount of available data and/or noisy environments). Second, an even more practical solution is developed, in the form of a recursive least-squares adaptive algorithm, which could represent an appealing choice in real-time applications. Overall, based on the proposed approach, a system identification problem that can be conventionally solved by using a system of L=L1L2 equations (with L unknown parameters) is reformulated as a combination of two systems of PL1 and PL2 equations, respectively, where usually P≪L2 (i.e., a total of PL1+PL2 parameters). This could lead to important advantages, in terms of both performance and complexity. Simulation results are provided in the framework of network and acoustic echo cancellation, supporting the performance gain and the practical features of the proposed algorithms.

Tensor-Based Recursive Least-Squares Adaptive Algorithms with Low-Complexity and High Robustness Features

The recently proposed tensor-based recursive least-squares dichotomous coordinate descent algorithm, namely RLS-DCD-T, was designed for the identification of multilinear forms. In this context, a high-dimensional system identification problem can be efficiently addressed (gaining in terms of both performance and complexity), based on tensor decomposition and modeling. In this paper, following the framework of the RLS-DCD-T, we propose a regularized version of this algorithm, where the regularization terms are incorporated within the cost functions. Furthermore, the optimal regularization parameters are derived, aiming to attenuate the effects of the system noise. Simulation results support the performance features of the proposed algorithm, especially in terms of its robustness in noisy environments.

Low-Complexity Recursive Least-Squares Adaptive Algorithm Based on Tensorial Forms

Modern solutions for system identification problems employ multilinear forms, which are based on multiple-order tensor decomposition (of rank one). Recently, such a solution was introduced based on the recursive least-squares (RLS) algorithm. Despite their potential for adaptive systems, the classical RLS methods require a prohibitive amount of arithmetic resources and are sometimes prone to numerical stability issues. This paper proposes a new algorithm for multiple-input/single-output (MISO) system identification based on the combination between the exponentially weighted RLS algorithm and the dichotomous descent iterations in order to implement a low-complexity stable solution with performance similar to the classical RLS methods.

High compression rate, based on the RLS adaptive algorithm in progressive image transmission

The purpose of this paper is to develop a novel method based on recursive least squares (RLS) adaptive algorithm for progressive image transmission (PIT). The image is divided into non-overlapping blocks. Having an agreed vector sequence between the transmitter and the receiver, each block is related to a regressive model. Meanwhile, at the transmitter the blocks are estimated using the RLS algorithm. The high correlation between error vectors, regarding to the RLS execution, causes a very high compression rate in their transmission. The error vectors at the receiver are used to run the RLS algorithm and to estimate the image in a same manner. The method is easy to implement with a low computational complexity and achieves high quality, compared to other well-known methods. In comparison with its counterparts, simulation results show how efficient the proposed method is.

Low Complexity Linear Channel Estimation for MIMO Communication Systems

Channel estimation is employed to get the current knowledge of channel states for an optimum detection in fading environments. In this paper, a new recursive multiple input multiple output (MIMO) channel estimation is proposed which is based on the recursive least square solution. The proposed recursive algorithm utilizes short training sequence on one hand and requires low computational complexity on the other hand. The algorithm is evaluated on a MIMO communication system through simulations. It is realized that the proposed algorithm provides fast convergence as compared to recursive least square (RLS) and robust variable forgetting factor RLS (RVFF-RLS) adaptive algorithms while utilizing lesser computational cost and provides independency on forgetting factor.

A family of sparse group Lasso RLS algorithms with adaptive regularization parameters for adaptive decision feedback equalizer in the underwater acoustic communication system

In this paper, we propose a family of sparse group Lasso (least absolute shrinkage and selection operator) Recursive Least Squares (RLS) algorithms for sparse underwater acoustic channel equalization. The proposed adaptive RLS algorithms employ a family of mixed norms, such as l1l2,1-norm, l1l∞,1-norm, l1l2,0-norm, l1l1,0-norm, l0l2,1-norm, l0l∞,1-norm, l0l2,0-norm, and l0l1,0-norm, as the sparsity constraint in the penalty function to exploit the sparsity of the underwater acoustic communication system. The proposed adaptive RLS algorithms can adaptively select the regularization parameters regardless of whether the channel of underwater acoustic channel is general sparse channel, group sparse channel or the mixed sparse channel consisting of general sparse channel and group sparse channel. Moreover, this paper presents a direct adaptive decision feedback equalizer (DA-DFE) that exploits any sparse channel structure with the proposed adaptive RLS algorithms in the lake and sea experiments. Experimental results verify that the DA-DFE receiver with the proposed family of sparse group Lasso RLS algorithms can achieve a better performance in terms of convergence rate, mean square deviation (MSD) and symbol error rate (SER) in the single-input single-output (SISO) single carrier underwater acoustic communication system.

