Least Mean Square Algorithm Research Articles

Complex MIMO RBF Neural Networks for Transmitter Beamforming over Nonlinear Channels.

The use of beamforming for efficient transmission has already been successfully implemented in practical systems and is absolutely necessary to even further increase spectral and energy efficiencies in some configurations of the next-generation wireless systems and for low earth orbit satellites. A remarkable capacity increase is then achieved and spectral congestion is minimized. In this context, this article proposes a novel complex multiple-input multiple-output radial basis function neural network (CMM-RBF) for transmitter beamforming, based on the phase transmittance radial basis function neural network (PTRBFNN). The proposed CMM-RBF is compared with the least mean square (LMS) algorithm for beamforming with six dipoles arranged in a uniform and circular array and with 16 dipoles in a 2D-grid array. Simulation results show that the proposed solution presents lower steady-state mean squared error, faster convergence rate and enhanced half-power beamwidth (HPBW) when compared with the LMS algorithm in a nonlinear scenario.

Comparative Study on Noise Reduction Effect of Fiber Optic Hydrophone Based on LMS and NLMS 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.

Efficient Estimation of Graph Signals With Adaptive Sampling

We propose two new least mean squares (LMS)-based algorithms for adaptive estimation of graph signals that improve the convergence speed of the LMS algorithm while preserving its low computational complexity. The first algorithm, named extended least mean squares (ELMS), extends the LMS algorithm by virtue of reusing the signal vectors of previous iterations alongside the signal available at the current iteration. Utilizing the previous signal vectors accelerates the convergence of the ELMS algorithm at the expense of higher steady-state error compared to the LMS algorithm. To further improve the performance, we propose the fast ELMS (FELMS) algorithm in which the influence of the signal vectors of previous iterations is controlled by optimizing the gradient of the mean-square deviation (GMSD). The FELMS algorithm converges faster than the ELMS algorithm and has steady-state errors comparable to that of the LMS algorithm. We analyze the mean-square performance of ELMS and FELMS algorithms theoretically and derive the respective convergence conditions as well as the predicted MSD values. In addition, we present an adaptive sampling strategy in which the sampling probability of each node is changed according to the GMSD of the node. Computer simulations using both synthetic and real data validate the theoretical results and demonstrate the merits of the proposed algorithms.

LMS Algorithm for Adaptive Transversal Equalization of a Linear Dispersive Communication Channel

The presence of any type of distortion in communication system, regardless of the causes, is undesirable and undeniably has a negative impacts on the system in general and therefore it is necessary to eliminate its effects. This study employs one of the well-known algorithms for adaptive equalization of linear dispersive communication channel which is Least Mean Square (LMS) algorithm. The LMS technique is basically utilized to eliminate the noise in communication channel. The novelty of this paper includes the profoundly analyzing of the influence of rate of convergence, miss-adjustment, computational requirement, and sensitivity to Eigen-value spread in sufficient details in a simple and plain way. Moreover, the system performance improvement employing the feedback equalizer technique is intensively presented which shows that our methodology is very effective to eliminate the noise in the system. The simulation work has been performed with MATLAB software.

A High-Speed Master-Slave ADALINE for Accurate Power System Harmonic and Inter-Harmonic Estimation

This paper presents a unique two-fold adaptive linear neural network (ADALINE) for fast and accurate measurement of fundamental, harmonics, sub-harmonics, inter-harmonics and decaying DC components of a distorted current signal with additive noise. The preceding parallel approach is termed as Master-Slave ADALINE (MS ADALINE). The Slave-ADALINE adopts least mean square (LMS) algorithm with a fixed and large step-size for weight vector adjustment. During the training interval or transients, this filter performs a significant role. On the other hand, the Master-ADALINE uses a variable step-size LMS algorithm for achieving a small steady-state error. At the end of each iteration, the local averages of the squared errors of both the ADALINE's are calculated and weights of the Master-ADALINE are updated accordingly. The amplitudes and phases of desired frequency components can be worked out from Master-ADALINE's weights. The proposed architecture improves the convergence speed by establishing an independent control action between the steady-state error and the speed of convergence. The simulation results of this method under various operating situations are analyzed and compared with single fold ADALINE structure that obeys dynamic step-size LMS (DSSLMS) adaptation rule. Eventually, a scaled laboratory prototype has been developed for the validation of the proposed technique in real-time utilization. This innovative research finding makes the power system smart and precise.

