NLMS Algorithm Research Articles

Set-Membership NLMS Algorithm With Robust Error Bound

A new robust error bound for the set-membership normalized least mean square (SMNLMS-REB) is proposed in this brief. The new robust set-membership error bound leads to improved robustness against impulsive noise and steady-state misalignment relative to those achieved in the set-membership normalized least mean square (SMNLMS) algorithm. Stability analysis shows that the proposed algorithm is stable. Using the individual weight error variance (IWV) analysis method, new expressions for the steady-state mean square deviation (MSD) of the SMNLMS-REB are also obtained. Simulation results on system identification show that the robustness and probability of the update (PU) of the proposed SMNLMS-REB considerably outperform the traditional SMNLMS and other robust set-membership NLMS algorithms in the presence of impulsive noise.

Study of Different Adaptive Filter Algorithms for Noise Cancellation in Real-Time Environment

Adaptive filters are used in the situation where the filter coefficients have to be changed simultaneously according to the requirement. Adaptive filters are needed for fast convergence rate and low mean square error. Many algorithms have been proposed and proved that they have better convergence speed and tracking abilities. This paper shows the ability of adaptive filter for noise cancellation i.e., estimating the desired speech corrupted by unwanted signal i.e., noise. This paper is going to compare the performance of adaptive algorithms for noise cancellation in real time signals like recorded speech with different background noise. In the existing papers the authors have taken the input signal as sinusoidal signal etc. In order to measure the performance step size is the main factor for the convergence speed and mean square error. Many analyses proved that RLS algorithm had faster convergence speed and smaller steady state error compared with basic LMS algorithm and normalized LMS algorithm (NLMS). The existing simulation results enable to measure the performance of filter and show the convergence speed improvement when using RLS algorithm, NLMS algorithm and LMS algorithm.

Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian Inputs

This paper studies the stochastic behavior of the LMS and NLMS algorithms for a system identification framework when the input signal is a cyclostationary white Gaussian process. The input cyclostationary signal is modeled by a white Gaussian random process with periodically time-varying power. Mathematical models are derived for the mean and mean-square-deviation (MSD) behavior of the adaptive weights with the input cyclostationarity. These models are also applied to the non-stationary system with a random walk variation of the optimal weights. Monte Carlo simulations of the two algorithms provide strong support for the theory. Finally, the performance of the two algorithms is compared for a variety of scenarios.

Stable adaptive sparse filtering algorithms for estimating multiple‐input–multiple‐output channels

Channel estimation problem is one of the key technical issues for broadband multiple-input-multiple-output (MIMO) signal transmission. To estimate the MIMO channel, a standard least mean square (LMS) algorithm was often applied to adaptive channel estimation because of its low complexity and stability. The sparsity of the broadband MIMO channel can be exploited to further improve the estimation performance. This observation motivates us to consider adaptive sparse channel estimation (ASCE) methods using sparse LMS (ASCE-LMS) algorithms. However, conventional ASCE methods have two main drawbacks: (i) sensitivity to random scaling of training signal and (ii) poor estimation performance in low signal-to-noise ratio (SNR) regime. The former drawback is tackled by proposing novel ASCE-NLMS algorithms. ASCE-NLMS mitigates interference of random scale of training signal and therefore it improves its algorithm stability. It is well-known that stable sparse normalised least-mean fourth (NLMF) algorithms can achieve better estimation performance than sparse NLMS algorithms. Therefore the authors propose an improved ASCE method using sparse NLMF algorithms (ASCE-NLMF) to improve the estimation performance in low SNR regime. Simulation results show that the proposed ASCE methods are shown to achieve better performance than conventional methods, that is, ASCE-LMS by computer simulations. Also, the stability of the proposed methods is confirmed by theoretical analysis.

Removal of Power Line Interference in ECG Signal by Adaptive LMS, NLMS and RLS Algorithms

Removal of Power Line Interference in ECG Signal by Adaptive LMS, NLMS and RLS Algorithms

Adaptive combination of affine projection and NLMS algorithms

We propose a novel scheme for combining two adaptation terms of affine projection algorithms with different projection orders and step-sizes. The selection of the mixing parameter that determines the performance of the proposed combination scheme is derived by the largest decrease of the mean-square deviation. The experimental results show that the proposed algorithm exhibits a fast convergence speed and a small steady-state misalignment. Moreover, the proposed algorithm achieves a low computational complexity in the steady-state.

