LMS Adaptive Algorithm Research Articles

Adaptive harmonic estimation for power system protection

Many power system protection problems necessitate the measurement and track of the underlying current/voltage phasors. Adaptive LMS spectrum analyzers provide an ideal solution to such problems. This paper introduces a class of adaptive trigonometric spectrum analyzers. The underlying current/voltage is fed as a desired signal to an LMS adaptive algorithm. The reference input is a periodic regression derived from the basis set of the specified trigonometric discrete transform. The proposed algorithm is simple, computationally efficient, and exhibits a guaranteed stability and uniform convergence. A comparative study recommends the discrete Hartley transform. Simulations are provided to prove that the proposed spectrum analyzer is efficient in modeling faulty power system currents/voltages such as these arising from an over‐excitation of a power transformer.

Experimental evaluation of leaky LMS algorithms for active noise reduction in communication headsets

An adaptive leaky LMS algorithm has been developed to optimize stability and performance of active noise cancellation systems. The research addresses performance issues related to insufficient excitation, nonstationary noise fields, and signal-to-noise ratio. The algorithm is based on a Lyapunov tuning approach in which three candidate algorithms, each of which is a function of the instantaneous measured reference input, measurement noise variance, and filter length, provide varying degrees of trade-off between stability and performance. Each algorithm is evaluated experimentally for reduction of low-frequency noise in communication headsets and compared with that of traditional LMS algorithms. Acoustic measurements are made in a specially designed acoustic test cell which is based on the original work of Shaw, Brammer and co-workers and which provides a highly controlled and uniform acoustic environment. The stability and performance of the ANR system, including prototype communication headsets, are investigated for a variety of noise sources ranging from stationary white noise to highly nonstationary measured F-16 aircraft noise over a 20-dB dynamic range. Results demonstrate significant improvements in stability of Lyapunov-tuned LMS algorithms over traditional leaky or nonleaky normalized algorithms while providing noise reduction performance equivalent to that of the NLMS algorithm for idealized noise fields.

An adaptive vector quantized flexible precoder for a dynamic continuous frequency selective mobile channel

Bandwidth efficient techniques are required to satisfy the demand for future public mobile radio communication systems. Precoding is a nonlinear pre-equalization technique that provides equalization equivalent to a decision-feedback equalizer (DFE) while not being affected by coding. Precoding is shown to be better than conventional equalization over a digital mobile channel that is dynamic in its characteristics. A novel precoding vector quantization scheme is applied to the prediction filter in the precoder and is shown to provide comparable results to the LMS adaptation algorithm while reducing the overheads.

A simple FIR-filter interpretation of the extreme eigenvalues of a Toeplitz autocorrelation matrix

The convergence of LMS adaptive algorithms is typically limited by the eigenvalue spread of a Toeplitz autocorrelation matrix with elements from the central portion of an autocorrelation function. If that autocorrelation function describes a random process input to an FIR filter, the ratio of the filter output power to that obtained in response to a unit-power white input varies, as the filter response is changed, across the closed interval from the minimum eigenvalue to the maximum eigenvalue of the autocorrelation matrix. From this simple fact this paper develops several important relationships between these extreme eigenvalues and the spectrum at the filter input and does so quite simply and without resort to the classic asymptotic approximation with a cyclic matrix. In particular, (1) a pure line spectrum with fewer distinct lines than the matrix order leads to a singular matrix; (2) the spectral minimum/maximum is a lower/upper bound on the minimum/maximum eigenvalue; and (3) those bounds are approached asymptotically with increasing matrix order (the classic result). But the primary purpose of the paper is to use these results to provide intuition, based on filter-optimization experience, for the values of the extreme eigenvalues and for their variation with matrix order and key spectral parameters.

Complexity evaluation for the implementation of a pre-FFT equalizer in an OFDM receiver

A pre-FFT equalizer (PFE) has been shown to offer a significant throughput efficiency improvement when applied to an OFDM receiver. Alternatively, the PFE can be used to increase the maximum delay spread conditions under which the OFDM system can operate effectively. Due to the manner of its operation, the PFE requires the use of modified adaptation algorithms if iterative, decision directed, adaptation is required. The computational complexity required to implement a PFE and a suitable adaptation strategy is evaluated. Initially, an LMS adaptation algorithm is investigated and evaluated in terms of its suitability for application in conjunction with the PFE to standards such as ETSI DVB-T and HIPERLAN/2 and IEEE 802.11a. The complexity requirements are found to be high, particularly in the case of DVB-T. The demand for a lower complexity adaptation algorithm is thus identified. As a result, a CSI-based adaptation method is subsequently considered. The complexity requirement of this algorithm is also analyzed and evaluated and is shown to be much lower than that of the LMS algorithm. Thus, it is shown that if the CSI-based adaptation method is used, the dominant complexity requirement is due to the implementation of the equalizing filter and not the adaptation method. Reduced filter complexity requirement is thus shown to be the key to enabling effective application of the PFE. The ATSC 8-VSB standard is identified as a possible source of techniques to reduce or facilitate the high complexity demands for implementation of the PFE filter.