Stabilization of a Modified LMS Algorithm for Canceling Nonlinear Memory Effects

The least-mean-square (LMS) is promising in a system whose signal statistics are time-varying, and it is preferred in adaptive digital predistortion techniques. In a nonlinear memory system, it is found that the high nonlinearity, the finite sampling rate and the finite number of digits will introduce colored noise that is dependent on signals. In this paper, the long-term stability of the conventional LMS in the presence of signal-dependent noise is analyzed using perturbation analysis. It is revealed that the cumulative effect of the signal-dependent noise may lead to a divergence of the conventional LMS, and a properly selected leaky coefficient is needed to suppress the divergence. Unfortunately, the compensation performance may be harmed by enlarging the leaky coefficient. To address this problem, a modified LMS (MLMS) algorithm is proposed. By adjusting the updating strategy in the iterations, the long-term stability of the algorithm is guaranteed, without harming the linearization performance. Numerical simulations verify that the MLMS outperforms the conventional LMS both in stability and compensation performance.

Behavior of the LMS algorithm with hyperbolic secant cost

This paper presents a new least mean square (LMS) algorithm with defining hyperbolic secant cost function. Then, the detailed analysis is conducted to reveal the behavior of the proposed algorithm. The transient analysis is conducted based on a Taylor expansion approach and energy conservation (EC) relation expression. Following the results of transient state analysis of excess means square-error (EMSE), we achieve the steady-state EMSE and mean-square deviation (MSD) expressions of the proposed algorithm. Moreover, the sufficient condition for the stability convergence is given. Simulation results validate the theoretical analyses and demonstrate the enhanced performance of the proposed algorithm as compared with conventional LMS algorithm in the presence of white Gaussian noise (WGN) and uniform noise.

The Precompression Processing of LMS Algorithm in Noise Elimination

In this study, the authors propose a novel precompression processing (PCP) of the least mean squares (LMS) algorithm based on a regulator factor. The novelty of the PCP algorithm is that the compressed input signals vary from each other on different components at each iteration. The input signal of the improved LMS algorithm is precompressed based on the regulator factor. The precompressed input signal is not only related to the regulator factor α and the current value of the input signal at each iteration but also related to the amplitude of the input signal before this iteration. The improved algorithm can eliminate the influence of input signal mutation on the filter performance. In the numerical simulations, we compare the improved LMS algorithm and NLMS algorithm in the cases of normal input signal and input signal with mutation and the influence of different regulator factors on the noise elimination. Results show that the PCP algorithm has good noise elimination effect when the input signal changes abruptly and the regulator factor α = 0.01 can meet the requirements.

Adaptive Filtering in Optical Coherent Flexible Bit-Rate Receivers in the Presence of State-of-Polarization Transients and Colored Noise

In this article, we analyze the performance of adaptive filtering in the context of dual-polarization coherent optical flexible bit-rate transceivers. We investigate the ability of different adaptive algorithms to track fast state-of-polarization (SOP) transients in the presence of colored noise. Colored noise exists due to the concatenation of Wavelength Selective Switches (WSSs) and polarization dependent loss (PDL) which can be considered as spatially dependent noise. We consider the use of different modulation formats, and the practical limitation of error signal feedback delay in decision-directed adaptive filters is also taken into account. The back-to-back required signal-to-noise ratio (RSNR) penalty that can be tolerated determines the maximum SOP rate of change that can be tracked by the adaptive filters as well as the filter’s adaptive step size. We show that the recursive least squares algorithm, using the covariance matrix as an aggressive “step size,” has a much better convergence speed compared to the least mean squares (LMS) and normalized LMS (NLMS) algorithms in the presence of colored noise in the fiber. However, the three algorithms have similar tracking capabilities in the absence of colored noise.

