Normalized Least Mean Square Research Articles

On the stochastic analysis of the NLMS algorithm for white and correlated Gaussian inputs in time-varying environments

This paper presents a stochastic model of the normalized least-mean-square (NLMS) algorithm aiming to study its behavior in time-varying environments for both white and correlated Gaussian input data. Particularly, comparing with other stochastic models from the open literature, here, a more general representation of time-varying systems is considered, allowing to assess the obtained model in an extensive range of practical scenarios. Moreover, to derive the proposed model, some simplifying assumptions commonly considered in the literature are avoided, resulting in very accurate model expressions describing the algorithm behavior for both transient and steady-state phases. Thus, based on the proposed model expressions, the impact of the algorithm parameters on its performance is assessed and some tracking properties of the NLMS algorithm for white and correlated input data are analyzed. Through simulation results, the effectiveness of the proposed model is verified for different operating scenarios.

The Volterra adaptive prediction method based on matrix decomposition

This paper comes up with the adaptive prediction method of Volterra series method in chaotic time series based on matrix factorization method. Taking the monthly runoff of the Huaxian Hydrological Station as example, based on phase-space reconstruction, it identifies the chaotic characteristic through correlation dimension and Lyapunov index. Based on Volterra adaptive filter model, use matrix factorization to solve the equation, which avoid the local optimum problem caused by selecting initial value in Normalized Least Mean Square (NLMS), and at the same time, obtain the global optimal Volterra filter coefficient. According to the Numerical experiments, the prediction performance based on matrix factorization method has no problems in selecting the initial value and can achieve highly-accurate prediction. The conclusions are as follows: (1) The monthly runoff in Huaxian has chaotic characteristic. It’s embedding dimension and optimal embedding dimension is 3; (2) Matrix factorization avoids square root operation and improves the speed; (3) Avoiding selecting the initial value improves the prediction accuracy of the optimal filter coefficient.

고막이식형 마이크로폰을 위한 이식형 인공중이 적응 피드백 제거기 구현

Many implantable hearing aids are being developed as alternatives to conventional hearing aids which has inconveniences for use and social stigma that make hearing-impaired people avoid to wear it. Particularly, the fully-implantable middle ear hearing devices (F-IMEHD) are being actively studied for mixed or sensorineural hearing impaired people. In development of F-IMEHD, the most difficult problem is improving the performance of implantable microphone. Recently, Cho et al. have studied the tympanic membrane installed microphone which has better sensitivity and is easier to operate on patient than the microphone implanted under the skin. But, it may cause howling problem due to the feedback signal via oval window and ossicle chain from the transducer on round window in the middle ear cavity, therefore, a feedback canceller is necessary. In this paper, we designed NLMS (normalized least mean square) adaptive feedback canceller for F-IMEHD with tympanic membrane installed microphone and a transducer implemented at round window, and computer simulation was performed to verify its operation. The designed adaptive feedback canceller has a delay filter, a 64 point FIR fixed filter and a 8-tap adaptive FIR filter. Computer simulation of the feedback path is modeled by using the data obtained through human cadaver experiment.

Motion Artifact Suppression in Impedance Pneumography Signal for Portable Monitoring of Respiration: An Adaptive Approach.

The focus of this paper is motion artifact (MA) reduction from the impedance pneumography (IP) signal, which is widely used to monitor respiration. The amplitude of the MA that contaminates the IP signal is often much larger than the amplitude of the respiratory component of the signal. Moreover, the morphology and frequency composition of the artifacts may be very similar to that of the respiration, making it difficult to remove these artifacts. The proposed filter uses a regularization term to ensure that the pattern of the filtered signal is similar to that of respiration. It also ensures that the amplitude of the filter output is within the expected range of the IP signal by imposing an ε-tube on the filtered signal. The adaptive ε-tube filter is 100 times faster than the previously proposed nonadaptive version and achieves higher accuracies. Moreover, the experimental results, using several different performance measures, suggest that the proposed method outperforms popular MA reduction methods such as normalized least mean squares (NLMS) and recursive least squares (RLS) as well as independent component analysis (ICA). When used to extract the respiratory rate, the adaptive ε-tube achieves a mean error of 1.27 breaths per minute (BPM) compared to 4.72 and 4.63 BPM for the NLMS and RLS filters, respectively. When compared to the ICA algorithm, the proposed filter has an error of 1.06 BPM compared to 3.47 BPM for ICA. The statistical analyses indicate that all of the reported performance improvements are significant.

