Normalized LMS Algorithm Research Articles

An acoustic echo canceller optimized for hands-free speech telecommunication in large vehicle cabins

Acoustic echo cancelation (AEC) is a system identification problem that has been addressed by various techniques and most commonly by normalized least mean square (NLMS) adaptive algorithms. However, performing a successful AEC in large commercial vehicles has proved complicated due to the size and challenging variations in the acoustic characteristics of their cabins. Here, we present a wideband fully linear time domain NLMS algorithm for AEC that is enhanced by a statistical double-talk detector (DTD) and a voice activity detector (VAD). The proposed solution was tested in four main Volvo truck models, with various cabin geometries, using standard Swedish hearing-in-noise (HINT) sentences in the presence and absence of engine noise. The results show that the proposed solution achieves a high echo return loss enhancement (ERLE) of at least 25 dB with a fast convergence time, fulfilling ITU G.168 requirements. The presented solution was particularly developed to provide a practical compromise between accuracy and computational cost to allow its real-time implementation on commercial digital signal processors (DSPs). A real-time implementation of the solution was coded in C on an ARM Cortex M-7 DSP. The algorithmic latency was measured at less than 26 ms for processing each 50-ms buffer indicating the computational feasibility of the proposed solution for real-time implementation on common DSPs and embedded systems with limited computational and memory resources. MATLAB source codes and related audio files are made available online for reference and further development.

Multikernel adaptive filtering over graphs based on normalized LMS algorithm

To address the difficulty and inflexibility associated with choosing kernel parameters for single kernel adaptive filters (KAFs), this article proposes a multikernel adaptive filter for graph signals based on the least mean square (LMS) algorithm. First, normalized by its largest eigenvalue, the combinatorial graph Laplacian is adopted as the graph shift operator (GSO) to preprocess graph input signals. Then, the graph multikernel normalized least mean square (GMKNLMS) algorithm is developed to estimate nonlinear graph filter coefficients. To limit the growth in dictionary size, a coherence-check (CC) based sparsification method is introduced to form the new GMKNLMS-CC algorithm. In addition, numerical simulation examples are presented to demonstrate the improved performance of the proposed algorithms compared with the linear graph least mean square (GLMS) and graph kernel normalized least mean square (GKNLMS) algorithms. Finally, the real sensor measurement data taken from the Intel Lab is used as time-varying graph signals to demonstrate the tracking performance of the GMKNLMS-CC algorithm.

Single line noise cancellation using derivative of normalized least mean square algorithm

Suppression of noise in noisy speech signal is required in many speech enhancement applications like signal recording and transmission from one place to other. In this paper a novel single line noise cancellation system is proposed using derivative of normalized least mean spare algorithm. The proposed system has two phases. The first phase is generation of secondary reference signal from incoming primary signal itself at initial silence period and pause between two words, which is essential while adaptive filter using as noise canceller. Second phase is noise cancellation using proposed modified error data normalized step size algorithm. The performance of the proposed algorithm is compared with normalized least mean square (NLMS) algorithm and original error data normalized step size (EDNSS) algorithm using standard IEEE sentence (SP23) of Noizeus data base with different types of real world noise at different level of signal to noise ratio (SNR). The output of proposed, NLMS and EDNSS algorithm are measured with output SNR, excessive mean square error (EMSE) and misadjustment (M). The results clearly illustrates that the proposed algorithm gives improved result over conventional NLMS and EDNSS algorithm. The speed of convergence is also maintained as same conventional NLMS algorithm.

Digital Self-Interference Cancellation for Full-Duplex UAV Communication System over Time-Varying Channels

Full-duplex unmanned aerial vehicle (UAV) communication systems are characterized by mobility, so the self-interference (SI) channel characteristics change over time constantly. In full-duplex UAV communication systems, the difficulty is to eliminate SI in time-varying channels. In this paper, we propose a pilot-aid digital self-interference cancellation (SIC) method. First, the pilot is inserted into the data sequence uniformly, and the time-varying SI is modeled as a linear non-causal function. Then, the time-varying SI channel is estimated by the discrete prolate spheroidal basis expansion model (BEM). The error of block edge channel estimation is reduced by cross-block interpolation. The result of channel estimation is convolved with the transmitted data to obtain the reconstructed SI, which is subtracted from the received signal to achieve SIC. The simulation results show that the SIC performance of the proposed method outperforms the dichotomous coordinate descent recursive least square (DCD-RLS) and normalized least mean square (NLMS) algorithms. When the interference to noise ratio (INR) is 25 dB, the performance index normalized least mean square (NMSE) is reduced by 5.5 dB and 4 dB compared with DCD-RLS and NLMS algorithms, which can eliminate SI to the noise floor, and the advantage becomes more obvious as the INR increases.