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.

Adapting CMAC neural networks with constrained LMS algorithm for efficient torque ripple reduction in switched reluctance motors

This paper presents a novel approach to learning control in switched reluctance motors (SRM) for torque ripple reduction using a cerebellar model articulation controller (CMAC) neural network. The approach modifies the conventional LMS adaptive algorithm using a variable learning rate function over the rotor angle of the motor under control. The criteria and method for the development of current profiles suitable for use over a wide range of motor speeds are described. In particular, current profiles can be designed to possess desirable characteristics by selection of learning rate function with appropriate switching angles during the training of the network. The approach allows the generation of optimal current profiles in terms of minimizing torque ripple and copper loss as the motor operates at low speeds, and of minimizing torque ripple, copper loss and rate of change of current as the motor runs at high speeds. Experimental measurement of the torque production characteristics of a 4 kW, four-phase switched reluctance motor forms the basis of simulation studies of this approach. Substantial simulation results are reported and the performance of learned current profiles analyzed. These demonstrate that developing CMAC-based adaptive controllers following this approach affords lower torque ripple with high power efficiency, while offering rapid learning convergence in system adaptation.

Control of structure-borne noise of a plate featuring piezoceramic actuators

This paper addresses active structural acoustic control of a flexible plate using piezoelectric actuators. The analytical model of a thin plate with simply supported boundary conditions is derived from Hamilton's principle and a control model represented by the transfer function is obtained. Optimal locations of the piezoelectric actuators are found such that it minimizes the radiated sound power at the farfield. With optimally designed actuators, an controller is designed by using the loop shaping design procedure to achieve robust acoustic control of the proposed system subjected to parameter variations and external disturbances. Control performance and robustness are presented in both frequency and time domains in order to demonstrate the effectiveness of the proposed approach. In addition, the comparison between the proposed robust controller and the conventional adaptive Filtered-x LMS algorithm is undertaken.

Active control of sound transmission through an industrial sound encapsulation

In this paper, an active control system is developed to enhance the sound transmission loss of a sound encapsulation at low frequencies. The sound encapsulation is used to shield a noise source, such as an air compressor. The control systems comprise two control loudspeakers and two error microphones. The Filtered-X LMS adaptive feedforward control algorithm is used to drive the signals at the error microphones to a minimum. The reference signal for the control algorithm is taken from the noise source, i.e., the tacho signal of the compressor. This study deals with the optimization of the location of control sources and error sensors in view of the achieved control performance. From this perspective it is important to note that minimizing the sound-pressure level at the error microphones, which are constrained to be located inside the sound encapsulation, does not necessarily reduce the acoustic intensity measured in the far field of the encapsulation (or at least, not to the same degree). Relevant issues which are considered are: the coupling of control sources with the acoustic modes of the enclosure, changes to the interior sound field due to active control, etc.

Convergence characteristics of frequency-domain LMS adaptive filters

The frequency-domain implementation of the adaptive LMS algorithm offers several advantages over the time-domain LMS algorithm. The primary advantage is that the orthogonality of the individual bins in the signal spectra permit the implementation of a single complex LMS filter for each FFT bin independently, each with a separate convergence parameter. The result is a uniform rate of convergence for all FFT bins as opposed to the time-domain algorithm which converges only as fast as the dominant eigenvalue of the input data. An additional parameter which affects frequency-domain LMS convergence is the overlap between successive FFT buffers. It is shown that the maximum advisable overlap between FFT buffers is 50%. Greater overlap between FFT buffers can lead to oscillations (and even instability) in the adaptive algorithm. Experimental results are presented which illustrate the convergence characteristics of a frequency-domain adaptive active noise control system for several different types of reference inputs.

Parallel Implementation of Control Algorithms

This paper presents an investigation of two approaches to parallel implementation of an LMS adaptive algorithm using several development platforms. The first approach is a modification of previously proposed parallel implementation of the algorithm and the second is the parallel implementation using the Development Framework. The target architecture consists of a two processor message-passing system. A comparative evaluation of the two approaches is presented on the basis of the execution time of the algorithm.

The Linear Prediction Method of Fading Channel Estimation for the RakeReceiver with Impulsive Interference

Parameter estimation of the multipath and fading channel is investigated for the Rake combiner used in a CDMA system with coherent demodulation. A linear predictor is proposed to obtain a better estimation. Since the industrial interference environment is generally impulsive, a parallel LMS adaptive algorithm is proposed to reduce the impact of impulsive noise on predictor weights adjustment. Performance analysis and computer simulations are presented.