Active control for vehicle interior noise using the improved iterative variable step-size and variable tap-length LMS algorithms

Active noise control (ANC) is used to reduce undesirable noise, particularly at low frequencies. There are many algorithms based on the least mean square (LMS) algorithm, such as the filtered-x LMS (FxLMS) algorithm, which have been widely used for ANC systems. However, the LMS algorithm cannot balance convergence speed and steady-state error due to the fixed step size and tap length. Accordingly, in this article, two improved LMS algorithms, namely, the iterative variable step-size LMS (IVS-LMS) and the variable tap-length LMS (VT-LMS), are proposed for active vehicle interior noise control. The interior noises of a sample vehicle are measured and thereby their frequency characteristics. Results show that the sound energy of noise is concentrated within a low-frequency range below 1000 Hz. The classical LMS, IVS-LMS and VT-LMS algorithms are applied to the measured noise signals. Results further suggest that the IVS-LMS and VT-LMS algorithms can better improve algorithmic performance for convergence speed and steady-state error compared with the classical LMS. The proposed algorithms could potentially be incorporated into other LMS-based algorithms (like the FxLMS) used in ANC systems for improving the ride comfort of a vehicle.

Multichannel Active Noise Control Based on Filtered-x Affine Projection-Like and LMS Algorithms with Switching Filter Selection

Affine projection (AP) algorithms have been demonstrated to have faster convergence speeds than the conventional least mean square (LMS) algorithms. However, LMS algorithms exhibit smaller steady-state mean square errors (MSEs) when compared with affine projection (AP) algorithms. Recently, several authors have proposed alternative methods based on convex combinations to improve the steady-state MSE of AP algorithms, even with the increased computational cost from the simultaneous use of two filters. In this paper, we present an alternative method based on an affine projection-like (APL-I) algorithm and least mean square (LMS) algorithm to solve the ANC under stationary Gaussian noise environments. In particular, we propose a switching filter selection criteria to improve the steady-state MSE without increasing the computational cost when compared with existing models. Here, we validate the proposed strategy in a single and a multichannel system, with and without automatically adjusting the scaling factor of the APL-I algorithm. The results demonstrate that the proposed scheme exploits the best features of each filter (APL-I and LMS) to guarantee rapid convergence with a low steady-state MSE. Additionally, the proposed approach demands a low computational burden compared with existing convex combination approaches, which will potentially lead to the development of real-time ANC applications.

Robust adaptive filter with lncosh cost

In this paper, a least lncosh (Llncosh) algorithm is derived by utilizing the lncosh cost function. The lncosh cost is characterized by the natural logarithm of hyperbolic cosine function, which behaves like a hybrid of the mean square error (MSE) and mean absolute error (MAE) criteria depending on adjusting a positive parameter λ. Hence, the Llncosh algorithm performs like the least mean square (LMS) algorithm for small errors and behaves as the sign-error LMS (SLMS) algorithm for large errors. It provides comparable performance to the LMS algorithm in Gaussian noise. When compared with several existing robust approaches, the superior steady-state performance and stronger robustness can be attained in impulsive noise. The mean behavior, mean-square behavior and steady-state performance analyses of the proposed algorithm are also provided. In addition, aiming to acquire a compromise between fast initial convergence rate and satisfactory steady-state performance, we introduce a variable-λ Llncosh (VLlncosh) scheme. Lastly, in order to resist the sparsity of the acoustic echo path, an improved proportionate least lncosh (PLlncosh) algorithm is presented. The good performance against impulsive noise and theoretical results of the proposed algorithm are validated by simulations.

Normalized LMS algorithm and data-selective strategies for adaptive graph signal estimation

This work proposes a normalized least-mean-squares (NLMS) algorithm for online estimation of bandlimited graph signals (GS) using a reduced number of noisy measurements. As in the classical adaptive filtering framework, the resulting GS estimation technique converges faster than the least-mean-squares (LMS) algorithm while being less complex than the recursive least-squares (RLS) algorithm, both recently recast as adaptive estimation strategies for the GS framework. Detailed steady-state mean-squared error and deviation analyses are provided for the proposed NLMS algorithm, and are also employed to complement previous analyses on the LMS and RLS algorithms. Additionally, two different time-domain data-selective (DS) strategies are proposed to reduce the overall computational complexity by only performing updates when the input signal brings enough innovation. The parameter setting of the algorithms is performed based on the analysis of these DS strategies, and closed formulas are derived for an accurate evaluation of the update probability when using different adaptive algorithms. The theoretical results predicted in this work are corroborated with high accuracy by numerical simulations.