Design and complexity analysis of an improved adaptive filtering algorithm for non-sparse impulse response

An improved adaptive filtering (IMPNLMS+) algorithm has been proposed for non-sparse impulse responses by incorporating an adaptive parameter μ of the μ-law compression into the improved μ-law PNLMS algorithm (IMPNLMS) algorithm. It not only achieves optimal step-size control factors but also overcomes that the convergence of classical μ-law PNLMS (MPNLMS) is even slower than conventional NLMS algorithm for dispersive channels. In this paper, we propose IMPNLMS++ algorithm, where normalized algorithm is analyzed to reduce computational complexity of proposed improved μ-law PNLMS (IMPNLMS+) algorithm. The validity has been proved by the simulation results.

An Efficient Adaptive Filtering Scheme Based on Combining Multiple Metrics

SUMMARY We propose a novel adaptive filtering scheme named metric-combining normalized least mean square (MC-NLMS). The proposed scheme is based on iterative metric projections with a metric designed by combining multiple metric-matrices convexly in an adaptive manner, thereby taking advantages of the metrics which rely on multiple pieces of information. We compare the improved PNLMS (IPNLMS) algorithm with the natural proportionate NLMS (NPNLMS) algorithm, which is a special case of MC-NLMS, and it is shown that the performance of NPNLMS is controllable with the combination coefficient as opposed to IPNLMS. We also present an application to an acoustic echo cancellation problem and show the efficacy of the proposed scheme.

Variable is better than invariable: sparse VSS-NLMS algorithms with application to adaptive MIMO channel estimation.

Channel estimation problem is one of the key technical issues in sparse frequency-selective fading multiple-input multiple-output (MIMO) communication systems using orthogonal frequency division multiplexing (OFDM) scheme. To estimate sparse MIMO channels, sparse invariable step-size normalized least mean square (ISS-NLMS) algorithms were applied to adaptive sparse channel estimation (ACSE). It is well known that step-size is a critical parameter which controls three aspects: algorithm stability, estimation performance, and computational cost. However, traditional methods are vulnerable to cause estimation performance loss because ISS cannot balance the three aspects simultaneously. In this paper, we propose two stable sparse variable step-size NLMS (VSS-NLMS) algorithms to improve the accuracy of MIMO channel estimators. First, ASCE is formulated in MIMO-OFDM systems. Second, different sparse penalties are introduced to VSS-NLMS algorithm for ASCE. In addition, difference between sparse ISS-NLMS algorithms and sparse VSS-NLMS ones is explained and their lower bounds are also derived. At last, to verify the effectiveness of the proposed algorithms for ASCE, several selected simulation results are shown to prove that the proposed sparse VSS-NLMS algorithms can achieve better estimation performance than the conventional methods via mean square error (MSE) and bit error rate (BER) metrics.

Adaptive Signal Processing for Improvement of Convergence Characteristics of FIR Filter

When the length of the filter and consequently the number of filter coefficients increase, the design of the filter becomes complex and therefore the popular NLMS algorithm has been replaced with MMax NLMS algorithm. But its performance in terms of convergence characteristics reduces to an extent though the filter design becomes very easy i.e., convergence occurs at a later stage taking too much computational time for the processing of the signal. In this paper, a proposal for improving the convergence characteristics is made without compromising the performance of the design and affecting the tap-selection process of the MMax NLMS algorithm. With the introduction of the concept of variable step-size for the filter coefficients, loss in the performance due to MMax NLMS algorithm can be effectively lowered and the convergence is better achieved in the filter deign.

Adaptive sparse system identification using normalized least mean fourth algorithm

SUMMARYNormalized least mean square (NLMS) was considered as one of the classical adaptive system identification algorithms. Because most of systems are often modeled as sparse, sparse NLMS algorithm was also applied to improve identification performance by taking the advantage of system sparsity. However, identification performances of NLMS type algorithms cannot achieve high‐identification performance, especially in low signal‐to‐noise ratio regime. It was well known that least mean fourth (LMF) can achieve high‐identification performance by utilizing fourth‐order identification error updating rather than second‐order. However, the main drawback of LMF is its instability and it cannot be applied to adaptive sparse system identifications. In this paper, we propose a stable sparse normalized LMF algorithm to exploit the sparse structure information to improve identification performance. Its stability is shown to be equivalent to sparse NLMS type algorithm. Simulation results show that the proposed normalized LMF algorithm can achieve better identification performance than sparse NLMS one. Copyright © 2013 John Wiley & Sons, Ltd.

