LMS Algorithm Research Articles

A Low-Complexity Volterra Filtered-Error LMS Algorithm with a Kronecker Product Decomposition

Nonlinear active control is very important in many practical applications. Many well-known nonlinear active noise control algorithms may suffer from high computational complexity and low convergence speed, especially in the nonlinear secondary path case. Thus, it is still an actively researched topic for reducing complexity and improving the convergence rate. This paper presents a low-complexity Volterra filtered-error least mean square algorithm when taking a decomposable Volterra model into account for active control of nonlinear noise processes, which is referred as DVMFELMS. The computational complexity analysis shows that the proposed DVMFELMS algorithm can significantly reduce the nonlinear active noise control system’s complexity. The simulation results further show that the proposed algorithm can achieve promising performance compared with the Volterra-based FELMS algorithm and other state-of-the-art nonlinear filters, while the decomposable error of the Volterra kernel may be introduced inevitably. Moreover, the proposed DVMFELMS algorithm shows a better convergence rate in the broadband primary noise case due to fewer parameters used in each sub-filter.

Online unbalance compensation of a maglev rotor with two active magnetic bearings based on the LMS algorithm and the influence coefficient method

Traditional rotor dynamic balancing requires equipment shutdown to add or subtract a counterweight mass so that a rotor can reach a certain level of dynamic balancing. However, a rotor may still have some residual unbalance. As the unbalance condition changes due to factors such as load changes and rust, the original dynamic balancing will be compromised. To solve this problem, an online unbalance compensation algorithm with active magnetic bearings (AMBs) based on the least mean squares (LMS) method and the influence coefficient method (ICM) was proposed. This algorithm first applies the LMS to extract the rotor unbalance vibration signal in real time. By implementing the AMB, the trial signal with the same frequency and phase with the rotor unbalance vibration signal is added to each AMB of the balancing plane, instead of mass addition or subtraction in the traditional dynamic balancing process. An eddy current displacement sensor is used to measure the rotor displacement response in each measuring plane, and the rotor unbalance vibration compensation current can be calculated to realize the online unbalance compensation during the normal operation. The online unbalance compensation converged through the iterative algorithm. The principle of the algorithm is simple and does not depend on the model of the controller. The effectiveness of the algorithm was verified by the online unbalance compensation experiment of a maglev rotor. The experimental results revealed that the vibration amplitude of the rotor decreased by 83.6%, 84.5%, 68.6%, and 84.3% after three iterations of the algorithm in each direction, and the amplitude of the main harmonic declined by 94.2%, 96.4%, 90%, and 96.1%. The vibration amplitude of the main harmonic in the Y direction at the left AMB specifically decreased by 28.8 dB. Moreover, the adaptability of the proposed algorithm to different unbalance masses and the phase of the rotor was verified through experiment validation.

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.

Simulation and analysis of a grid integrated distribution system based on LMS algorithm for hybrid types of load

Simulation and analysis of a grid integrated distribution system based on LMS algorithm for hybrid types of load

Simplified fast transversal filter algorithms for multichannel active noise control

In recent years, more attention has been paid to the performance of algorithm in active noise control (ANC). Compared with filtered-x LMS (FxLMS) algorithm based on stochastic gradient descent, filtered-x RLS (FXRLS) algorithm has faster convergence speed and better tracking performance at the cost of high computational complexity. In order to reduce the computation, fast transversal filter (FTF) algorithm can be used in ANC system. In this paper, simplified multi-channel FXFTF algorithms are presented, and the convergence speed and noise reduction performance of different multichannel algorithms are simulated and compared, and the numerical stability of the algorithms are analyzed.

Active noise control without secondary path modeling: algorithm and implementation

Active noise control (ANC) has been intensively studied for decades. The most classical ANC algorithm should be the filtered-x least mean square (FxLMS) algorithm, which needs the model of the secondary path to work. Thus, the residual error of the ANC system is closely related to the preciseness of the secondary path model. In many applications, the secondary path is often time-varying. Therefore, off-line identification of the secondary path is not applicable. However, on-line identification often requires an additional white noise as a stimulating signal of the secondary path, which will deteriorate the final noise reduction effect. This paper proposes an improved artificial bee colony (ABC) algorithm for ANC system, which does not require identification of the secondary path. In order to guarantee the convergence of the algorithm and accelerate the convergence speed, this paper introduces a variable forgetting factor into the fitness function, and improves the traditional ABC algorithm by integrating LMS algorithm into the ABC algorithm. A single channel ANC system equipped with an FPGA hardware platform is set up in an anechoic chamber, and experiments show that the proposed algorithm can produce a satisfactory noise reduction effect without modeling the secondary path.