A PSO-Based Hybrid Adaptive Equalization Algorithm for Asynchronous Cooperative Communications

This paper proposes an adaptive equalization algorithm for asynchronous cooperative communications in ad hoc networks, where amplify-and-forward relays are adopted, each of which is equipped with single antenna. Adaptive equalization technique is carried out at the destination node in this paper to remove inter-symbol interference, which is caused by the retransmissions of the asynchronous relays. Least mean squares (LMS) has been regarded as an effective adaptive method, but it has difficulty in obtaining the optimal solution. In this paper, we present a hybrid adaptive scheme by combining particle swarm optimization (PSO) with conventional LMS algorithm, where PSO is utilized to search the optimal solution during the iterative process, and LMS is employed to avoid the local convergence, which is usually caused in PSO. Numerical simulation results show that, the proposed scheme outperforms conventional LMS algorithm in convergence performance over Rayleigh flat fading channel, and meanwhile, a signal–noise-ratio gain of 6 dB or so is obtained when BER is 10−3.

A Novel Self-Interference Cancellation Method Using an Optimized LMS Algorithm in CCFD Systems for a 5G Communication Network

The Co-frequency Co-time Full Duplex (CCFD) is a key concept in 5G wireless communication networks. The biggest challenge for CCFD wireless communication is the strong self-interference (SI) from near-end transceivers. Aiming at cancelling the SI of near-end transceivers in CCFD systems in the radio frequency (RF) domain, a novel time-varying Least Mean Square (LMS) adaptive filtering algorithm which is based on step-size parameters gradually decrease with time varying called the DTV-LMS algorithm is proposed in this paper. The proposed DTV-LMS algorithm in this paper establishes the non-linear relationship between step factor and the evolved arct-angent function, and using the relationship between the time parameter and error signal correlation value to coordinately control the step factor to be updated. This algorithm maintains a low computational complexity. Simultaneously, the DTV-LMS algorithm can also attain the ideal characteristics, including the interference cancellation ratio (ICR), convergence speed, and channel tracking, so that the SI signal in the RF domain of a full duplex system can be effectively cancelled. The analysis and simulation results show that the ICR in the RF domain of the proposed algorithm is higher than that in the compared algorithms and have a faster convergence speed. At the same time, the channel tracking capability has also been significantly enhanced in CCFD systems.

Adaptive Noise Cancellation Techniques for Impedance Cardiography Signal Analysis

Impedance Cardiography (ICG) evaluation facilitates the volume of heart stroke in the sudden cardiac arrest. It is a noninvasive method for measurement of stroke volume, cardiac output monitoring and observing the hemodynamic parameters by changes in the body blood volume. Bloodvolume changes caused due to various physiological processes is extracted in the form of the variations in the impedance of the body segment. In the real time clinical environment during the extraction the ICG signals are influenced with several artifacts.As these artifacts are not stationary in nature, we can’t predict their characteristics. Hence,we developed several hybrid adaptive filtering mechanisms to improve the ICG signals resolution. Least mean square (LMS) algorithm is the basic enhancement technique in the adaptive filtering. However, in the non-stationery situation the LMS algorithm suffers with low rate of convergence and weight drift problems. In this paper we developed some hybrid variantsof LMS algorithm those are Leaky LMS (LLMS) for ICG signal enhancement. More over to progress the convergence rate, filtering capability and to reduce the computational complexity we also developed various sign versions of LLMS algorithms. The sign variants of LLMS algorithms are sign regressor LLMS (SRLLMS), Sign LLMS (SLLMS), and Sign Sign LLMS (SSLLMS). Severaladaptive signal enhancement units (ASEUs) are developed based on adaptive algorithms and performance is evaluated on the real ICG signal taken from MIT-BIT database. To ensure the efficiency of these algorithms, four experiments were performed to eliminate the various artifacts such as sinusoidal artifacts (SA), respiration artifacts (RA), muscle artifacts (MA) and electrode artifacts (EA). Among these techniques, the ASEU associated with SRLLMS performs better in the artifacts filtering process. The signal to noise ratio improvement (SNRI) for this algorithm is calculated as 9.3388 dBs, 5.7514 dBs, 8.4449 dBs and 8.7358 dBs respectively for SA, RA, MA and EA. Hence, the SRLLMS based ASEUs are more suitable in ICG signal filtering in real time health care sensing systems.

