Mean square deviation analysis of LMS and NLMS algorithms with white reference inputs

In this paper, the average mean square deviation (MSD) analysis of the normalized least mean square (NLMS) and least mean square (LMS) algorithms is carried out for cyclostationary input signals. It is shown that the NLMS algorithm has good transient response, while the steady-state MSD of the LMS algorithm does not depend on the periodic input power. In addition, the theoretical results reveals that for cyclostationary input signals, under small step-size conditions, the LMS algorithm can offer smaller steady-state average MSD than the NLMS algorithm at the same convergence rate. That is to say, the NLMS algorithm will suffer from large steady-state MSD for cyclostationary input signals. The theoretical results are validated by computer simulations.

A new combined-step-size normalized least mean square algorithm for cyclostationary inputs

MIMO-OFDM Systems are widely used nowadays because of their improved performance in terms of link reliability, high data rates and capacity. Channel Estimation is one of the major challenges faced by a MIMO-OFDM system. For a rapidly time varying wireless channel, Adaptive Channel Estimation (ACE) algorithms are widely used for the purpose of channel estimation. Least Mean Square (LMS) algorithm is the commonly used ACE algorithm, as it has low complexity and numerical robustness. Its main disadvantage is high Mean Square Error (MSE). This disadvantage is overcome in Normalized LMS algorithm with low MSE but its complexity is high and convergence performance is poor. Inorder to further reduce the complexity of LMS algorithm, several simplified LMS algorithms can be used. Simplified algorithms includes Sign Data LMS (SDLMS) algorithm, Sign Error LMS (SDLMS) algorithm, Sign Data Normalized LMS (SDNLMS) algorithm, Sign Data Sign Error Least Mean Square (SDSELMS) algorithm etc. In all these algorithms there occurs a trade-off between convergence rate and MSE. In order to overcome this trade-off, a Variable Step Size (VSS) algorithm can be used. By combining VSS algorithm with such simplified algorithms, we can realize CE algorithms that can reduce the complexity as well as the trade-off between convergence rate and MSE performance. In this paper, a new fast convergence, low complex Variable Step Size-Sign Data Sign Error Least Mean Square (VSS-SDSELMS) algorithm is proposed which further improves the convergence performance along with low computational complexity and comparable MSE performance.

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 .

The authors prove that for zero-mean white data input, the optimum algorithm which modifies the data vector in the LMS (least mean square) gradient estimate to achieve the lowest excess mean-square error for a given convergence rate is the normalized LMS (NLMS) algorithm. It is shown that this adaptive filtering algorithm is equivalent to recursive least-squares adaptation with a known diagonal data covariance matrix. Moreover, the algorithm can be interpreted as a modified LMS algorithm in which the iterated weight vector is used to form the error estimate. Both theoretical calculations and simulations for white Gaussian data show that this NLMS algorithm performs as much as 3.6 dB better than standard LMS for the input. >

In this paper, we have presented the design, implementation and comparison result of Least Mean Square (LMS) algorithm and Normalized LMS (NLMS) algorithm using a 4 channel microphone array for noise reduction as well as speech enhancement. Adaptive sub band Generalized Side lobe Canceller (GSC) beam former has been used for experiment and analysis. Tested results were done by using one speech signal and a small number of noise sources. The side lobe canceller was evaluated with the adaptation of LMS and NLMS. The overall development of Signal to Noise Ratio (SNR) has been determined from the input and output powers of signal and noise, with signal only as input and noise, as input to the GSC. The NLMS algorithm considerably improves speech quality with noise suppression levels of up to 13 dB, while the LMS algorithm is giving up to 10 dB. In different ways of SNR measure was under various types of blocking matrix, step sizes and various noise locations. The whole process will be used for hands-free telephony, video conferencing etc. in a noisy environment.

Signal denoising is an important research direction in the field of signal processing, with widespread applications in communication, audio processing, medical signal analysis, and other areas. With the development of technology, traditional noise reduction methods are gradually facing bottlenecks in efficiency and accuracy, especially in dynamically changing noise environments. Adaptive filtering algorithms have become effective tools for solving noise elimination problems due to their ability to adjust filter parameters in real time based on the characteristics of the input signal. However, classical adaptive algorithms, such as Least Mean Square (LMS) and Normalized Least Mean Square (NLMS) algorithms, despite their success in many applications, still face issues such as slow convergence and insufficient performance when handling different types of noise. This study aims to explore the application of adaptive filtering algorithms in signal denoising, particularly those based on second-order statistics, evaluate their performance in different noise environments, and optimize their enhancement. Initially, simulations were undertaken to implement the LMS, NLMS, and second-order statistics-based adaptive filtering algorithms for noise removal experiments. These experiments employed various noise power levels and signal types to assess the performance of each algorithm, focusing on metrics such as Signal-to-Noise Ratio (SNR), Mean Squared Error (MSE), and the convergence speed of filter parameters. The research results show that the adaptive filtering algorithm based on second-order statistics has significant advantages over LMS and NLMS algorithms in various noise environments, especially in cases of higher noise power, where its denoising effect is more significant, and the convergence speed is also faster. Additionally, to address the computational complexity of the algorithm, this study proposes a simplification strategy to optimize the practical application performance of the algorithm.

