Frequency-domain LMS Research Articles

Adaptive inverse control of random vibration based on the filtered-X LMS algorithm

Random vibration control is aimed at reproducing the power spectral density (PSD) at specified control points. The classical frequency-spectrum equalization algorithm needs to compute the average of the multiple frequency response functions (FRFs), which lengthens the control loop time in the equalization process. Likewise, the feedback control algorithm has a very slow convergence rate due to the small value of the feedback gain parameter to ensure stability of the system. To overcome these limitations, an adaptive inverse control of random vibrations based on the filtered-X least mean-square (LMS) algorithm is proposed. Furthermore, according to the description and iteration characteristics of random vibration tests in the frequency domain, the frequency domain LMS algorithm is adopted to refine the inverse characteristics of the FRF instead of the traditional time domain LMS algorithm. This inverse characteristic, which is called the impedance function of the system under control, is used to update the drive PSD directly. The test results indicated that in addition to successfully avoiding the instability problem that occurs during the iteration process, the adaptive control strategy minimizes the amount of time needed to obtain a short control loop and achieve equalization.

Analysis of Convergence of a Frequency-Domain LMS Adaptive Filter Implemented as a Multi-Stage Adaptive Filter

We present an analysis of the convergence of the frequency-domain LMS adaptive filter when the DFT is computed using the LMS steepest descent algorithm. In this case, the frequency-domain adaptive filter is implemented with a cascade of two sections, each updated using the LMS algorithm. The structure requires less computations compared to using the FFT and is modular suitable for VLSI implementations. Since the structure contains two adaptive algorithms updating in parallel, an analysis of the overall system convergence needs to consider the effect of the two adaptive algorithms on each other, in addition to their individual convergence. Analysis was based on the expected mean-square coefficient error for each of the two LMS adaptive algorithms, with some simplifying approximations for the second algorithm, to describe the convergence behavior of the overall system. Simulations were used to verify the results.

FREQUENCY DOMAIN NLMS ALGORITHM FOR ENHANCED JAM RESISTANT GPS RECEIVER

An optimal beamformer attempts to increase SNR at the array output by adapting its pattern to minimize some cost function. This is to say that, the cost function is inversely associated with the quality of the signal. Therefore by minimizing the cost function we can maximize signal at the array output. The primary optimal beamforming technique discussed in this paper will be MMSE, LMS, Frequency Domain LMS for GPS multipath reduction. In case of a GPS satellite, the DOA of the desired signal is mathematically known because the position of a satellite in an orbit is fixed at a particular time instant. So in some particular adaptive antenna algorithm the DOA of the desired signal is directly given as input.

Variable step-size multichannel frequency-domain LMS algorithm for blind identification of finite impulse response systems

The choice of step size is a critical factor in blind identification of single-input multi-output systems using adaptive multichannel frequency-domain least-mean-squares (MCFLMS) algorithm. The proper step size is dependent on the signal power and it influences the speed of convergence and the final misalignment error. Applying normalised MCFLMS (NMCFLMS) algorithm, the dependency of the step-size parameter on signal power can be eliminated; however, it is shown that even for a moderate signal-to-noise ratio, the algorithm fails to converge to the eigenvector corresponding to the minimum eigenvalue of the data correlation matrix and hence misconverges to a fictitious solution. A self-adaptive variable step-size MCFLMS (VSS-MCFLMS) algorithm that optimises the performance of the algorithm in each iteration in order to achieve minimum misalignment with the true channel impulse response is proposed. The convergence analysis of the proposed algorithm is performed and it is shown that the VSS-MCFLMS algorithm converges, both in noise-free and noisy conditions, to the eigenvector corresponding to the minimum eigenvalue and is therefore more noise robust when compared with the NMCFLMS. The algorithm also shows the optimal speed of convergence in a noise-free case and the proposed variable step size guarantees the stability of the algorithm. Simulation results are presented to demonstrate that the proposed VSS-MCFLMS algorithm gives lower final misalignment when compared with the NMCFLMS algorithm without sacrificing the speed of convergence and computational efficiency.