Performance analysis of the selective coefficient update NLMS algorithm in an undermodeling situation

The selective coefficient update normalized least mean-square (SCU-NLMS) algorithm was proposed to reduce computational complexity while preserving close performance to the full-update NLMS algorithm, which brought it a lot of attention. In practical applications, the length of the unknown system impulse response is not known and, therefore, the length of the adaptive filter can be less than that of the unknown system particularly in situations when the unknown system impulse response is long. In all existing analysis of the SCU-NLMS algorithm, exact modeling of the unknown system is assumed, i.e., the length of the adaptive filter is equal to that of the unknown system impulse response. In this paper, we present mean-square performance analysis for the SCU-NLMS algorithm in an undermodeling situation and assuming independent and identically distributed (i.i.d.) input signals. The analysis model takes into account order statistics employed in the SCU-NLMS algorithm leading to accurate transient and steady state theoretical results. Analysis extends easily to the exact modeling case where expressions quantifying the algorithm mean-square performance are presented and shown to be more accurate than the ones reported in the literature. Simulation experiments validate the accuracy of the theoretical results in predicting the actual behavior of the algorithm.

FPGA IMPLEMENTATION OF OPTIMAL STEP SIZE NLMS ALGORITHM AND ITS PERFORMANCE ANALYSIS

The Normalized Least Mean Square error (NLMS) algorithm is most popular due to its simplicity. The conflicts of fast convergence and low excess mean square error associated with a fixed step size NLMS are solved by using an optimal step size NLMS algorithm. The main objective of this paper is to derive a new nonparametric algorithm to control the step size and also the theoretical performance analysis of the steady state behavior is presented in the paper. The simulation experiments are performed in Matlab. The simulation results show that the proposed algorithm as superior performance in Fast convergence rate, low error rate, and has superior performance in noise cancellation. Index Terms: Least Mean square algorithm (LMS), Normalized least mean square algorithm (NLMS)

Evaluating and comparing algorithms for respiratory motion prediction

In robotic radiosurgery, it is necessary to compensate for systematic latencies arising from target tracking and mechanical constraints. This compensation is usually achieved by means of an algorithm which computes the future target position. In most scientific works on respiratory motion prediction, only one or two algorithms are evaluated on a limited amount of very short motion traces. The purpose of this work is to gain more insight into the real world capabilities of respiratory motion prediction methods by evaluating many algorithms on an unprecedented amount of data. We have evaluated six algorithms, the normalized least mean squares (nLMS), recursive least squares (RLS), multi-step linear methods (MULIN), wavelet-based multiscale autoregression (wLMS), extended Kalman filtering, and ε-support vector regression (SVRpred) methods, on an extensive database of 304 respiratory motion traces. The traces were collected during treatment with the CyberKnife (Accuray, Inc., Sunnyvale, CA, USA) and feature an average length of 71 min. Evaluation was done using a graphical prediction toolkit, which is available to the general public, as is the data we used. The experiments show that the nLMS algorithm—which is one of the algorithms currently used in the CyberKnife—is outperformed by all other methods. This is especially true in the case of the wLMS, the SVRpred, and the MULIN algorithms, which perform much better. The nLMS algorithm produces a relative root mean square (RMS) error of 75% or less (i.e., a reduction in error of 25% or more when compared to not doing prediction) in only 38% of the test cases, whereas the MULIN and SVRpred methods reach this level in more than 77%, the wLMS algorithm in more than 84% of the test cases. Our work shows that the wLMS algorithm is the most accurate algorithm and does not require parameter tuning, making it an ideal candidate for clinical implementation. Additionally, we have seen that the structure of a patient’s respiratory motion trace has strong influence on the outcome of prediction. Further work is needed to determine a priori the suitability of an individual’s respiratory behaviour to motion prediction.

A New Learning Algorithm Based on MCC for Colored Noise Interference Cancellation

In view of the defect of adaptive filtering algorithm based on the LMS in colored noise interference cancellation, we put forward a kind of new adaptive iterative learning algorithm using correntropy and Maximum Correntropy Criterion (MCC). The MCC and the gradient descent algorithm are used to update the weights of filter. The proposed algorithm can obtain an optimal factor of step length μ(k) from the square error of angle to undertake an analysis, and in order to illustrate the feasibility of the algorithm, the convergence of the algorithm from the sequence of the convergence in norm were analyzed. At the same time, a step-size control parameters was introduced in the algorithm, according to the parameters set constant values or variable values, the algorithm is defined as NC-MCC (Normalized Constant-MCC) and NV-MCC (Normalized Variable-MCC). The simulation results show that, in the signal adding the colored noise, compared with NLMS algorithm, the proposed algorithm is better and has good stability.