Certain conditions require a delay in the coefficient update of the least mean square (LMS) and normalized least mean square (NLMS) algorithms. This paper presents an in-depth analysis of these modificated versions for the important case of spherically invariant random processes (SIRPs), which are known as an excellent model for speech signals. Some derived bounds and the predicted dynamic behavior of the algorithms are found to correspond very well to simulation results and a real time implementation on a fixed-point signal processor. A modification of the algorithm is proposed to assure the well known properties of the LMS and NLMS algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Among all adaptive noise cancellers, Widrow and Hoff's least mean square (LMS) algorithm has probably become the most popular because of its robustness, good tacking properties and simplicity of implementation. An important limitation of LMS algorithm is that the selection of a certain value for the step size implies compromise between speed of convergence and steady-state misadjustment, The variable step size normalized least-mean-square (VSS- NLMS) algorithm is appropriate to solve the conflicting requirement of fast convergence and low misadjustment of the LMS algorithm. To reduce noise in the output signal of the ANC, a step size for coefficient update is controlled according to the signal-to-noise ratio (SNR). This paper investigates the performance of a noise canceller with DSP processor (TI TMS320C6713) using the LMS algorithm, normalized least-mean-square (NLMS) algorithm, and VSS-NLMS algorithm. Results show the proposed combination of hardware and VSS-NLMS algorithm has not only a faster convergence rate but also lower distortion when compared with the fixed step size LMS algorithm and NLMS algorithm in real-time environments.

Due to the time-delay spread of the channel, the equalizers for high data rate mobile communication systems has critical importance in mitigation of inter-symbol interference (ISI). One of the most important channel equalization algorithms is the least mean squares (LMS) algorithm. However, the slow convergence rate and the need for long training sequences are the major disadvantages of the LMS algorithm. In this paper, a faststart-up modified LMS (FSU-M-LMS) algorithm based on channel matched filter (CMF) has been proposed to increase the convergence speed and performance of the LMS algorithm. In order to prove the performance of the proposed method, computer simulations are performed on stationary and nonstationary frequency selective Rayleigh fading channels. The obtained simulation results illustrate that the proposed FSU-M-LMS algorithm has better mean square error (MSE), bit error rate (BER) and channel tracking performances than the conventional LMS, modified LMS (M-LMS), normalized LMS (N-LMS) and conventional RLS algorithm.

In the radio observation based on the large single antenna, in order to reduce the interference of navigation signal L 2 from observation of the red-shifted H I spectral line at L-band, we used the an auxiliary channel and normalized LMS algorithm, and proposed new evaluating indicators deduced by theoretical method. Finally, we verified the suppression performance and the indicators' utility by multiple simulations and statistical method.

This paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares (NLMS) and the block recursive least squares (BRLS) algorithms. All these algorithms use small block lengths, thus allowing easy implementation and small input-output delay. It is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares (LMS) algorithm, while converging much faster. A precise evaluation of the arithmetic complexity is provided, and the adaptive behavior of the algorithm is analyzed. Simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the NLMS algorithm. The conclusions of the theoretical analysis are checked by simulations, illustrating that, even in the case where noise is added to the reference signal, the proposed algorithm allows altogether a faster convergence and a lower residual error than the NLMS algorithm. Finally, a sample-by-sample version of this algorithm is outlined, which is the link between the NLMS and recursive least squares (RLS) algorithms. >

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 proposed techniques are applied in the acquisition stage of the receiver. 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.

Adaptive filtering has the advantages of real-time processing, small computational complexity, and good adaptability and robustness. It has been widely used in communication, navigation, signal processing, optical fiber sensing, and other fields. In this paper, by adding an interferometer with the same parameters as the signal interferometer as the reference channel, the sensing signal of the interferometric fiber-optic hydrophone is denoised by two adaptive filtering schemes based on the least mean square (LMS) algorithm and the normalized least mean square (NLMS) algorithm respectively. The results show that the LMS algorithm is superior to the NLMS algorithm in reducing total harmonic distortion, improving the signal-to-noise ratio and filtering effect.

One of the most important applications of adaptive filter is Interference or noise cancellation. The objective of adaptive interference cancellation is to obtain an estimate of the interfering signal and to subtract it from the corrupted signal and hence obtain a noise free signal. The tracking performances of the LMS and NLMS algorithms are compared when the input of the adaptive filter is no stationary For this purpose, the filter uses an adaptive algorithm to change the value of the filter coefficients, so that it acquires a better approximation of the signal after each iteration. The LMS (Least Mean Square), and its variant the NLMS (Normalized LMS) are two of the adaptive algorithms widely in use. This paper presents a comparative analysis of the LMS and the NLMS in case of interference cancellation from speech signals. For each algorithm, the effects of two parameters-filter length and step size have been analyzed. Finally, the performances of the two algorithms in different cases have been compared.