Recursive Least Squares-Algorithm-Based Normalized Adaptive Minimum Symbol Error Rate Equalizer

The adaptive minimum symbol error rate (AMSER) equalizer is known to have better symbol error rate (SER) performance than the adaptive minimum mean square error equalizer. Furthermore, the normalized AMSER (NAMSER) equalizer outperforms the AMSER equalizer, which can be regarded as the improvement of the normalized least mean square (NLMS) equalizer by incorporating the minimum SER (MSER) criterion. Inspired by that, we propose an improved recursive least squares-based NAMSER equalizer (RLS-NAMSER) that takes the advantage of faster convergence of the RLS algorithm over the NLMS algorithm. The RLS algorithm is first reconsidered from the perspective of optimization problem and an approximate RLS (ARLS) algorithm is proposed which converges faster than the NLMS algorithm. The RLS-NAMSER equalizer is then proposed by combining the ARLS equalizer with the MSER criterion. Simulation results show that the RLS-NAMSER equalizer has better convergence performance than the NAMSER equalizer while having nearly the same steady state performance as the NAMSER equalizer.

Coefficients-Switched Normalized Least-Mean- Squares Adaption in Echo Canceler of Sparse-Echo-Path

The Normalized Least-Mean-Squares (NLMS) algorithm commonly used in echo cancelers suffers from a number of limitations due to the existing sparsity in the echo path. Although some sparsity-aware algorithms have been proposed, the high computational complexity greatly increases the their difficulty of implementation. To reduce the complexity and improve the performance in echo cancelers, we introduce a Coefficients-Switched (CS) processing into the NLMS algorithm and propose the CS-NLMS algorithm and the Mean-square-deviation (MSD) analysis to evaluate its effectiveness. Simulations of the MSD were performed with different system parameters. The performance of the proposed algorithm is verified by comparison with the simulation results of the previously proposed algorithms. The superiority of the proposed algorithm in terms of computational complexity is also discussed.

Diffusion Bayesian Decorrelation Algorithms Over Networks

The convergence rate of the diffusion normalized least mean squares (NLMS) algorithm can be speeded up by decorrelation of signals. However, the diffusion decorrelation NLMS algorithm confronts the conflicting requirements of fast convergence rate and small steady-state error. To address the issue, this paper proposes a family of diffusion Bayesian decorrelation least mean squares (DBDLMS) algorithms based on decorrelated observation models. Firstly, the weight update equations of the proposed DBDLMS algorithms are obtained by performing Bayesian inference over the decorrelated observation models, with variable step-sizes emerging naturally to help address the conflicting requirement. Secondly, the update equations of the decorrelation coefficient vectors are inferred from the Bayesian perspective, with the variable step-sizes emerging again. Subsequently, the performance analysis of the proposed DBDLMS algorithms is carried out. Moreover, a simple and effective approach is derived to estimate the free parameters for the proposed DBDLMS algorithms. Finally, the learning performance of the proposed algorithms are verified by Monte Carlo simulations.