Use of passive hearing protectors and adaptive noise reduction for field recording of otoacoustic emissions in industrial noise

Distortion product otoacoustic emissions (DPOAEs) can detect noise-induced hearing loss in-field, but their data extraction is very sensitive to background noise. This paper investigates how passive and active noise reduction enhance DPOAE recording based on data collected in white noise from 54 dB(A) to 90 dB(A). Despite considerable high-frequency attenuation from a proper placed DPOAE probe, 54 dB(A) background noise deteriorates the test outcome substantially. More low-frequency attenuation by an extra passive earmuff enables measurements in white noise levels of 70 dB(A). The relationship between external sound level and noise recorded by the DPOAE system has been statistically modeled. Additionally, the upper limits of attenuation improvement are analyzed by quantifying residual physiological noise. Furthermore, for an earplug integrating microphone and speakers of the DPOAE measurement probe, adaptive noise reduction processing on the DPOAE signal is used to improve the signal-to-noise ratio. The adaptive noise reduction (ANR) is implemented using the NLMS algorithm to filter out the ambient noise, measured by the first microphone measuring the DPOAE signal, with a second miniature microphone mounted flush with the external faceplate of the isolating DPOAE probe. Simulated data show that DPOAE response extraction is possible in an environment with noise levels exceeding 70 dB(A).

Robust Auxiliary-Noise-Power Scheduling in Active Noise Control Systems With Online Secondary Path Modeling

This paper deals with the auxiliary noise-based methods for active noise control (ANC) systems with online secondary path modeling (SPM). The proposed method comprises two adaptive filters: the modified Filtered-X normalized least-mean-square algorithm-based ANC filter, and the normalized least-mean-square algorithm-based SPM filter excited by auxiliary noise. The auxiliary noise injected for online SPM, degrades the noise-reduction performance of the ANC system. A two-stage gain scheduling strategy is proposed to vary power of the auxiliary noise. In the first stage the gain is varied on the basis of power of the error signal of SPM filter, and in the second stage the gain is varied on the basis of the correlation estimate of the two adjacent samples of the error signal of SPM filter. The main idea is to inject large-power auxiliary noise at the start up or when a change in the acoustic paths is detected, and to reduce the power as the system converges. The proposed method achieves a fast convergence of the SPM filter and gives a robust performance in the presence of strong perturbation in acoustic paths. Furthermore, the proposed method improves the noise-reduction performance at steady-state even in the presence of an uncorrelated disturbance at the error microphone. Moreover, the improved performance is achieved at a lower computational cost as compared with a recent method proposed in [A. Carini, and S. Malatini, “Optimal variable step-size NLMS algorithms with auxiliary noise power scheduling for feedforward active noise control,”IEEE Trans. Audio, Speech Lang. Process., vol. 16, no. 8, pp. 1383-1395, Nov. 2008]. Extensive simulations are carried out to verify the effectiveness of the proposed method.

Area Optimized Adaptive Noise Cancellation System Using FPGA for Ultrasonic NDE Applications

This paper describes a method for noise removal from ultrasonic signals used in NDE (Non Destructive Evaluation) applications. The method used is FPGA based adaptive noise cancellation. Indeed adaptive filtering is one of the core technologies in digital signal processing. We can find numerous application areas in science as well as in industry. Adaptive filtering techniques are used in a wide range of applications, including system identification, adaptive equalization, adaptive noise cancellation and echo cancellation. Characteristics of signals that are generated by systems of the above application are not known a priori. Under this condition, a significant improvement in performance can be achieved by using adaptive rather than fixed filters. An adaptive filter is a self-designing filter that uses a recursive algorithm (known as adaptation algorithm or adaptive filtering algorithm) to design itself. Here the algorithm used is normalized least mean square algorithm, which has good convergence and stability. Keywords; Adaptive noise cancellation, NLMS algorithm, NDE applications, ultrasonic grain noise.

Comparison of Power System Harmonic Prediction

Abstract Due to the advance in technology nowadays the application of nonlinear load is very demanding. The nonlinear loads that consist of power electronics devices in many applications may leads to power quality problems, and one of the major problems in power quality is harmonics. Active filter is a common tool has been used for harmonic mitigation, however the active filter use digital signal processing (DSP) to calculate the harmonic information which cause time delay between measured and injected harmonic that can results in failure to fully cancel the harmonics. This paper presents the concept, method and function of adaptive filters using Least Mean Square (LMS) and Recursive Least Square (RLS) to predict real time harmonics that may use in active filter to compensate for the time delay caused by the process of acquiring harmonic information. The results shown that the RLS and NLMS algorithms present a better performance than LMS and the mean square error (MSE) in general is increased when the harmonic order numbers that construct the signal increases.

Efficient adaptive identification of linear-in-the-parameters nonlinear filters using periodic input sequences

This paper introduces computationally efficient NLMS and RLS adaptive algorithms for identifying non-recursive, linear-in-the-parameters (LIP) nonlinear systems using periodic input sequences. The algorithms presented in the paper are exact and require a real-time computational effort of a single multiplication, an addition and a subtraction per input sample. The transient, steady state, and tracking behavior of the algorithms as well as the effect of model mismatch is studied in the paper. The low computational complexity, good performance and broad applicability make the approach of this paper a valuable alternative to the current techniques for nonlinear system identification.