Distributed dynamic adaptive‐neighbour selection strategy under event‐trigger communication

In wireless sensor networks, dynamic environmental changes may lead to the distribution of some sensors becoming very dense, which leads to the waste of communication resources in distributed estimation. In this paper, it is proposed that Event-triggered distributed dynamic adaptive-neighbour selection LMS (ET-dyANDLMS) algorithm can effectively solve the problems mentioned above. On the one hand, the network communication resources are reduced by the adaptive-neighbour selection. On the other hand, the network data redundancy is reduced by the event-trigger mechanism. From a theoretical point of view, the algorithm converges stably in mean meaning and mean square meaning, and the communication cost is reduced compared with other distributed algorithms. The theoretical analysis results verified by experimental simulation demonstrate the effectiveness of the proposed algorithm.

Implementation of a low power and high speed adaptive noise canceller using LMS algorithm

The basic polite NLMS adaptive channel calculation is ordinarily utilized in applications where a framework needs to adjust to its condition. Structures are analyzed as far as the accompanying criteria: speed, power utilization and FPGA utilized. Present day FPGAs contain numerous assets that help signal processing applications. This posits are actualized in the programmable ICs texture and enhanced for superior and less power consumption The LMS adaptive finite impulse channelsarevery well known adaptive calculation process and is probably going to keep on so within a reasonable time-frame. In spite of theories that the LMS calculation is losing it is built up status as the workhorse for the plan of straight adaptive frameworks, there are as yet various continuous looks into and best in class propels right now. An expected new book titled — Least Mean-Square Adaptive Filters, altered by Bernard Widrow (originator of LMS) and Simon Haykin is a decent delegate of gave interests right now appeared by scientists around the globe.The LMS calculation can be effectively altered to a standardized advance size adaptation known as the Normalized LMS (NLMS) calculation. NLMS, gives a possibly quicker adaptive calculation, yet in addition ensures an increasingly steady combination in light of varieties of input signal power. Following this methodology, the fundamental goals of this postulation is to execute the NLMS-based adaptive calculation for awardee framework in outlaying communication to show its great gathering figure and reduce the error. Fartheriproposedone more design for DFS consumption it transfer about the usage of reduced memory use. The fundamental downside of the “absolute” least mean square computation this one touchy to the measuring the original signal X(N). It creates a difficult to pick a known rate µ that ensures good measurement. This is very useful for lowering the power consumption.

Research of adaptive nonlinear model by integrated irrigation of water and soils in greenhouse for environment and ecological balance

In view of the high control cost and water consumption of the current commercial greenhouse automatic irrigation system, this paper presents an adaptive nonlinear model identification control algorithm based on the integrated irrigation of water, fertilizer and medicine in the greenhouse, and establishes an adaptive nonlinear model identification control model based on the integrated irrigation of water, fertilizer and medicine in the greenhouse: the adaptive blood equalizer theory is analyzed Based on the known theory, the LMS adaptive equalizer is simulated. The simulation results show that the denoising effect of the adaptive equalizer based on LMS algorithm is very significant, and the algorithm has small amount of calculation and is easy to be implemented in engineering. It has strong applicability. Under the premise of achieving effective greenhouse irrigation effect, the control system reduces the water consumption by 30%, and reduces the opening time of the irrigation system and the control cost.

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.

Selective Partial Update of NLMS Adaptive Filter Algorithm

In view of the low convergence speed of the LMS algorithm and the high computational complexity of the NLMS algorithm in wireless communication system, a selective partial update NLMS algorithm is proposed. This algorithm only updates part of the filter coefficients instead of all filter coefficients during each adaptation. It effectively reduce the complexity of classic adaptive filtering algorithms. In this paper, a selective partial update of the NLMS algorithm is deduced, and the simulation verification is carried out to compare with the LMS algorithm and the NLMS algorithm, and the superiority of the algorithm is verified.