An accurate quality factor tuning scheme for IF and high-Q continuous-time filters

An important aspect of reducing power and area of RF/IF systems is putting high-frequency filters on-chip instead of using off-chip crystal, ceramic, or SAW filters now used. The largest challenge facing designers is the vulnerability of high-frequency and high-Q continuous-time filters to parasitics and process variations, requiring automatic tuning of both center frequency and quality factor. Automatic center frequency tuning is well documented, with accuracies of <1% error. Q-tuning is not as well defined, with the best reported results at about 20-30% error. The Q-tuning method proposed here improves the accuracy of Q-tuning, with experimental Q-tuning error about 1%. The basis for the proposed method is the magnitude-locked-loop (MLL) Q-tuning technique. The scheme removes the peak detectors and utilizes the continuous-time adaptive LMS algorithm to update the biquad quality factor. As a test verification of the proposed Q-tuning scheme, a fourth order OTA-C 10.7 MHz bandpass filter is designed and fabricated in a 1.2 /spl mu/m n-well CMOS process. The filter consists of two cascaded biquads, each with a desired quality factor of 20 and the same center frequency. Center frequency tuning is provided by the conventional phase-locked loop using a voltage controlled oscillator scheme, and Q-tuning is by the proposed scheme. The reference signal for the Q-tuning circuit is simply the frequency control oscillator's output.

On-line measurement of error-path impulse response for an adaptive ANR headset

A digital, adaptive ANR headset system has been developed and tested in the laboratory, using a filtered-X LMS adaptive control algorithm and a floating-point digital signal processor (DSP). The implementation of the filtered-X LMS adaptation algorithm requires an impulse response (IR) model of the so-called ‘‘error-path,’’ which consists of the serial connection of an earphone, earcup acoustics, microphone, and electronic amplifiers and filters. Though the IR model can be measured off-line for laboratory studies using standard measurement procedure, on-line measurement or identification, using the DSP engine and digital signal processing techniques, is considered necessary and advantageous for practical applications. This paper discusses a DSP-based identification technique for the error-path IR model, which employs the well-known pseudorandom binary signal (PRBS), also called the maximum length sequence (MLS) signal, as the input to the error path. In this paper, the measurement method and system will be discussed. As an example, the error-path impulse response and the corresponding ANR results obtained in a laboratory setup will be presented. [Work supported by DCIEM, Toronto, Canada.]

Leaky LMS algorithm: MSE analysis for Gaussian data

Despite the widespread usage of the leaky LMS algorithm, there has been no detailed study of its performance. This paper presents an analytical treatment of the mean-square error (MSE) performance for the leaky LMS adaptive algorithm for Gaussian input data. The common independence assumption regarding W(n) and X(n) is also used. Exact expressions that completely characterize the second moment of the coefficient vector and algorithm steady-state excess MSE are developed. Rigorous conditions for MSE convergence are also established. Analytical results are compared with simulation and are shown to agree well.

Effect of delay on the performance of the leaky LMS adaptive algorithm

This correspondence studies the effect of a nonzero delay on the performance of the leaky LMS algorithm. The stability bound on the step size is derived for error convergence. It is shown that leakage allows for larger bounds on the step size of the delayed LMS algorithm. Theoretical bounds are verified by simulations.

Capacity of the linear decorrelating detector for QS-CDMA

We study the performance and capacity of a quasi-synchronous code-division multiple-access (QS-CDMA) cellular system employing the decorrelating detector. It is assumed that each of N users has a GPS generated local clock, and attempts to transmit in synchrony with the other users in its cell. The detector makes use of the small timing uncertainties to build the interference signal space and perfectly cancel the interference. Results are compared with those of an adaptive MSE receiver. It is shown that when the LMS adaptive algorithm is employed, the mean-squared-error misadjustment significantly affects the receiver performance. Finally, system capacities in terms of users/cell are evaluated.

Modified LMS adaptive algorithm for CMAC neuralnetwork basedcontrol of switched reluctance motors

A novel approach to adapting the weights of a CMAC neural network for torque ripple reduction in switched reluctance motors is proposed, using a variable learning rate function within the standard LMS algorithm. Simulation results demonstrate that training CMAC networks following this approach affords low torque ripple with high power efficiency.

A new efficient LMS adaptive filtering algorithm

A new efficient LMS adaptive filtering algorithm is proposed. The algorithm has comparable performance to that of the direct-form LMS algorithm (DLMS), while it costs N/2-1 fewer multiplications at the expense of N/2+5 more additions than the DLMS algorithm, where N is the number of filter taps. The new algorithm has one more parameter adaptation than the DLMS algorithm. Further, the algorithm was combined with sign LMS algorithm (SA), signed regressor algorithm (SRA) and zero forcing (ZFA) algorithm for more complexity reduction. Simulation results showed that the new combined algorithms converge as fast as the direct-form SA, SRA and ZFA algorithms, while still maintaining comparable performances.

A fast response split-path median LMS algorithm

An adaptive median LMS algorithm based on a split FIR filter structure is presented. The algorithm has a better tracking capability and a faster convergence rate by means of reducing the eigenvalue spread of the input correlation matrix. The performance of the adaptive system is evaluated in a line enhancement application. It is found that the algorithm is effective in both the suppression of impulsive interference and preservation of edge details of the desired signal.