Low complex direction of arrival estimation method based on adaptive filtering algorithm

Conventional subspace decomposition-based direction of arrival (DOA) estimation methods require eigenvalue decomposition of spatial covariance matrix, therefore these methods are computationally intensive, and their implementation is difficult in real-time applications. However, a DOA estimation method based on fixed step size least mean square (LMS) algorithm has overcome this deficiency but the suitable selection of step size is very difficult. A DOA estimation method based on the variable step size LMS algorithm is proposed in this article. In the proposed method, the step size is updated by using the estimated error signal. The spatial spectrum is obtained by the reciprocal of array pattern, where the peak values indicate the estimated DOAs of signals. The proposed method can provide better performance with low computational cost. The performance of proposed method is verified by the simulations and compared with some existing methods.

Performance analysis of adaptive algorithms for space‐time adaptive processor (STAP) in phased array radar

The most challenging task in phased array radar system is the mitigation or suppression of noise and interferences to enhance the useful signal in radar received signals. Multiple solutions have been proposed by researchers for suppression of unwanted signals or interferences which have highly degraded the overall system performance. Nowadays, space-time adaptive processor (STAP) which is a two-dimensional filtering technique is commonly used in phased array antenna with multiple spatial channels. A detailed study is performed on the well-known adaptive algorithms least mean square (LMS), normalized least mean square (NLMS) and recursive least square (RLS), to suppress the high state sea clutter by updating the adaptive STAP weight vector. However, RLS is considered as the suitable adaptive algorithm in STAP because of its good convergence rate, but has high computational complexity. To overcome this issue, two variants of RLS (QRD-RLS and Inverse QRD-RLS) are also discussed which reduce the computational complexity of the algorithm. MATLAB simulations are done to verify the performance of LMS and RLS algorithms in terms of accuracy and convergence rate. Finally, hardware implementations of STAP-QRD-RLS and STAP-IQRD-RLS adaptive beamformers are done and evaluated in terms of latency, throughput and efficiency. The selected platform is the Virtex-5 field-programmable gate array.

Widely Linear Complex-Valued Estimated-Input LMS Algorithm for Bias-Compensated Adaptive Filtering With Noisy Measurements

In this paper, a novel widely linear complex-valued estimated-input adaptive filter (WLC-EIAF) is first proposed for processing noisy input and output data in the complex domain. The WLC-EIAF consists of two steps: (i) estimation of noise-free input and (ii) update of the weight vector, which is realized by alternating the minimization of an instantaneous perturbation with both input and output data. Based on the WLC-EIAF method and adopting the least mean-square (LMS) scheme, a widely linear complex-valued estimated-input LMS (WLC-EILMS) algorithm is developed. It is able to achieve an unbiased parameter estimation and, thus, outperforms the widely linear complex-valued LMS (WL-CLMS) algorithm in the presence of noisy input and output. In particular, for Gaussian signals, closed-form expressions are derived for its steady-state excess mean-square error performance. Furthermore, the linear complex-valued estimated-input LMS and linear real-valued estimated-input LMS algorithms are presented, which are two simplified versions of the WLC-EILMS for circular and real-valued signals, respectively. Simulation results demonstrate that the proposed methods achieve significantly improved performance in terms of mean-square deviation and mean-square error when compared to the WL-CLMS and CLMS algorithms.

LMSK: a robust higher‐order gradient‐based adaptive algorithm

It has been shown that, in intensely noisy environments, adaptive algorithms based on higher-order statistics can enjoy better performance, as compared with the well known second-order least-mean-square (LMS) algorithm. By contrast, this advantage diminishes for low signal-to-noise ratio (SNR) levels, where the LMS algorithm outperforms. One remedy is to employ the LMS algorithm in conjunction with a higher-order adaptation algorithm, in a mixed mode. Least-mean kurtosis (LMK) is a higher-order algorithm that has been shown to be advantageous to use if the noise distribution is Gaussian or super-Gaussian. In this study, the authors propose the LMS/kurtosis algorithm, a stochastic gradient-based adaptive algorithm that is a combination of the LMS and the LMK algorithms. Simulation results demonstrate the privilege of the proposed algorithm, in comparison with its counterparts, for a wide range of noise distributions and SNR levels. This improvement is achieved in spite of a negligible increase in computational complexity. An analytical model is also derived for the mean weight as well as the weight-error covariance matrix, from which the mean-square-error behaviour of the algorithm can be predicted. Simulation results show the high accuracy of the derived model in different conditions.