VFF ‐norm penalised WL‐RLS algorithm using DCD iterations for underwater acoustic communication

Based on dichotomous coordinate descent (DCD) iterations and with the use of the variable forgetting factor (VFF), a widely linear (WL) l1-norm recursive least squares (RLS) adaptive filtering algorithm is proposed for sparse underwater acoustic channelequalization. In the proposed l1-norm WL-RLS algorithm with VFF, the WL model is employed to exploit the second order statistics of the non-circular signals and the VFF is employed to improve the tracking ability of the RLS algorithms. DCD iterations are incorporated in the proposed l1-norm WL-RLS-DCD algorithm with VFF to reduce the computing complexity. Moreover, the proposed algorithms are employed by the direct adaptive decision feedback equalizer (DA-DFE). Numerical results indicate that compared with the conventional RLS, l1-norm RLS, WL-RLS with VFF, l1-norm WL-RLS-DCD algorithms, the proposed algorithms achieve a better performance in terms of the convergence rate, mean square errorand symbol error ratein the DA-DFE receiver. Experimental results also show that the proposed algorithms can promote the DA-DFE receiver to obtain a better performance in the sparse time-varying underwater acoustic communication system. Even though the transmitted signals are circular quadrature phase-shift keying (QPSK) through the underwater acoustic channel, the proposed adaptive RLS algorithms can still obtain a better performance.

A Space-Time RLS Algorithm for Adaptive Equalization: The Camera Communication Case

This paper presents a novel space-time recursive least-squares adaptive algorithm, which performs filter coefficients updates in space and postponed filtering in time. The algorithm is used for intersymbol interference suppression in optical camera communications, which is a subgroup of visible light communication systems. Optical camera communications uses image sensor receivers, as those available in smartphones, tablets, and laptops, to detect changes in light intensity in order to allow data transmission. The achievable data transmission rate of optical camera communication systems is nowadays constrained by the frame-per-second rate achieved by those devices, so that the spatial dimension, e.g., multiple-input multiple-output techniques, are typically exploited. Spatial intersymbol interference could arise and image blurring can be an issue especially when the link distance grows and/or when the receiver is in mobility. We present here a semiblind spatial fractionally spaced equalizer that uses a novel space-time recursive least-square adaptive algorithm to counteracts the blur introduced by the optical channel. Numerical results show how the bit error rate can be drastically reduced in both motion and out-of-focus blur scenarios.

Muscle and Baseline Wander Artifact Reduction in ECG Signal Using Efficient RLS Based Adaptive Algorithm

When we acquiring the Electrocardiogram (ECG) signal from the person, the signal amplitude (PQRST) and timing values are changes due to various artefacts. The different artefacts are Baseline wander, power line interference, muscle artefact, motion artefact and the channel noise also added sometimes during the transmission of the signal for diagnosis purpose. The adaptive filters play vital role for reduction of noise in the desired signals. In this paper we proposed, block based error normalized Recursive Least Square (RLS) adaptive algorithm and sign based RLS adaptive algorithm, which are used for reduction of muscle artifact noise and base line wander noise in the ECG signal. From the simulation result we analyzed that, comparing to Least Mean Square algorithm, the proposed RLS algorithm gives fast convergence rate with high signal to noise ratio and less mean square error. Index Terms—RLS Adaptive algorithms, Signal to noise ratio, artifacts, mean square error, ECG signal.