Analysis of the SNR Estimator for Speech Enhancement Using a Cascaded Linear Model

Elimination of tainted noise and improving the overall quality of a speech signal is speech enhancement. To gain the advantage of individual algorithms we propose a new linear model and that is in the form of cascade adaptive filters for suppression of non-stationary noise. We have successfully deployed NLMS (Normalized Least Mean Square) algorithm, Sign LMS (Least Mean Square) and RLS (Recursive Least Square) as the main de-noising algorithms. Moreover, we are successful in demonstrating that the prior information about the noise is not required otherwise it would have been difficult to estimate for fast-varying noise in non-stationary environment. This approach estimates clean speech by recognizing the long segments of the clean speech as one whole unit. During experiment/implementation we used in-house database (includes various types of non stationary noise) for speech enhancement and proposed model results have shown improvement over conventional algorithms not only in objective but in subjective evaluations as well. Simulations present good results with a new linear model that are compared with individual algorithm results.

On the Distribution of Indefinite Quadratic Forms in Gaussian Random Variables

In this work, we propose a unified approach to evaluating the CDF and PDF of indefinite quadratic forms in Gaussian random variables. Such a quantity appears in many applications in communications, signal processing, information theory, and adaptive filtering. For example, this quantity appears in the mean-square-error (MSE) analysis of the normalized least-mean-square (NLMS) adaptive algorithm, and SINR associated with each beam in beam forming applications. The trick of the proposed approach is to replace inequalities that appear in the CDF calculation with unit step functions and to use complex integral representation of the the unit step function. Complex integration allows us then to evaluate the CDF in closed form for the zero mean case and as a single dimensional integral for the non-zero mean case. Utilizing the saddle point technique allows us to closely approximate such integrals in non zero mean case. We demonstrate how our approach can be extended to other scenarios such as the joint distribution of quadratic forms and ratios of such forms, and to characterize quadratic forms in isotropic distributed random variables. We also evaluate the outage probability in multiuser beamforming using our approach to provide an application of indefinite forms in communications.

전이중 통신 방식을 사용하는 무선랜을 위한 간섭 제거 기법

In this paper, we employ the single channel full duplex radio for wireless local area network (WLAN) systems, and design digital interference cancellers using adaptive signal processing. When the full duplex scheme is used for WLAN systems with multiple transmit and receive antennas, some interference is caused through the feedback of transmit signals from multiple antennas. To remove the feedback interference, we derive the least mean square (LMS), normalized LMS (NLMS), and recursive least squares (RLS) algorithms based on adaptive signal processing techniques. In addition, we analyze the theoretical convergence of the proposed LMS and RLS methods. The channel capacity of full duplex radios increases by two times than that of half duplex radios, when the packet error rate (PER) performances for the two systems are identical. Through numerical simulations in WLAN systems, it is shown that the full duplex method with the proposed interference cancellers has a similar PER performance with the conventional half duplex transmission scheme.

An overview on optimized NLMS algorithms for acoustic echo cancellation

Acoustic echo cancellation represents one of the most challenging system identification problems. The most used adaptive filter in this application is the popular normalized least mean square (NLMS) algorithm, which has to address the classical compromise between fast convergence/tracking and low misadjustment. In order to meet these conflicting requirements, the step-size of this algorithm needs to be controlled. Inspired by the pioneering work of Prof. E. Hansler and his collaborators on this fundamental topic, we present in this paper several solutions to control the adaptation of the NLMS adaptive filter. The developed algorithms are “non-parametric” in nature, i.e., they do not require any additional features to control their behavior. Simulation results indicate the good performance of the proposed solutions and support the practical applicability of these algorithms.

