Convergence analysis of a continuous-time nonlinear LMS-type algorithm using stochastic calculus

Structural system identification using Least Mean Square (LMS) adaptive technique

This paper surveys recent advances related to sparse least mean square (LMS) algorithms. Since standard LMS algorithm does not take advantage of the sparsity information about the channel being estimated, various sparse LMS algorithms that are aim at outperforming standard LMS in sparse channel estimation are discussed. Sparse LMS algorithms force the solution to be sparse by introducing a sparse penalty to the standard LMS cost function. Under the reasonable conditions on the training datas and parameters, sparse LMS algorithms are shown to be mean square stable, and their mean square error performance and convergence rate are better than standard LMS algorithm. We introduce the sparse algorithms under Gaussian noises model. The simulation results presented in this work are useful in comparing sparse LMS algorithms against each other, and in comparing sparse LMS algorithms against standard LMS algorithm.

본 논문에서 ICS(Interference Cancellation System) 중계기에서 간섭제거를 위한 새로운 CSS(Complex Signed-Signed) CMA(Constant Modulus Algorithm) 알고리즘을 제안한다. 중계기가 궤환 신호를 가질 때 CSS CMA 알고리즘은 궤환 경로로부터 간섭 신호를 제거하기 위한 디지털 신호 처리를 사용한 ICS 중계기에 대해 제안한다. 제안된 Complex Signed Signed CMA 알고리즘은 스텝 사이즈를 조절함에 따라 하드웨어 복잡도와 성능이 개선된다. 제안된 Complex Signed Signed CMA 알고리즘에서 스텝사이즈가 0.00043인 경우 수렴상태에서 평균 자승 에러는 기존 CMA 알고리즘보다 약 4dB정도 더 낮다. 그리고, 평균 자승 에러 -25dB를 기준으로 LMS(Least Mean Square)와 Signed LMS(Normalized Least Mean Square)보다 수렴회수가 1950 ~ 2150회 정도 줄어든다. In the paper, we propose a new CSS(Complex Signed-Signed) CMA(Constant Modulus Algorithm) algorithm for ICS(Interference Cancellation System). When the repeater get the feedback signal, the CSS CMA algorithm is proposed at the ICS repeater using DSP(Digital Signal Processing) for the removal of interfering signals from the feedback paths. The proposed CSS CMA algorithm improved performances and hardware complexity by adjusting step size values. the steady state MSE(Mean Square Error) performance of the proposed CSS CMA algorithm with step size of 0.00043 is about 4dB better than the conventional CMA algorithm. And the proposed Complex Signed Signed CMA algorithm requires 1950 ~ 2150 less iterations than the LMS(Least Mean Square) and Signed LMS(Normalized Least Mean Square) algorithms at MSE of -25dB.

A major complaint of individuals with normal hearing and hearing impairments is a reduced ability to understand speech in a noisy environment. This paper is proposed to remove the noise from the speech signal in various real time environments and to make the hearing impaired to understand the information by transforming speech in to text format. The quality of audio signal can be improved by filtering the degraded speech signal through adaptive filters. For Noise cancellation widrow & hoff’s Least Mean Square (LMS) algorithms are being used for simplicity in implementation. The LMS algorithm was simple in it's derivation and robust in a number of applications but it also have limitation in selection of a certain values such as step size and results in computational complexity. Hence to overcome all the limitations and to present an enhanced speech signal, a novel approach named VSSNDLMS algorithm is proposed. The performance of algorithms like Variable Step Size Normalised LMS , Normalised Differential LMS with proposed VSSNDLMS with different input signals are analysed in this paper . Finally, through simulation results the proposed VSSNDLMS algorithm converges fastly with minimum mean square error and it is useful in predicting the adaptive filter performance of various algorithms and the implementation indicate the improvement in quality of the speech signal and it appears to be favourable for hearing impaired. Keywords: VSSNDLMS, LMS Algorithm, Noise Cancellation, Speech Processing, Adaptive Filter

Multikernel adaptive filtering over graphs based on normalized LMS algorithm

An efficient adaptive filtering algorithm named as the unconstrained Hartley domain least mean square (UHLMS) algorithm has been proposed. It is found from computer simulation that the proposed algorithm has similar performance to the time domain least mean square (LMS) algorithm for uncorrelated signals; but yields faster and better convergence for highly correlated signals. The UHLMS algorithm has identical performance to that of the unconstrained frequency domain least mean square (UFLMS) algorithm, but requires significantly less computation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

portion of the traffic carried by high speed packet-switched broadband integrated services digital networks (B-ISDN). The high peak-to-mean ratio of VBR traffic, however, makes allocation of network resources, such as bandwidth, quite difficult. If bandwidth is allocated based on the peak rate, it will be highly inefficient and would, in fact, mitigate the gains of statistical multiplexing. On the other hand, choosing the mean rate means of allocating bandwidth would lead to congestion in the network, specially if multiple sources become active at the same time and start delivering video traffic into the network at their peak rates. The dynamics of the VBR traffic, coupled with the delay-bandwidth product of the high-speed networks, add to the complexity of congestion control and render conventional reactive based congestion control schemes as highly inefficient. Bandwidth allocation, based on the mean rate aided by a preventative congestion control scheme that could predict the onset of congestion, well in advance, is the desired solution. One such technique is proposed that estimates the current traffic state, predicts the future traffic states and forecasts the occurrence of congestion in the network. The emphasis is on demonstrating the applicability of least mean square (LMS) filters in estimating the current state of the VBR traffic sources accessing the networks. Some simulation results are presented.