Pedestrian mobility management for heterogeneous networks

<p>Pending the arrival of the next generation of 5G which is not yet deployed in<br />some countries like Algeria, 4G LTE remains one of the main mobile networks to ensure adequate quality services. Mostly, the deployment of femtocells to support the macrocell structure is crucial in the handover decision process. This paper presents a new approach called the epsilon Kalman Filter with normalized least-mean-square (ϵKFNLMS) to realize the handoff triggering in two-tier long-term evolution networks to ensure communication continuity to the pedestrian UE and improve mobility management. ϵKFNLMS uses a two-step process: a tracking process and a prediction process, to produce an optimal future state estimate at ”t+p”, where ”p” is the prediction footstep. The tracking process is performed by the Kalman filter, known for its precision in the state of the signal at time ”t”. It perfectly reduces the estimation error, injected afterward in the variable step-size NLMS algorithm (VSS-NLMS). While the prediction<br />process is performed by the VSS-NLMS algorithm, an adaptive filter<br />known for its prediction of the future state at ”t+p”. Thus, the goal is to achieve a faster convergence with a steady-state. ϵ value provides a precise setting of the handover trigger. Through different numerical simulations in several indoor environments, the results show that the performance and effectiveness of the proposed approach (ϵKFNLMS) provide lower mean square error (MSE), stable physical appearance in the prediction process (convergence with a steady-state), and excellent speed of convergence compared to the classical Normalized LMS (NLMS) and Li-NLMS adaptive filters.</p>

An efficient normalized LMS algorithm

An efficient normalized LMS algorithm

Robust NLMS algorithms with combined step-size against impulsive noises

In the presence of impulsive noises, the normalized least mean M-estimate (NLMM) algorithm has behaved better robustness and convergence than the normalized least mean square (NLMS) algorithm. In order to further solve the trade-off of the NLMM algorithm between convergence rate and steady-state misadjustment, we design a combined step-size (CSS) scheme that combines large and small step-sizes through an adaptive mixing factor, and the resulting CSS-NLMM algorithm obtains fast convergence and low steady-state misadjustment simultaneously. Importantly, the proposed CSS scheme can be straightforwardly extended to other robust NLMS algorithms. Moreover, the performance analysis of the CSS-NLMM algorithm is provided. Simulation results in impulsive noises have supported the effectiveness of the proposed CSS-NLMM algorithm and its performance analysis.

A two-gain NLMS algorithm for sparse system identification

This paper introduces a modified normalized least-mean-square (NLMS) algorithm for sparse system identification. The proposed approach is in line with the proportionate NLMS (PNLMS)-type algorithms in the sense that different gains are considered in the coefficient update equation. However, in contrast to the PNLMS-type algorithms, the proposed approach considers only two different gains, one related to the active coefficients and other related to the inactive ones. Such an approach allows obtaining closed-form expressions for both gains without relying on proportionality functions and activation factors. As a result of the proposed strategy, the new algorithm, termed here two-gain NLMS (TG-NLMS), leads to both fast convergence and low computational complexity. Simulation results are shown aiming to confirm the effectiveness of the proposed algorithm.

A Variable Step Size Normalized Least-Mean-Square Algorithm Based on Data Reuse

The principal issue in acoustic echo cancellation (AEC) is to estimate the impulse response between the loudspeaker and microphone of a hands-free communication device. This application can be addressed as a system identification problem, which can be solved by using an adaptive filter. The most common one for AEC is the normalized least-mean-square (NLMS) algorithm. It is known that the overall performance of this algorithm is controlled by the value of its normalized step size parameter. In order to obtain a proper compromise between the main performance criteria (e.g., convergence rate/tracking versus accuracy/robustness), this specific term of the NLMS algorithm can be further controlled and designed as a variable parameter. This represents the main motivation behind the development of variable step size algorithms. In this paper, we propose a variable step size NLMS (VSS-NLMS) algorithm that exploits the data reuse mechanism, which aims to improve the convergence rate/tracking of the algorithm by reusing the same set of data (i.e., the input and reference signals) several times. Nevertheless, we involved an equivalent version of the data reuse NLMS, which provides the convergence modes of the algorithm. Based on this approach, a sequence of normalized step sizes can be a priori scheduled, which is advantageous in terms of the computational complexity. The simulation results in the context of AEC supported the good performance features of the proposed VSS-NLMS algorithm.

On the behavior of a combination of adaptive filters operating with the NLMS algorithm in a nonstationary environment

This paper presents a stochastic model describing the behavior of either affine or convex combination scheme involving two adaptive filters operating in parallel with the normalized least-mean-square (NLMS) algorithm under a nonstationary environment. Specifically, considering both uncorrelated and correlated Gaussian input data, model expressions are obtained for predicting the evolution of the mean weight vector, learning curve, and weight-error correlation matrices, as well as the steady-state values of both the mixing parameter and the excess mean-square error (EMSE). Based on these model expressions, some characteristics of combination schemes operating in a nonstationary environment are then discussed. Simulation results are shown, confirming the accuracy of the proposed model for different operating conditions.