NEXT cancellation system with improved convergence rate and tracking performance

A near-end crosstalk (NEXT) cancellation system that uses frequency-domain least-mean-squares (FDLMS) adaptive filters is proposed. The new system is equipped with a mechanism whereby the NEXT signals are detected and then FDLMS adaptive filters are assigned to cancel only the significant NEXT signals. The paper also explores various schemes of assigning step sizes to the adaptive filters. It has been found that by making the step sizes proportional to the magnitudes of the NEXT signals during the initial phases of adaptation, and equal later on, significant improvement in the convergence rate can be achieved. By returning after convergence to step sizes that are proportional to the magnitudes of the NEXT signals, a much better tracking performance can also be achieved.

LMI design of frequency domain LMS filters for active noise control

Recently, a frequency-domain adaptive filter design method for active noise control has been proposed based on the so-called least mean square algorithm. However, this method does not sufficiently exploit the degree of freedom of the step parameter of the recursive rule in the case where a priori information on an uncertain plant is available. This paper proposes a design method of the step parameter such that noise cancellation is guaranteed against the plant uncertainty. The design problem of the step parameter is reduced to a semidefinite programming problem which is efficiently solvable. Experimental results are provided to illustrate the effectiveness of the proposed method.

Experimental energetic analyses of an actively controlled one-dimensional acoustic waveguide

Technological development has made it possible to implement digital active noise control systems in real time. This work compares the performance of different adaptive control methods applied to a one-dimensional waveguide. The compared control methods are the frequency-domain filtered-X LMS using potential energy density and kinetic energy density as cost functions, and the active sound intensity control (ASIC), which uses active intensity as the cost function. The ASIC controller is implemented with both the P–U approach (measuring pressure and particle velocity at the same time) and the P–P approach (using two microphones to estimate the active intensity). The waveguide is a circular PVC duct with a primary source placed at one end, the secondary source placed near the mid-span of the duct, and with an open-ended termination. The analyses were performed comparing the results in terms of the potential energy density, the active intensity, and the acoustic power radiated by the sources. Moreover, it is shown how to choose suitable error sensors and their influence in the performance of the ASIC controller. The results show that the control methods achieved the same final result and, as expected, when the volume velocity of the secondary source was driven to the optimal volume velocity, the primary source and the secondary source radiated less acoustic power than the uncontrolled primary source. Besides, the sound intensity was effectively attenuated throughout the duct.

Improving the response of a wheel speed sensor using an adaptive line enhancer

In this paper, an Adaptive Line Enhancer (ALE) based on a Frequency-Domain Least-Mean-Square (FDLMS) adaptive algorithm is used to predict the response of a wheel speed sensor embedded in a car undergoing performance tests. In this case, an ALE is used to predict a signal buried in a broad-band noise background where we have little or no prior knowledge of the signal or noise characteristics. The results of the experiment show that this device behaves as an adaptive notch filter whose null points are determined by the frequency of the noise and/or interference corrupting the electrical signal, and these also show a significant improvement in the signal-to-noise ratio at the system output.

A class of frequency-domain adaptive approaches to blind multichannel identification

We extend our previous studies on adaptive blind channel identification from the time domain into the frequency domain. A class of frequency-domain adaptive approaches, including the multichannel frequency-domain LMS (MCFLMS) and constrained/unconstrained normalized multichannel frequency-domain LMS (NMCFLMS) algorithms, are proposed. By utilizing the fast Fourier transform (FFT) and overlap-save techniques, the convolution and correlation operations that are computationally intensive when performed by the time-domain multichannel LMS (MCLMS) or multichannel Newton (MCN) methods are efficiently implemented in the frequency domain, and the MCFLMS is rigorously derived. In order to achieve independent and uniform convergence for each filter coefficient and, therefore, accelerate the overall convergence, the coefficient updates are properly normalized at each iteration, and the NMCFLMS algorithms are developed. Simulations show that the frequency-domain adaptive approaches perform as well as or better than their time-domain counterparts and the cross-relation (CR) batch method in most practical cases. It is remarkable that for a three-channel acoustic system with long impulse responses (256 taps in each channel) excited by a male speech signal, only the proposed NMCFLMS algorithm succeeds in determining a reasonably accurate channel estimate, which is good enough for applications such as time delay estimation.

