Standard Least Mean Square Algorithm Research Articles

Cosine Least Mean Square Algorithm for Adaptive Beamforming

Beamforming and multiple-input multiple-output (MIMO) antenna configurations have received worldwide interest during the recent time. Various beamforming algorithm has been proposed and employed in different applications. The Least Mean Square (LMS) algorithm has become one of the most widespread adaptive beamforming techniques because of its simplicity and robustness. This paper presents a new variant of LMS algorithm named as Cosine Least Mean Square (Cos-LMS) which uses the efficient computation of array factor for linear antenna array.This algorithm gives improved performance in beam width reduction, side lobe level reduction, null depth, and stability as compared to standard LMS and other variants of LMS algorithm. The performance improvement by Cos-LMS algorithm is accomplished without increasing the computationalcomplexity of standard LMS algorithm.

Enhanced Adaptive Filtering Algorithm Based on Sliding Mode Control for Active Vibration Rejection of Smart Beam Structures

This article investigates vibration rejection for a continuous smart structure using piezoelectric bimorph patches. Such a structure has inherent nonlinearities, such as hysteresis and creep, and the whole system may experience unexpected disturbances, uncertainties, and noise from external sources. Thus, it is very important to design the active control scheme carefully with adaptive filtering systems to deal with these conditions. An advanced adaptive filtering algorithm was developed based on the conventional least mean squares (LMS) method and sliding mode control for the active vibration rejection system. The sliding mode controller is applied to the standard LMS algorithm to overcome problems with misadjustment and excess error in an optimal manner. A numerical analysis and laboratory experiment show that the technique can significantly attenuate the vibration of the smart structure at different levels and broadband frequency spectra. In addition, unidentified impedance is chosen to change the distribution of the mass, and the robustness and the adaptivity of the proposed approach are verified. The experimental results show that the method can isolate impulse-type vibrations of at least 2.8 dB, even with the adjusted mass arrangement.

Adaptive Filtering Based on Time-Averaged MSE for Cyclostationary Signals

Adaptive filters are commonly used in many signal processing and communications systems. In many practical digital communications scenarios, including, for example, interference-limited wireless and wireline communications, as well as narrowband power line communications, the considered signals are jointly cyclostationary . Yet, most works on adaptive filtering of cyclostationary signals used ad hoc application of adaptive algorithms designed for stationary signals, e.g., the least-mean-squares (LMS). It is known that these algorithms may not converge for jointly cyclostationary signals. In this paper, we rigorously study the optimal adaptive filtering of jointly cyclostationary signals. We first identify the relevant objective as the time-averaged mean-squared error criterion (TA-MSE), and obtain an adaptive algorithm as the stochastic approximation of the TA-MSE minimizer. When the considered signals are jointly stationary, the algorithm specializes to the standard LMS algorithm. We provide a comprehensive transient and steady-state performance analysis without imposing a specific distribution on the considered signals, and derive conditions for convergence and stability. The algorithm, which we call time-averaged LMS , is applied to practical scenarios in a simulations study, and an excellent agreement between the theoretical and the empirical performance is observed.

Hybrid Nelder-Mead search based optimal Least Mean Square algorithms for heart and lung sound separation

Algorithms for separation of heart sounds from background lung sound noises are vital for accurate diagnosis of heart diseases. In this paper, an improved adaptive noise cancellation technique based on the Least Mean Square (LMS) algorithm is used to separate heart sounds from lung sounds. The step size parameter in the LMS algorithm is optimally chosen using a hybrid Nelder-Mead (H-NM) optimization algorithm. The NM algorithm is initialized with a good initial solution by using computationally cheap random search to compute a rough estimate of the global minimum. Initialization of the NM algorithm with a good initial guess avoided convergence to shallow local minima and improved the quality of the final solution. The effects of using two state-of-the-arts biologically inspired heuristic optimization algorithms instead of the H-NM algorithm and three variants of the standard LMS algorithm are investigated. The correlation coefficient between the ideal and filtered heart sound signal and running time-complexity of different algorithms are taken as the metric for comparison of different heart sound separation approaches. Simulation results indicate that the approach presented in this paper performs significantly better than a variety of alternate approaches on heart sound separation problems.