An ALO Optimized Adaline Based Controller for an Isolated Wind Power Harnessing Unit

A power generating system should be able to generate and feed quality power to the loads which are connected to it. This paper suggests a very efficient controlling technique, supported by an effective optimization method, for the control of voltage and frequency of the electrical output of an isolated wind power harnessing unit. The wind power unit is modelled using MATLAB/SIMULINK. The Leaky least mean square algorithm with a step size is used by the proposed controller. The Least Mean Square (LMS) algorithm is of adaptive type, which works on the online modification of the weights. LMS algorithm tunes the filter coefficients such that the mean square value of the error is the least. This avoids the use of a low pass filter to clean the voltage and current signals which makes the algorithm simpler. An adaptive algorithm which is generally used in signal processing is applied in power system applications and the process is further simplified by using optimization techniques. That makes the proposed method very unique. Normalized LMS algorithm suffers from drift problem. The Leaky factor is included to solve the drift in the parameters which is considered as a disadvantage in the normalized LMS algorithm. The selection of suitable values of leaky factor and the step size will help in improving the speed of convergence, reducing the steady-state error and improving the stability of the system. In this study, the leaky factor, step size and controller gains are optimized by using optimization techniques. The optimization has made the process of controller tuning very easy, which otherwise was carried out by the trial-and-error method. Different techniques were used for the optimization and on result comparison, the Antlion algorithm is found to be the most effective. The controller efficiency is tested for loads that are linear and nonlinear and for varying wind speeds. It is found that the controller is very efficient in maintaining the system parameters under normal and faulty conditions. The simulated results are validated experimentally by using dSpace 1104. The laboratory results further confirm the efficiency of the proposed controller.

Beam Tracking Channel for Millimeter-Wave Communication System Using Least Mean Square Algorithm

Millimeter-wave (mmwave)is an attractive option for high data rate applications in the 5G wireless communication that requires proper beamforming, channel tracking, and channel change. Adaptive beams are formed by relying on adaptive algorithms. In this paper, we study, analyze, and compare the performance of the least mean square algorithm (LMS) and normalized least mean square (NLMS) for tracking channel status and transmit array beam. When using LMS algorithms and natural NLMS algorithms, an adaptive filter usually results in a trade-off between convergence velocity and adaptive accuracy. The results showed that the LMS algorithm is one of the simplest types of algorithm but it needs a large step size to obtain faster system convergence and stability. NLMS algorithm is a special application for the LMS algorithm, in which NLMS algorithm takes into account the change in the signal level when applying the filter and specifies the normal step size parameter μ. this leads to stability as well as rapid convergent adaptation of the algorithm.

Sound source localization based on improved adaptive beamforming

In adaptive systems, the least mean square error (LMS) adaptive algorithm is widely used. The variable step size LMS algorithm (SVSLMS) based on the Sigmoid function has greatly improved the convergence speed, and the normalized LMS algorithm is stable Sexual performance has certain advantages. Therefore, improvement is made on this basis, the SVSLMS algorithm is normalized, and the iteration speed is increased by changing the iteration factor, and the stability of the algorithm is also improved. This paper uses MATLAB simulation tools to verify the superiority of the new algorithm. Finally, the improved algorithm is applied to beamforming to estimate the azimuth of arrival of the simulated sound source signal at the partial discharge point of the submarine power cable.

Nonlinear adaptive normalized least mean absolute third algorithm for the control of five‐level distribution static compensator

SummaryThis paper presents the design and control of single‐phase five‐level cascaded H‐bridge multilevel inverter (CHB‐MLI) as a shunt active power filter (SAPF) unit to mitigate the various power quality (PQ) problems such as reactive power burden, injection of harmonics in the supply, poor power factor, and so on. The control of CHB‐MLI has been done using the normalized least mean absolute third (NLMAT) algorithm, which overcomes the shortcoming of conventional least mean square (LMS), normalized LMS (NLMS), and least mean absolute third (LMAT) algorithm. The control algorithm is designed in MATLAB Simulink, and its scaled down prototype model is developed in the laboratory to find the fundamental active component of load current and to mitigate the aforementioned PQ problems. The proposed system is tested for single‐phase grid‐connection, and it works satisfactorily under steady state and dynamic load conditions. A dSpace1104 microcontroller is used to test the proposed algorithm and to generate firing pulses. Besides, the detailed comparison in the context of mean square error (MSE), weights convergence and intermediate error with conventional LMS, NLMS, and LMAT algorithm have also been discussed. Moreover, the harmonic distortion observed in the source current is within stipulated IEEE‐519 limits.