This paper proposes a new application of fuzzy logic to variable step size least mean square (VS-LMS) adaptive beamforming algorithm in CDMA systems. The proposed algorithm adjusts the step size of the least mean square (LMS) by using the application of fuzzy logic in which the increase or decrease of step size depends on the fuzzy inference results of the mean square error (MSE). Computer simulation results show that the proposed algorithm has a better capacity of tracking compared with the conventional LMS algorithms and other variable step size LMS algorithms.

In Electrocardiogram (ECG) application, we face various types of artifacts added to the ECG signal. Different Researchers have been interested in this problem due to its importance. In this paper we introduce a study of different algorithms and their effects on the performance of the ECG noise canceller. We have used many kinds of algorithms such as: LMS (Least Mean Square), NLMS (Normalized Least Mean Square), Signed Regressor LMS (SRLMS), Sign LMS (SLMS), Sign-Sign LMS (SSLMS) and a new proposed modified LMS called Variable Step size Least Mean Square (VSLMS) using MATLAB software package as well as Unbiased Linear output Neural Network (ÜLNN) and Unbiased Non Linear output Neural Network (UNLNN). It is promising to clarify the difference among these algorithms with the aim of obtaining better performance.

In recent times noise cancellation is a vital issue, as it is responsible for reducing undesired disturbances in the process of communication. Active Noise Cancellation (ANC) is the most effective technique to cancel noise. ANC has been an active area of research and various adaptive methodologies have been employed to achieve a better ANC scheme. In the ANC technique, the aim is to minimize the noise interference that corrupts the original signal. ANC has a broad variety of applications in common commercial products, industrial uses and other machinery. An analysis of the prevailing adaptive methodologies is necessary for future research as we need to know the demerits of all the prevailing adaptive methodologies in ANC. This paper provides an analysis of various adaptive algorithms for noise cancellation and a comparison is made between them. The strengths, weaknesses and practical effectiveness of all the algorithms have been discussed. This paper deals with cancellation of noise on speech signal using three existing algorithms- Least Mean Square (LMS) algorithm, Normalized Least Mean Square (NLMS) algorithm and Recursive Least Square (RLS) algorithm and a proposed algorithm- advanced Block Least Mean Square (BLMS) algorithm. The algorithms are simulated in MATLAB platform and a tabular comparison of the algorithms is drawn. Finally, conclusions have been drawn by choosing the algorithms that provide efficient performance with less computational complexity.

The celebrated least mean square (LMS) algorithm is the widely used system identification approach which can be easily implemented. With the assumption of no dependence among the tapped-delay input vectors, the mean square analysis of LMS algorithm based on independence theory is only an approximate description of its convergence behavior, especially when updated with a large step-size. In this paper, we propose a modified mean square error (MSE) update formula that exactly describes the convergence process of LMS for tapped-delay independent identical distributed (i.i.d.) input data. The qualitative analysis is presented to reveal the significance and rationality of the proposed formula. Moreover, the simulations in various conditions validate that, even with a large step-size used, the study curves produced by the proposed formula are much more accurate in predicting the convergence behavior, compared with that based on independence assumption.

Analysis and simulations to compare the standard least mean square (LMS) algorithm to the noncanonical LMS (NCLMS) algorithm are presented. The NCLMS algorithm is implemented using a variant of the standard FIR, called the non-canonical FIR (NCFIR). Simulation results are given which show a reduced excess mean square error (EMSE) level and an improved performance in an impulsive noise environment for the NCLMS over the conventional LMS algorithm.

Adaptive digital filters (ADFs) are, in general, the most sophisticated and resource intensive components of modern digital signal processing (DSP) and communication systems. Improvements in performance or the complexity of ADFs can have a significant impact on the overall size, speed, and power properties of a complete system. The least mean square (LMS) algorithm is a popular algorithm for coefficient adaptation in ADF because it is robust, easy to implement, and a close approximation to the optimal Wiener-Hopf least mean square solution. The main weakness of the LMS algorithm is the slow convergence, especially for non Markov-1 colored noise input signals with high eigenvalue ratios (EVRs). Since its introduction in 1993, the turbo (supercharge) principle has been successfully applied in error correction decoding and has become very popular because it reaches the theoretical limits of communication capacity predicted 5 decades ago by Shannon. The turbo principle applied to LMS ADF is analogous to the turbo principle used for error correction decoders: First, an "interleaver" is used to minimize crosscorrelation, secondly, an iterative improvement which uses the same data set several times is implemented using the standard LMS algorithm. Results for 6 different interleaver schemes for EVR in the range 1-100 are presented.

The method of least mean square (LMS) is the commonly used algorithm in Adaptive filter due to its simplicity and robustness in implementation. In Active Noise Control application, a filtered reference signal is used prior to LMS algorithm to overcome the constraint on stability and convergence performance of the system due to the existence of the auxiliary path. This is known as Filtered-X LMS algorithm. In conventional Filtered-X LMS algorithm, each filter weight is updated once on every audio sample. This paper proposes the improved version of Filtered-X LMS algorithm with the use of multiple iteration of filter weight on every sample of audio signal. The proposed work uses field programmable gate arrays to realize real-time simulation on hardware for the noise signal of 500 Hz. Results from the real-time hardware simulations have shown much faster error convergence and better adaptation performance for different selections of learning constant μ, as compared with the conventional method.

A parameter estimation problem in a class of nonlinear systems is considered where the input-output relation of a nonlinear system is approximated by a polynomial model (e.g., a Volterra series). A least mean squares (LMS) type algorithm is utilized for the recursive estimation of the polynomial coefficients, and its resulting mean square error (MSE) convergence properties are investigated. Conditions for the algorithm stability (in the mean square sense) are established, steady-state MSE bounds are obtained, and the convergence rate is discussed. In addition, modeling accuracy versus steady-state performance is examined; it is found that an increase of the modeling accuracy may result in a deterioration of the asymptotic performance, that is, yielding a larger steady-state MSE. Linear system identification is studied as a special case.