Zero‐attracting variable‐step‐size least mean square algorithms for adaptive sparse channel estimation

SummaryRecently, sparsity‐aware least mean square (LMS) algorithms have been proposed to improve the performance of the standard LMS algorithm for various sparse signals, such as the well‐known zero‐attracting LMS (ZA‐LMS) algorithm and its reweighted ZA‐LMS (RZA‐LMS) algorithm. To utilize the sparsity of the channels in wireless communication and one of the inherent advantages of the RZA‐LMS algorithm, we propose an adaptive reweighted zero‐attracting sigmoid functioned variable‐step‐size LMS (ARZA‐SVSS‐LMS) algorithm by the use of variable‐step‐size techniques and parameter adjustment method. As a result, the proposed ARZA‐SVSS‐LMS algorithm can achieve faster convergence speed and better steady‐state performance, which are verified in a sparse channel and compared with those of other popular LMS algorithms. The simulation results show that the proposed ARZA‐SVSS‐LMS algorithm outperforms the standard LMS algorithm and the previously proposed sparsity‐aware algorithms for dealing with sparse signals. Copyright © 2015 John Wiley & Sons, Ltd.

Reweighted l1-norm penalized LMS for sparse channel estimation and its analysis

A new reweighted l1-norm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel impulse response (CIR), sparsity-aware modifications of the LMS algorithm aim at outperforming the standard LMS by introducing a penalty term to the standard LMS cost function which forces the solution to be sparse. Our reweighted l1-norm penalized LMS algorithm introduces in addition a reweighting of the CIR coefficient estimates to promote a sparse solution even more and approximate l0-pseudo-norm closer. We provide in depth quantitative analysis of the reweighted l1-norm penalized LMS algorithm. An expression for the excess mean square error (MSE) of the algorithm is also derived which suggests that under the right conditions, the reweighted l1-norm penalized LMS algorithm outperforms the standard LMS, which is expected. However, our quantitative analysis also answers the question of what is the maximum sparsity level in the channel for which the reweighted l1-norm penalized LMS algorithm is better than the standard LMS. Simulation results showing the better performance of the reweighted l1-norm penalized LMS algorithm compared to other existing LMS-type algorithms are given.

Light wave transmission through free space using atmospheric laser links with adaptive equalization

The utilization of adaptive equalization in the design of atmospheric laser link transceiver architectures that can be used for television and broadcast signal interconnect between the external place of event and the master control room is suggested. At the transmitter side of the proposed transceiver; an array of atmospheric laser sources, digital signal processing, and optical radiators are used to send light waves in free space. At the receiver side, an adaptive finite impulse response least mean square (LMS) equalizer with activity detection guidance (ADG) and tap decoupling (TD) is used to mitigate the effect of channel impairments. The performance of the suggested adaptive equalizer is compared with that of the conventional adaptive equalizer based only on the standard LMS algorithm. The simulation results revealed that the adaptive LMS equalizer with ADG and TD is a promising solution for the inter-symbol interference problem in optical wireless communication systems.

Algorithm for Suppression of Wideband Probing in Adaptive Array with Multiple Desired Signals

The integrity of signal environment for a navigation system among other factors depends critically on the capability of the adaptive antenna array in controlling (reconfiguring) its radiation pattern for various signal scenarios. For a signal environment consisting of simultaneous multiple desired signals and probing sources, the output signal-to-noise ratio of the adaptive antenna array depends on the efficiency of the adaptive algorithm employed for weight estimation. Sufficient antenna gain is required to be maintained towards each of the desired signals, while simultaneously suppressing returns towards the sources probing from distinctly different directions. The weight estimation for the multiple desired signal environments is carried out using a novel modified version of the improved least mean square (LMS) algorithm. This modified scheme effectively suppresses the narrowband/wideband probing towards the antenna array (linear/planar). The weight estimation and the steering vector are adapted according to the multiple desired signal environments. Each spectral line of the wideband source is considered as an independent narrowband source. This is incorporated in the correlation matrix of the received signal. The simulation results demonstrate the efficacy of this novel algorithm in active cancellation of narrowband/wideband probing sources, even while the simultaneous multiple signals in desired directions are maintained. The performance of the proposed algorithm is reported to be better than that of standard LMS and recursive LMS algorithm. Defence Science Journal, 2011, 61(4), pp.325-330 , DOI:http://dx.doi.org/10.14429/dsj.61.1092

LMS Coefficient Filtering for Time-Varying Chirped Signals

This paper presents coefficient filtering techniques in the least mean squares (LMS) algorithm to improve adaptive predictor tracking performance for time-varying chirped signals. The example application used in this paper is an electronic support measure (ESM) receiver for detecting radar chirped pulses. The leakage LMS, momentum LMS, and the proposed future-state coefficient (FC-LMS) filtering algorithms have been studied. The leakage LMS algorithm has the ability to remove the memory effect of the initial converged time-varying frequency of the chirped signal, thus improving the radar pulse detection performance. The momentum LMS is able to search for the time-varying optimum weight solution more efficiently, and the FC-LMS uses a parallel technique to retain the LMS throughput while being able to show a better tracking performance for chirped signals compared with the standard LMS algorithm.