A computationally efficient frequency-domain LMS algorithm with constraints on the adaptive filter

The frequency domain implementation of the LMS algorithm is attractive due to both the reduced computational complexity and the potential of faster convergence compared with the time domain implementation. Another advantage is the potential of using frequency-domain constraints on the adaptive filter, such as limiting its magnitude response or limiting the power of its output signal. This paper presents a computationally efficient algorithm that allows the incorporation of various frequency domain constraints into the LMS algorithm. A penalty function formulation is used with a steepest descent search to adapt the filter so that it converges to the new constrained minimum. The formulation of the algorithm is derived first, after which the use of some practical constraints with this algorithm and a simulation example for adaptive blind equalization are described.

Analysis of partitioned frequency-domain LMS adaptive algorithm with application to a hands-free telephone system echo canceller

For adaptive filters with long impulse responses and requiring modelling by an FIR filter, algorithms incorporating computationally efficient DFT-based adaptive block filters are the design of choice. The reduction in computational complexity is very significant in applications such as active noise control and the hands-free telephone system echo cancellation problem where impulse responses of more than a 1000 samples are common. The performance of frequency-domain adaptive algorithms is analysed and, when properly designed, shown to be equivalent to time-domain algorithms with uncorrelated input signals. The design parameters include: block length, DFT length and partitioning of the impulse response. The study includes both constrained and unconstrained parameter adaptation. Guidelines to the design of partitioned frequency-domain LMS (PFLMS) algorithms are given. Copyright © 2000 John Wiley & Sons, Ltd.

On the structure and invertibility of the autocorrelation matrix in the unconstrained FDLMS problem

We consider the stationary (nonadaptive) unconstrained frequency domain LMS problem and show that the autocorrelation matrix appearing in the normal equations can be expressed as a sum of the standard Toeplitz autocorrelation matrix and its cyclic shifts. We then derive necessary and sufficient conditions for the invertibility, slightly generalizing the existing results in the published literature.

The generalized multidelay adaptive filter: structure and convergence analysis

Frequency-domain adaptive filters have long been recognized as an attractive alternative to time-domain algorithms when dealing with systems with large impulse response and/or correlated input. New frequency-domain LMS adaptive schemes have been proposed. These algorithms essentially retain the attractive features of frequency-domain implementations, while requiring a processing delay considerably smaller than the length of the impulse response. The authors show that these algorithms can be seen as particular implementations of a more general scheme, the generalized multidelay filter (GMDF). Within this general class of algorithms, we focus on implementations based on the weighted overlap and add reconstruction algorithms; these variants, overlooked in previous contributions, provide an independent control of the overall processing delay and of the rate of update of the filter coefficients, allowing a trade-off between the computational complexity and the rate of convergence. We present a comprehensive analysis of the performance of this new scheme and to provide insight into the influence of impulse response segmentation on the behavior of the adaptive algorithm. Exact analytical expressions for the steady-state mean-square error are first derived. Necessary and sufficient conditions for the convergence of the algorithm to the optimal solution within finite variance are then obtained, and are translated into bounds for the stepsize parameter. Simulations are presented to support our analysis and to demonstrate the practical usefulness of the GMDF algorithm in applications where large impulse response has to be processed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Generalized sliding FFT and its application to implementation of block LMS adaptive filters

This paper has two contributions. First, the concept of the generalized sliding fast Fourier transform (GSFFT) as an efficient implementation of the hopping FFT is introduced. Application of the GSFFT is broad and not limited to what has been considered in this paper. The frequency domain block LMS (FBLMS) adaptive filters are then revised, and their implementations for block lengths less than the length of the adaptive filter are studied. The GSFFT and the available pruned FFTs are used to give an efficient implementation of these filters. In the particular case of the block length equal to one, where the FBLMS algorithm reduces to the frequency domain LMS (FLMS) algorithm, it is shown that the latter can be implemented with the order of M complexity, where M is the length of the adaptive filter. >

Speech enhancement using sub-band intermittent adaptation

A sub-band multisensor structure using intermittent adaption is proposed for speech enhancement. The convergence of the proposed method is compared with conventional LMS and frequency domain LMS and a dramatic increase in convergence rate is shown using both simulated and real data. Preliminary investigation of sub-band filter order is also reported.