Highly Efficient Multi-Hop Packet Transmission Using Intra-Flow Interference Cancellation and Maximal-Ratio Combining

Conventional Carrier Sense Multiple Access/Collision Avoidance (CSMA/CA) multi-hop transmission suffers severely from intra-flow interference (IFI) in dense traffic, due to the hidden terminal (HT) problem. We propose a non-CSMA/CA multi-hop transmission scheme with IFI-canceler (IFIC) that can efficiently relay packets under high traffic loads in fading environments. This interference cancellation technique employs adaptive equalization with a normalized least mean square (NLMS) algorithm for channel estimation and has good BER/PER performance under a wide range of SNR and SIR conditions. It is also capable of canceling multiple interference sources. A multi-hop packet transmission frame format dedicated to the IFIC proposal is designed. An analysis model is created that considers possible outage events in multi-hop traffic flows. Simulations of multi-hop transmission indicate that IFIC throughput under slow Rayleigh fading linearly increases with traffic load and is 3.5 times higher than that of current CSMA/CA systems at the highest normalized traffic load. When 2-branch maximal-ratio combining (MRC) reception is added after IC, the throughput is further improved to a level very close to the theoretical maximum for additive white Gaussian noise (AWGN) channels. We also assess the impact of maximum Doppler frequency, and show that the best performance is maintained if the frequency is less than 10 Hz and the performance under higher Doppler frequencies can be effectively improved by retransmission.

A Normalized Least Mean Square Algorithm Based on the Arctangent Cost Function Robust Against Impulsive Interference

In this paper, a normalized least mean square (NLMS) adaptive filtering algorithm based on the arctangent cost function that improves the robustness against impulsive interference is proposed. Owing to the excellent characteristics of the arctangent cost function, the adaptive update of the weight vector stops automatically in the presence of impulsive interference. Thus, this eliminates the likelihood of updating the weight vector based on wrong information resulting from the impulsive interference. When the priori error is small, the NLMS algorithm based on the arctangent cost function operates as the conventional NLMS algorithm. Simulation results show that the proposed algorithm can achieve better performance than the traditional NLMS algorithm, the normalized least logarithmic absolute difference algorithm and the normalized sign algorithm in system identification experiments that include impulsive interference and abrupt changes.

Spoofing Mitigation of GPS Receiver using Least Mean Squares-Based Adaptive Filter

The Global Positioning System (GPS) signals are very weak signal over wireless channels, so they are vulnerable to in-band interferences. Therefore, even a low-power interference can easily spoof GPS receivers. Among the variety of GPS signal interference, spoofing is considered as the most dangerous intentional interference. The spoofing effects can mitigate with an appropriate strategy in the receiver. In this paper, we use methods of adaptive filter based on Least Mean Squares (LMS) and Normalized Least Mean Squares (NLMS) algorithms in order to defense against spoofing. The new approaches based on LMS and NLMS are applied in the acquisition stage of the receiver. The new approaches are operated to mitigate effect of spoofing from the received signal in GPS valid receiver. LMS-based algorithm is a class of adaptive filter that modify the filter coefficients to minimize the error signal. NLMS algorithm is a modified form of the normal LMS algorithm that solves the LMS problem by normalizing with the power of the input signal. The proposed methods have been implemented on real dataset. The results explain that the suggested algorithms significantly decrease spoofing. Also, they improve Position Dilution of Precision (PDOP) parameter. Based on the results, NLMS algorithm has better performance than LMS algorithm.