An RLS Tracking and Iterative Detection Engine for Mobile MIMO-OFDM Systems

This paper presents a tracking and detection engine for 2 $\times$ 2 spatial-multiplexing multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems under highly time-selective fading channels. A recursive least-squares (RLS) adaptive algorithm is adopted to track time-varying channel frequency response. Besides, iterative MIMO signal detection is used, including inter-carrier interference (ICI) cancellation, to enhance system performance. To avoid error propagation in the decision-directed RLS adaptation, ordered-selection mechanism and signal strength criteria are incorporated so that more reliable detection results can be selected for calculating channel statistics. The scheduling strategies and hardware reduction techniques are proposed for implementation of the computation-intensive RLS adaptive algorithm and ICI cancellation. This baseband processor has been fabricated in 90 nm CMOS technology and has 1023K gates. At the nominal operating frequency of 15.36 MHz, it provides throughput of 76.8 Mbps with 64-QAM up to 240 Km/hr. For constellation of 16-QAM and QPSK, the mobility of 360 Km/hr is supported. The power consumption is 11.8 mW at 0.7 V supply voltage. The operating frequency can be raised up to 103 MHz to offer 515 Mbps throughput with power consumption of 202 mW at 1.2V.

The Use of LMS and RLS Adaptive Algorithms for an Adaptive Control Method of Active Power Filter

This paper deals with the adaptive control mechanism management meant for shunt active power filters (SAPF). Systems driven this way are designed to improve the quality of electric power (power quality) in industrial networks. The authors have focused on the implementation of two basic representatives of adaptive algorithms, first, the algorithm with a stochastic LMS (least mean square) gradient adaptation and then an algorithm with recursive RLS (recursive least square) optimal adaptation. The system examined by the authors can be used for non-linear loads for appliances with rapid fluctuations of the reactive and active power consumption. The proposed system adaptively reduces distortion, falls (dip) and changes in a supply voltage (flicker). Real signals for measurement were obtained at a sophisticated, three-phase experimental workplace. The results of executed experiments indicate that, with use of the certain adaptive algorithms, the examined AHC system shows very good dynamics, resulting in a much faster transition during the AHC connection-disconnection or during a change in harmonic load on the network. The actual experiments are evaluated from several points of view, mainly according to a time convergence (convergence time) and mistakes in a stable state error (steady state error) of the investigated adaptive algorithms and finally as a total harmonic distortion (THD). The article presents a comparison of the most frequently used adaptive algorithms.

Recursive Least-Squares Source Tracking using One Acoustic Vector Sensor

An acoustic vector-sensor (a.k.a. vector-hydrophone) is composed of three acoustic velocity-sensors, plus a collocated pressure-sensor, all collocated in space. The velocity-sensors are identical, but orthogonally oriented, each measuring a different Cartesian component of the three-dimensional particle-velocity field. This acoustic vector-sensor offers an azimuth-elevation response that is invariant with respect to the source's center frequency or bandwidth. This acoustic vector-sensor is adopted here for recursive least-squares (RLS) adaptation, to track a single mobile source, in the absence of any multipath fading and any directional interference. A formula is derived to preset the RLS forgetting factor, based on the prior knowledge of only the incident signal power, the incident source's spatial random walk variance, and the additive noise power. The work presented here further advances a multiple-forgetting-factor (MFF) version of the RLS adaptive tracking algorithm, that requires no prior knowledge of these aforementioned source statistics or noise statistics. Monte Carlo simulations demonstrate the tracking performance and computational load of the proposed algorithms.

Performance Comparison of STFT, WT, LMS and RLS Adaptive Algorithms in Denoising of Speech Signal

Different types of noise cancellation techniques are prevalent in recent literatures. The performance of a particular technique depends on mean, variance and maximum amplitude of error. At the same time the process time of signal and complexity of practical implementation of circuits is also a measuring tool for performance of a technique. The objective of this paper is to compare performance among the short time Fourier transform (STFT), wavelet transform (WT), least mean square (LMS) and recursive least square (RLS) methods in cancellation of noise from a speech signal. The analysis of the paper provides us the way of selection of the best denoising technique based on the statistical parameters of the above four mentioned techniques. Index Terms—Signal denoising, CPU time, statistical parameters of adaptive filter, wavelet transform, short-time Fourier transform, least mean square and recursive least square.

Sparsity regularised recursive least squares adaptive filtering

The authors propose a new approach for the adaptive identification of sparse systems. This approach improves on the recursive least squares (RLS) algorithm by adding a sparsity inducing weighted l 1 norm penalty to the RLS cost function. Subgradient analysis is utilised to develop the recursive update equations for the calculation of the optimum system estimate, which minimises the regularised cost function. Two new algorithms are introduced by considering two different weighting scenarios for the l 1 norm penalty. These new l 1 relaxation-based RLS algorithms emphasise sparsity during the adaptive filtering process, and they allow for faster convergence than standard RLS when the system under consideration is sparse. The authors test the performance of the novel algorithms and compare it with standard RLS and other adaptive algorithms for sparse system identification.