A novel acoustic feedback compensation filter for nonlinear active noise control system

The acoustic feedback is widely seen in the active noise control (ANC) system for short acoustic duct such as the intake system of an automobile engine, which severely destabilizes the stability of the original ANC system. The conventional acoustic feedback compensation methods based on IIR filter can only be applied to the linear acoustic path and is not suitable for a nonlinear ANC (NANC) system. To solve this problem, this paper proposes a Volterra recursive even mirror Fourier nonlinear (VREMFN) filter, which can effectively suppress both linear acoustic feedback and nonlinear acoustic feedback in the NANC system. In this paper, we show the solutions for the linear acoustic feedback and nonlinear acoustic feedback of VREMFN and discuss its stability condition. Moreover, a new leaky normalized LMS algorithm is also developed to further improve the performance of NANC system based on VREMFN. Simulated results comparing IIR, Volterra and VREMFN based on parameter adaptive algorithm (PAA), FXLMS and FULMS show that the proposed VREMFN dramatically improves the noise reduction performance of NANC system both in linear acoustic feedback path and nonlinear acoustic feedback path. Furthermore, two experiments with different acoustic feedback paths also demonstrate the effectiveness of the proposed VREMFN.

Optimization of Normalized Least Mean Square Algorithm of Smart Antenna Beamforming for Interference Mitigation

A smart antenna is an array of antennas with signal processing capabilities to transmit/receive information in an adaptive manner. This capability continues to be investigated to find the best adaptive algorithm for the desired beamforming capability. This paper aims to provide a study and analysis of the effect of the normalized least mean square (NLMS) algorithm on step size parameter settings which have an impact on the desired minimum square error (MSE) value and on the nulling beam radiation pattern arrangement of smart antennas in its role in mitigating interference. The simulation for beamformer performance for 1000 iterations was carried out using the Matlab tool on the additional white noise gaussian (AWGN) channel and the simulation parameters were changed to some step size values (μ) with the NLMS algorithm for 16 antenna elements. The effect of the value of the step size μ is seen in the iterations number that takes place before the minimum error noise is obtained, where the increase in the value of this step size reduces the iterations number required; at the same time further improving MSE levels. From the pattern of amplitude response after the beamforming process, the result is an escalation in the number of nulling to increase the distance between the spaced elements taken. The interference source is eliminated/closed by placing the nulls in the path of the interference source where the worst interference level is obtained around -90 dB when the smallest step size is taken.

Recovery and noise cancelling of the fetal heart signal using a combination of NLMS algorithm and S-G filter

PurposeThe purpose of this paper is to provide appropriate methods for reducing the abnormalities on the extracted fetal heart signal from the maternal electrocardiogram (ECG).Design/methodology/approachIn this regard, the extracted signal of the fetal heart from the mother, improved using an active noise cancelation (ANC) system. It uses commonly adaptive algorithms of normalized least mean squares (NLMS). In the present paper, fetal extraction and denoising methodology are proposed. This methodology uses a combination of the NLMS algorithm with Savitzky–Golay (S-G) filter.FindingsThe obtained results show that a combination of NLMS algorithm with filter coefficient of 15 and µ = 0.02 and S-G filter has a better qSNR (qSNR = 3.6727) and good performance for fetal ECG extraction in comparison with the other works for average fmSNR in the range of −30 to −15 dB. Also, with considering the SNR value of −24.7 dB before filtering and SNR = 3.1861 dB after filtering; the SNR improvement of 27.8861 dB has been obtained.Originality/valueA new method in the extract and noise reduction of fetal ECG from maternal ECG by the combination of NLMS algorithm and S-G filter is proposed.