A Novel Quaternion Kernel LMS Algorithm With Variable Kernel Width

The quaternion Gaussian kernel is usually used when solving quaternion nonlinear problems. However, how to choose a proper value of kernel width is still an important issue. In most previous studies, the kernel width was set manually or estimated in advance by using Silvermans rule based on the sample distribution, which can easily degrade the performance of algorithms. In this brief, the variable kernel width quaternion kernel least mean squares algorithm (VKW-QKLMS) aims to develop an online technique for optimizing the kernel width of the quaternion kernel LMS (QKLMS) algorithm, in which the filter weight and the kernel width are alternately updated by using stochastic gradient algorithm. Simulation results show that the performance of the VKW-QKLMS algorithm does not depend on the selection of initial value of the kernel width. The VKW-QKLMS algorithm can usually achieve better performances than other competing algorithms. Only when the kernel width in the QKLMS algorithm is empirically selected as a proper value, the QKLMS algorithm can achieve much the same performance as that of the VKW-QKLMS algorithm.

Analysis of Existing and Proposed 3-Bit and Multi-Bit Multiplier Algorithms for FIR Filters and Adaptive Channel Equalizers on FPGA

Different multiplication algorithms have different performance characteristics. Some are good at speed while others consume less area when implemented on hardware, like Field Programmable Gate Array (FPGA)-the advanced implementation technology for DSP systems. The eminent parallel and sequential multiplication algorithms include Shift and Add, Wallace Tree, Booth, and Array. The multiplier optimization attempts have also been reported in adders used for partial product addition. In this paper, analogous to conventional multipliers, two new multiplication algorithms implemented on FPGA are shown and compared with conventional algorithms as stand-alone and by using them in the implementation of FIR filters and adaptive channel equalizer using the LMS algorithm. The work is carried out on Spartan-6 FPG that may be extended for any type of FPGA. Results are compared in terms of resource utilization, power consumption, and maximum achieved frequency. The results show that for a small length of coefficients like 3-bit, the proposed algorithms work very well in terms of achieved frequency, consumed power, and even resource utilization. Whilst for the length greater than 3-bit, the Pipelined multiplier is much better in frequency than the proposed and conventional ones, and the Booth multiplier consumes fewer resources in terms of lookup tables.

An Effective Adaptive Combination Strategy for Distributed Learning Network

In this paper, we develop a modified adaptive combination strategy for the distributed estimation problem over diffusion networks. We still consider the online adaptive combiners estimation problem from the perspective of minimum variance unbiased estimation. In contrast with the classic adaptive combination strategy which exploits orthogonal projection technology, we formulate a non-constrained mean-square deviation (MSD) cost function by introducing Lagrange multipliers. Based on the Karush–Kuhn–Tucker (KKT) conditions, we derive the fixed-point iteration scheme of adaptive combiners. Illustrative simulations validate the improved transient and steady-state performance of the diffusion least-mean-square LMS algorithm incorporated with the proposed adaptive combination strategy.

Selective partial-update augmented complex-valued LMS algorithm and its performance analysis

Adaptive filtering applications such as acoustic echo cancellation may require a large number of filter weights in order to estimate the unknown system with a long response, leading to high computational complexity. Using partial-update techniques is an effective method to alleviate this issue, and two partial-update augmented complex-valued LMS (PU-ACLMS) algorithms have been recently proposed. However, their convergence rates severely deteriorate due to using a stochastic or sequential weight update manner. This paper proposes a new PU-ACLMS, which selects the weights corresponding to the M largest moduli of input samples to update, with M less than the number of all weights. The mean and mean-square performance of the proposed algorithm is then analyzed to predict its stochastic behavior. In order to achieve this goal, the values of two scale factors are derived by using multiple integrals, which play an important role in our performance analysis. Finally, the performance of the proposed algorithm is compared with that of the sequential PU-ACLMS and stochastic PU-ACLMS, and the theoretical findings are verified by extensive simulations.