Implementation of Adaptive Filters on TMS320C6713 using LabVIEW - A Case Study

Adaptive filters are playing a vital role in signal processing and communication filed of engineering for the purpose of filtering the unwanted signal, signal denoising, signal enhancement, etc. The main characteristic of the adaptive filter is the adjustment of filter coefficients dynamically with respect to the input signal which helps a lot in signal processing applications. This study main focus on implementing such adaptive filters on digital signal processors. The adaptive filtering algorithms such as Least Mean Square (LMS) algorithm and Normalized LMS (NLMS) algorithms are implemented with TMS320C6713 floating-point DSP processor using LabVIEW environment in real time. To test the functionality of the algorithms, the sinusoid signal is added with noisy and applied as an input the filter and the resultant denoising output is obtained with both the algorithms. We implement it with TMS320C6713 floating-point Digital Signal Processor using LabVIEW environment in real time. Our objective is to reduce or filter the noise using these algorithms and obtain the performance metrics like peak output, Mean Square Error (MSE), Peak Signal-to-Noise Ratio (PSNR) as a part of simulation results. The PSNR produced by the NLMS algorithm is obtained as 18.414 is very high as compared with 3.28416 produced by the LMS algorithm. Interfacing the TMS320C6713 DSP board with the LabVIEW application is done using the Code Composer Studio software tool. This study focuses the principle of adaptive filters by implementing the Least Mean Square (LMS) algorithm and Normalized LMS algorithms and can be further extended with Kalman filters too. er .

Variable bit rate video traffic prediction based on kernel least mean square method

In this study, the problem of variable bit rate (VBR) video traffic prediction is addressed. VBR traffic prediction is necessary in dynamic bandwidth allocation for multimedia quality of service control strategies. Autoregressive (AR) models have been widely used in VBR traffic prediction where the least mean square (LMS)-based methods were utilised for parameter estimation. However, they are ineffective when the traffic is dynamic in nature. In this study, using the Brock, Dechert, and Scheinkman (BDS) test, it is shown that the video traffic is non-linear. Kernel is an efficient tool to convert non-linear data into linear one in a higher-dimensional space. The kernel LMS (KLMS) method is proposed to forecast the next frame sizes of I, B and P frames as well as the next group-of-pictures (GOP) size of video traffic. Extensive simulations were performed on different video traces where different performance metrics were considered. KLMS results were very close to those of the Wiener–Hopf optimum solution and better than the results of commonly used normalised LMS and other algorithms such as the least mean kurtosis (LMK), wavelet LMK, adaptive network fuzzy inference system (ANFIS) and neural networks.

Statistical convergence behavior of affine projection algorithms

Class of algorithms referring to the affine projection algorithms (APA) applies updates to the weights in a direction that is orthogonal to the most recent input vectors. This speeds up the convergence of the algorithm over that of the normalized least mean square (NLMS) algorithm, especially for highly colored input processes. In this paper a new statistical analysis model is used to analyze the APA class of algorithms with unity step size. Four assumptions are made, which are based on the direction vector for the APA class. Under these assumptions, deterministic recursive equations for the weight error and for the mean-square error are derived. We also analyze the steady-state behavior of the APA class. The new model is applicable to input processes that are autoregressive as well as autoregressive-moving average, and therefore is useful under more general conditions than previous models for prediction of the mean square error of the APA class. Simulation results are provided to corroborate the analytical results.

Digitally assisted analog front-end power management strategy via dynamic reconfigurability for robust heart rate monitoring

This paper presents a reconfiguration methodology to digitally assist a reconfigurable analog front-end (AFE), with the objective of reducing the power consumption of an ECG-based cardiac activity monitoring system, while maintaining an acceptable performance for the desired signal processing. In this study, we focus on the performance of ECG-based heart rate estimation as an example to demonstrate our proposed strategy. Utilizing the consistency and quasi-periodicity of the ECG waveform, two regions are pre-defined based on the prediction of the R peak by a normalized least mean square (NLMS) adaptive filter. The power consumption and performance of the AFE is dynamically reconfigured accordingly. Experimental evaluations show the system can measure heart rate variability (HRV) with an error of 0.5-4 beats/min with the sampling rate reduced from 488 sps to 100 sps and 40 sps for the two regions respectively, bit resolution reduced from 10-bit to 6-bit and noise tolerance substantially relaxed, offering an estimated 62% total power saving.