On the Steady State Performance of Frequency Domain LMS Algorithms

The use of the fast Fourier transform (FFT) in the implementation of the least mean square (LMS) algorithm in the frequency Manuscript received May 24, 1990; revised May 4, 1992. A. Feuer is with the Department of Electrical Engineering, TechnionIsrael Institute of Technology, Haifa 32000, Israel. R. Cristi is with the Department of Electrical and Computer Engineering, Naval Postgraduate School, Monterey, CA 93943. IEEE Log Number 9203376. 1053-587X/93$03.00 © 1993 IEEE 420 IEEE TRANSACTIONS ON SIGNAL PROCESSING. VOL. 41. NO. I. JANUARY 1993 domain results in several types of algorithms, two of which can be classified as constrained and unconstrained. In this correspondence, we point out that, in general, especially with correlated data, the unconstrained algorithm may have a significant performance advantage in steady state if block mean square error is the criterion. Furthermore, we point out here that, in the constrained algorithms, the choice of different step sizes in different frequency bins (as is commonly done) will very likely result in a deterioration of steady state performance. This does not happen in the unconstrained algorithm.

Frequency-domain implementation of Griffiths–Jim adaptive beamformer

It is well known that the drawback of the time-domain least-mean-square (LMS) algorithm proposed by Widrow [Proc. IEEE 63, 719–720 (1975)] in adaptive filter applications is that its convergence speed decreases as the eigenvalue spread of the input autocorrelation matrix increases. However, this problem can be overcome by employing the transform-domain LMS method [Narayan et al., IEEE Trans. ASSP 31, 609–615 (1983)] which first transforms input time-domain signals into another transform-domain signals through DFT or some orthogonal transforms and then uses the self-orthogonalizing algorithm [Gitlin and Magee, IEEE Trans. Commun. 25, 666–672 (1977)] to optimize the variable weights of an adaptive filter. This method has been shown to offer great improvement in convergence rate over the time-domain LMS method. The objective of this paper is to apply the frequency-domain LMS algorithm with the self-orthogonalizing technique, called FLMS, to the Griffiths–Jim adaptive beamformer to accelerate the convergence rate for real-time processing of adaptive array signals. It is shown that the two minimum mean-square errors of the beamformer implemented in the time and frequency domains are identical. Computer simulations show that the adaptive beamformer using the FLMS exhibits faster convergence behavior and better performance of nulling jammers than that using the LMS, especially for the larger eigenvalue spread.

On the implementation of the frequency-domain LMS adaptive filter

Alternative implementations for the frequency-domain LMS adaptive filter are presented. One of the implementations uses an LMS steepest-descent algorithm to compute the discrete Fourier transform (DFT). Therefore, the frequency-domain LMS adaptive filter is implemented as a cascade of two parts, with each one running the LMS adaptive algorithm. This requires fewer computations than the FFT for large filter lengths. Simulations of practical applications of frequency-domain LMS adaptive filters are carried out to determine their suitability, and comparisons are made with simulations using the FFT. For real input data, another frequency-domain LMS adaptive filter is suggested based on the discrete Hartley transform (DHT). >

A frequency-domain LMS comb filter

A new application of the least mean squares algorithm (LMS) to signal analysis and enhancement is presented. The LMS is implemented in the frequency domain to simulate a fixed-notch filter that nulls sinusoids with harmonically related frequencies. In the proposed structure, the Fourier transform (FT) block length is set to represent the fundamental period of the undesired periodic signal. The paper shows that by applying constant deterministic signals to the reference input, the frequency-domain LMS adaptive structure operates on eliminating all constant values in the transform and, therefore, cancels all harmonic frequency components, leaving out other components in the signal to propagate to the error with minimum distortion. >

Adaptive filtering using the fast Walsh-Hadamard transformation

A fast implementation of the least-mean-square error (LMS) adaptive transversal filter is proposed. The fast Walsh-Hadamard transform technique is adopted in this implementation. This filter is shown to promise a significant reduction in computation over both the conventional time-domain and the frequency-domain LMS adaptive filters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>