Fast hierarchical least mean square algorithm

We propose a hierarchical least mean square (LMS) algorithm where the taps of a filter are organized into a hierarchy, and the minimization process is performed repeatedly from the bottom level to the top level. The results of performance evaluation indicate that the proposed hierarchical LMS algorithm can speed up convergence rate and reduce the excess mean squared error (MSE) of the standard LMS algorithm.

Adaptive Volterra filters for active control of nonlinear noise processes

This paper presents a Volterra filtered-X least mean square (LMS) algorithm for feedforward active noise control. The research has demonstrated that linear active noise control (ANC) systems can be successfully applied to reduce the broadband noise and narrowband noise, specifically, such linear ANC systems are very efficient in reduction of low-frequency noise. However, in some situations, the noise that comes from a dynamic system may he a nonlinear and deterministic noise process rather than a stochastic, white, or tonal noise process, and the primary noise at the canceling point may exhibit nonlinear distortion. Furthermore, the secondary path estimate in the ANC system, which denotes the transfer function between the secondary source (secondary speaker) and the error microphone, may have nonminimum phase, and hence, the causality constraint is violated. If such situations exist, the linear ANC system will suffer performance degradation. An implementation of a Volterra filtered-X LMS (VFXLMS) algorithm based on a multichannel structure is described for feedforward active noise control. Numerical simulation results show that the developed algorithm achieves performance improvement over the standard filtered-X LMS algorithm for the following two situations: (1) the reference noise is a nonlinear noise process, and at the same time, the secondary path estimate is of nonminimum phase; (2) the primary path exhibits the nonlinear behavior. In addition, the developed VFXLMS algorithm can also be employed as an alternative in the case where the standard filtered-X LMS algorithm does not perform well.

Low-power pipelined LMS adaptive filter architectures with minimal adaptation delay

The use of delayed coefficient adaptation in the least mean square (LMS) algorithm has enabled the design of pipelined architectures for real-time transversal adaptive filtering. However, the convergence speed of this delayed LMS (DLMS) algorithm, when compared with that of the standard LMS algorithm, is degraded and worsens with increase in the adaptation delay. Existing pipelined DLMS architectures have large adaptation delay and hence degraded convergence speed. We in this paper, first present a pipelined DLMS architecture with minimal adaptation delay for any given sampling rate. The architecture is synthesized by using a number of function preserving transformations on the signal flow graph representation of the DLMS algorithm. With the use of carry-save arithmetic, the pipelined architecture can support high sampling rates, limited only by the delay of a full adder and a 2-to-1 multiplexer. In the second part of this paper, we extend the synthesis methodology described in the first part, to synthesize pipelined DLMS architectures whose power dissipation meets a specified budget. This low-power architecture exploits the parallelism in the DLMS algorithm to meet the required computational throughput. The architecture exhibits a novel tradeoff between algorithmic performance (convergence speed) and power dissipation.

Combined LMS/F algorithm

A new adaptive filter algorithm has been developed that combines the benefits of the least mean square (LMS) and least mean fourth (LMF) methods. This algorithm, called LMS/F, outperforms the standard LMS algorithm judging either constant convergence rate or constant misadjustment. While LMF outperforms LMS for certain noise profiles, its stability cannot be guaranteed for known input signals even For very small step sizes. However, both LMS and LMS/F have good stability properties and LMS/F only adds a few more computations per iteration compared to LMS. Simulations of a non-stationary system identification problem demonstrate the performance benefits of the LMS/F algorithm.

Learning characteristics of transpose-form LMS adaptive filters

Transpose-form filter structures have several advantages over direct-form structures for high-speed, parallel implementation of finite impulse response (FIR) filters. Transpose-form least mean square (LMS) adaptive filter architectures are often used in parallel implementations; however, the behavior of these filters differs from the standard LMS algorithm and has not been adequately studied. A method for determining the maximum convergence factor yielding convergence of the mean of the transpose-form LMS adaptive filter taps is developed. The analysis reveals the great similarity of transpose-form LMS adaptive filters to delayed-update LMS adaptive filters, which have been much more fully characterized. >

Performance improvement of LMS algorithm

AbstractWith the recent rapid progress of VLSI, digital signal processing is used in a wide variety of areas. Recently, the adaptive system has been used widely in many applications.This paper describes a new algorithm to improve the rate of the adaptation of the LMS (Least Mean Square) algorithm, which is used most commonly as the adaptive filtering algorithm. The new algorithm is based on the dynamics of the network in the Hopfield model, which is the one of the neural networks.Also, in the new algorithm, the coefficients are updated a few times on each sampled datum. The rate of adaptation of the new algorithm is faster than the rate of the well‐known LMS algorithm. However, the use of the new algorithm requires more operations than the standard LMS algorithm, and it is easy to implement. A system with the rate of the adaptation which does not converge in the conventional LMS algorithm can be realized.