ECG SIGNALS NOISE REMOVAL: SELECTION AND OPTIMIZATION OF THE BEST ADAPTIVE FILTERING ALGORITHM BASED ON VARIOUS ALGORITHMS COMPARISON

The electrocardiogram (ECG) is generally used for the diagnosis of cardiovascular diseases. In many of the biomedical applications, it is necessary to remove the noise from ECG recordings. Several adaptive filter structures have been proposed for noise cancellation. Compared to the least mean square (LMS) method, the unbiased and normalized adaptive noise reduction (UNANR) algorithm has better performance, as mentioned in previous investigations. In this paper, we review various kinds of ECG noise reduction algorithms. To provide a detailed and fair comparison, all normalized LMS (NLMS), Block LMS (BLMS), recursive least squares (RLS) and UNANR algorithms are implemented and their performance have been assessed using the same dataset and compared to different state-of-the-art approaches. Then, the performance analysis of all five algorithms is presented and compared in term of mean squared error (MSE), computational complexity and stability. The obtained results revealed that RLS method is much more effective and powerful than other methods in ECG noise cancellation, and even better than UNANR. Then, in order to reach the best performance of the mentioned filter and also, to minimize the output signal error, the optimized parameters of the algorithm were defined and results were investigated. The obtained outcomes show that the best Lambda (λ) occurs between 0.05 and 0.9, so that the convergence rate of the optimized RLS filter is faster than others. It not only decreases the noise, but also the ECG waveform is better conserved. Furthermore, the introduced optimized method with adaptive threshold value would have great potential in biomedical application of signal processing and other fields.

An optimized NLMS algorithm for system identification

The normalized least-mean-square (NLMS) adaptive filter is widely used in system identification. In this paper, we develop an optimized NLMS algorithm, in the context of a state variable model. The proposed algorithm follows a joint-optimization problem on both the normalized step-size and regularization parameters, in order to minimize the system misalignment. Consequently, it achieves a proper compromise between the performance criteria, i.e., fast convergence/tracking and low misadjustment. Simulations performed in the context of acoustic echo cancellation indicate the good features of the proposed algorithm.

Performance comparison between packet and continuous data transmission using two adaptive equalizers in shallow water

Transmitted signals are markedly affected by sea surface and bottom boundaries in shallow water. The time variant reflection signals from such boundaries characterize the channel as a frequency-selective fading channel and cause intersymbol interference (ISI) in underwater acoustic communication. A channel-estimate-based equalizer is usually adopted to compensate for the reflected signals under this kind of acoustic channel. In this study, we apply two approaches for packet and continuous data transmission of the quadrature phase shift keying (QPSK) system. One is the use of a two-dimensional (2D) rotation matrix in a non-frequency-selective channel. The other is the use of two equalizers of types — the feed forward equalizer (FFE) and decision-directed equalizer (DDE) — with a normalized least mean square (NLMS) algorithm in a frequency-selective channel. The percentage improvement of packet transmission is notably better than that of continuous transmission.

Entropy Coder for Audio Signals

Abstract In the paper an effective entropy coder designed for coding of prediction errors of audio signals is presented. The coder is implemented inside a greater structure, which signal modeling part is a lossless coding backward adaptation algorithm consisting of cascaded Ordinary Least Squares (OLS), three Normalized Least Mean Square (NLMS), and prediction error bias correction sections. The technique performance is compared to that of four other lossless codecs, including MPEG-4 Audio Lossless (ALS) one, and it is shown that indeed, on the average the new method is the best. The entropy coder is an advanced context adaptive Golomb one followed by two context adaptive arithmetic coders.

A New Approach to Adaptive Signal Processing

A unified linear algebraic approach to adaptive signal processing (ASP) is presented. Starting from just Ax=b, key ASP algorithms are derived in a simple, systematic, and integrated manner without requiring any background knowledge to the field. Algorithms covered are Steepest Descent, LMS, Normalized LMS, Kaczmarz, Affine Projection, RLS, Kalman filter, and MMSE/Least Square Wiener filters. By following this approach, readers will discover a synthesis; they will learn that one and only one equation is involved in all these algorithms. They will also learn that this one equation forms the basis of more advanced algorithms like reduced rank adaptive filters, extended Kalman filter, particle filters, multigrid methods, preconditioning methods, Krylov subspace methods and conjugate gradients. This will enable them to enter many sophisticated realms of modern research and development. Eventually, this one equation will not only become their passport to ASP but also to many highly specialized areas of computational science and engineering.