Adaptive nonlinear ANC system based on time-domain signal reconstruction technology

When the primary reference signal obtained by the existing Active noise control (ANC) system is not accurate, the control effect of interior noise will be reduced or even fail. Considering the fault-tolerate and robustness of the system, the study proposes an adaptive nonlinear ANC system for interior noise, which contains noise signal decomposition, multi-network reconstruction model and Variable step-size LMS (VSS-LMS) algorithm. The noise signal decomposition method is used to address the non-stationary of the interior noise; Based on the signal components, the multi-network model for the noise signal reconstruction of passenger ear-sides is designed, which is pre-trained by a restricted Boltzmann machine for improved reconstruction accuracy and realize the adaptive extraction of signal features; And then based on the reconstruction signal components, the controller weights of corresponding components are adaptively updated by the VSS-LMS algorithm to control the passenger ear-sides noise. The effectiveness of the proposed adaptive nonlinear ANC system is validated using noise signal sources collected from a vehicle. Compared with the different ANC systems, the proposed system is superior in terms of fault-tolerant and robustness, which can guarantee stable work of the interior noise control.

Design and Analysis of the Fractional-Order Complex Least Mean Square (FoCLMS) Algorithm

In this work, a new class of stochastic gradient algorithm is developed based on fractional calculus. Unlike the existing algorithms, the concept of complex fractional gradient is introduced by employing Caputo’s fractional derivative which results in a fractional steepest descent algorithm and a fractional-order complex LMS (FoCLMS) algorithm. We demonstrate that with the Caputo’s fractional gradient definition, the Weiner solution remains invariant. Convergence analysis of the proposed FoCLMS algorithm is presented for both transient and steady state scenarios. Consequently, expressions for the learning curves and steady state EMSE are derived. Our theoretical developments are validated by simulation experiments. Extensive simulations are presented to investigate all possible scenarios: channel with negative weights and real input data, channel with positive weights and complex input data, and channel with complex weights and complex input data.

Frequency domain analysis of the mirror‐modified filtered‐x least mean squares algorithm with low ambient noise

SummaryThe mirror‐modified filtered‐x least mean squares (MMFxLMS ) algorithm is a variation of the FxLMS algorithm with online secondary path modeling that cannot diverge due to secondary path modeling errors. However, problems may occur when the ambient noise is not limited due to insufficient modeling power. This work shows that under a frequency domain analysis without ambient noise, the MMFxLMS algorithm is always stable, and expressions for the maximum residual noise level at any given time are obtained. It is also shown that, under the same context, convergence to the minimum residual noise is guaranteed. Still, convergence can be much slower for high secondary path modeling errors than that of the LMS or MFxLMS algorithms. Simulations confirm these results.

Stochastic analysis of the diffusion LMS algorithm for cyclostationary white Gaussian inputs

This paper studies the stochastic behavior of a specific version of the Diffusion Least-Mean Square (DLMS) algorithm in a system identification framework for a cyclostationary white Gaussian input. The considered DLMS version has a fusion center. The input cyclostationary signal is modeled by a white random process with periodically time-varying power. The system parameters vary according to a random walk model. The paper focusses on the behavior of the fusion center for DLMS for the special case when the nodes communicate only with the fusion center and vice versa. Mathematical models are derived for the mean and mean-square-deviation (MSD) behavior of the fusion center adaptive weights as a function of the input cyclostationarity. It is shown that the behavior of the fusion center is the same for both Combine-Then-Adapt (CTA) and Adapt-Then-Combine (ATC) diffusion strategies. Monte Carlo simulations are shown in excellent agreement with the theory. Finally the model is used to study the design of the DLMS algorithm for different nodal step-sizes, cyclostationarities, noise powers and weighting coefficients.

Micro-Jitter Control of Magnetically Suspended Control Moment Gyro Using Adaptive LMS Algorithm

Imbalanced vibration generated during the operation of a high-speed rotor inside a gyro is transmitted to the magnetically suspended control moment gyro through a magnetic bearing stator, resulting in micro-jitter. This greatly affects the control accuracy of the spacecraft attitude. In order to effectively suppress micro-jitter, the dynamic model of the magnetically suspended rotor with imbalanced mass is established in this article, and the imbalanced characteristics of the high-speed rotor are analyzed. Finally, a double-channel adaptive least mean square error algorithm is proposed. By utilizing that the radial X- and Y- displacement signals from the rotor displacement sensor are orthogonal to each other, a feedforward correction is applied to adaptively compensate the residual displacement stiffness of the magnetically suspended rotor system due to mass imbalance. While eliminating this synchronous current, the proposed algorithm also offsets the adverse effects of the low-pass characteristics of the power amplifier. Simulation and experimental results show that the method compensates the synchronous displacement stiffness force generated by the system with high precision, and realizes the micro-jitter control of the magnetically suspendedcontrol moment gyro.