Use of adaptive RLS, LMS, and NLMS algorithms for nonlinearity modeling in a modified laser interferometer

Laser heterodyne interferometer is one kind of nano-metrology systems which has been widely used in industry for high-accuracy displacement measurements. The accuracy of the nano-metrology systems based on the laser heterodyne interferometers can be effectively limited by the periodic nonlinearity. In this paper, we present the nonlinearity modeling of the nano-metrology interferometric system using some adaptive filters. The adaptive algorithms consist of the least mean squares (LMS), normalized least mean squares (NLMS), and recursive least squares (RLS). It is shown that the RLS algorithm can obtain optimal modeling parameters of nonlinearity.

Adaptive reduced-rank LCMV beamforming algorithms based on joint iterative optimization of filters: Design and analysis

This paper presents reduced-rank linearly constrained minimum variance (LCMV) beamforming algorithms based on joint iterative optimization of filters. The proposed reduced-rank scheme is based on a constrained joint iterative optimization of filters according to the minimum variance criterion. The proposed optimization procedure adjusts the parameters of a projection matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe LCMV expressions for the design of the projection matrix and the reduced-rank filter. We then describe stochastic gradient and develop recursive least-squares adaptive algorithms for their efficient implementation along with automatic rank selection techniques. An analysis of the stability and the convergence properties of the proposed algorithms is presented and semi-analytical expressions are derived for predicting their mean squared error (MSE) performance. Simulations for a beamforming application show that the proposed scheme and algorithms outperform in convergence and tracking the existing full-rank and reduced-rank algorithms while requiring comparable complexity.

Recursive and Fast Recursive Capon Spectral Estimators

The Capon algorithm, which was originally proposed for wavenumber estimation in array signal processing, has become a powerful tool for spectral analysis. Over several decades, a significant amount of research attention has been devoted to the estimation of the Capon spectrum. Most of the developed algorithms thus far, however, rely on the direct computation of the inverse of the input correlation (or covariance) matrix, which can be computationally very expensive particularly when the dimension of the matrix is large. This paper deals with fast and efficient algorithms in computing the Capon spectrum. Inspired from the recursive idea established in adaptive signal processing theory, we first derive a recursive Capon algorithm. This new algorithm does not require an explicit matrix inversion, and hence it is more efficient to implement than the direct-inverse approach. We then develop a fast version of the recursive algorithm based on techniques used in fast recursive least-squares adaptive algorithms. This new fast algorithm can further reduce the complexity of the recursive Capon algorithm by an order of magnitude. Although our focus is on the Capon spectral estimation, the ideas shown in this paper can also be generalized and applied to other applications. To illustrate this, we will show how to apply the recursive idea to the estimation of the magnitude squared coherence function, which plays an important role for problems like time-delay estimation, signal-to-noise ratio estimation, and doubletalk detection in echo cancellation.

A research of UWB rake receiver based on novel RLS adaptive algorithm

A modified RAKE receiver based on novel Recursive Least Squares (RLS) adaptive algorithm is proposed. The receiver uses L-fingered correlators, which are composed of RLS adaptive filters, to enhance the performance of multipath receiving. It can also track the amplitude of the received signal to form a real-time amplitude estimation which is correlated with the power of excess delay bin. The simulation results based on the IEEE UltraWide Band (UWB) channel models (CM1 to CM4) show that the novel RLS algorithm can alter the attenuation estimation with the finger’s power delay profile, and RAKE receiver with few fingers can be employed to get high performance.

Using a fast RLS adaptive algorithm for efficient speech processing

In this paper, a new method is presented that offers efficient computation of Linear Prediction Coefficients (LPC) via a new Recursive Least Squares (RLS) adaptive filtering algorithm. This method can be successfully used in speech coding and processing. The introduced algorithm is numerically robust, fast, parallelizable and has particularly good tracking properties. By means of this scheme, Linear Prediction Coefficients are obtained that offer an improvement in the reconstruction of the speech signal before coding, as compared to the signal obtained by various classical algorithm. An analogous improvement is observed in speech coding experiments too, while a subjective test confirms the improvement of the quality of synthesized speech. The overall processing time of the proposed method of speech coding is a bit greater, but comparable to the time the classical methods need.