Least Mean Square Algorithm Research Articles

Hybrid wideband multipath self-interference cancellation with an LMS pre-adaptive filter for in-band full-duplex OFDM signal transmission.

A wideband multipath self-interference cancellation (SIC) system employing both dual-drive Mach-Zehnder modulator-based analog SIC and least mean square (LMS) algorithm-based pre-adaptive filter digital SIC is proposed and demonstrated for the cancellation of multipath self-interference (SI) and facilitation of in-band full-duplex (IBFD) orthogonal frequency-division multiplexing (OFDM) signal transmission. The multipath effect is an unavoidable challenge in SIC due to the dynamic and unpredictable properties in each path, as well as the need for separate matching components for compensating for each path. In this Letter, an LMS algorithm-based adaptive filter is used as a pre-equalizer to adapt and generate the matching signal to the closest approximate of the multipath SI signal. The adaptation is based on the minimization of the error signal generated from the matching signal and multipath SI signal in the LMS algorithm. With the introduction of the LMS adaptive filter to the analog SIC, an additional 9 dB cancellation improvement is obtained, resulting in a total of 32 dB cancellation depth over a cancellation bandwidth of 2.7 GHz at a center frequency of 1.65 GHz. To the best of our knowledge, the achieved performance is by far the widest cancellation bandwidth in a multipath SIC system, which is essential in a large bandwidth and high data rate transmission system. With the help of the proposed LMS adaptive filter digital SIC assisted analog SIC located at the remote node, power-efficient IBFD transmission of an OFDM signal through a 25 km fiber is experimentally demonstrated with a 6 dB bit error rate and 8% error vector magnitude improvements.

Proportionate Adaptive Filtering Algorithms Derived Using an Iterative Reweighting Framework.

In this paper, based on sparsity-promoting regularization techniques from the sparse signal recovery (SSR) area, least mean square (LMS)-type sparse adaptive filtering algorithms are derived. The approach mimics the iterative reweighted ℓ 2 and ℓ 1 SSR methods that majorize the regularized objective function during the optimization process. We show that introducing the majorizers leads to the same algorithm as simply using the gradient update of the regularized objective function, as is done in existing approaches. Different from the past works, the reweighting formulation naturally leads to an affine scaling transformation (AST) strategy, which effectively introduces a diagonal weighting on the gradient, giving rise to new algorithms that demonstrate improved convergence properties. Interestingly, setting the regularization coefficient to zero in the proposed AST-based framework leads to the Sparsity-promoting LMS (SLMS) and Sparsity-promoting Normalized LMS (SNLMS) algorithms, which exploit but do not strictly enforce the sparsity of the system response if it already exists. The SLMS and SNLMS realize proportionate adaptation for convergence speedup should sparsity be present in the underlying system response. In this manner, we develop a new way for rigorously deriving a large class of proportionate algorithms, and also explain why they are useful in applications where the underlying systems admit certain sparsity, e.g., in acoustic echo and feedback cancellation.

Adaptive Processing for EM Telemetry Signal Recovery: Field Data from Sichuan Province

This paper deals with the study of multi-channel adaptive noise cancellation with a focus on its application in electromagnetic (EM) telemetry. We presented new variable step-size least mean square (LMS) techniques: regularized variable step-size LMS and regularized sigmoid variable size LMS, for electromagnetic telemetry data processing. Considering the complexity and spatial distribution of environmental noise, algorithms with multiple reference signals were used to retrieve transmitted EM signals. The feasibility of the regularized variable step size LMS algorithms with numerical simulation was analyzed and presented. The adaptive processing techniques were applied in the recovery of frequency and binary phase shift key modulated signal. The proposed multi-channel adaptive technique achieves fast convergence speed, low mean squared error and is shown to have good convergence characteristics compared to conventional methods. In addition to attaining good results from the multi-channel adaptive filter and performing the signal analysis in real-time, we implemented combined fast effective impulse noise removal techniques. The combination of median and mean filters was effective in removing a wide range of impulsive noises without distorting any other data points. Further, electromagnetic telemetry data were acquired during a drilling operation in Sichuan province, China, for real field application. Data processing workflow was designed for EM telemetry data processing based on the noise characteristics, simulation results and expected result for demodulation. To establish a comprehensive overview, a performance comparison of the acquisition array system is also provided. Conclusively, the introduced multichannel adaptive noise canceling techniques are very effective in recovering transmitted EM telemetry signals.

Bayesian step least mean squares algorithm for Gaussian signals

Selecting the step of the least mean squares (LMS) algorithm is an old problem. This study uses a new approach to address this problem resulting in a new algorithm with excellent system identification performance. The LMS algorithm, with time-varying step, size can be shown to be equivalent to the Kalman filter in some conditions. This is as long as the state noise of the Kalman filter and the step size of the LMS algorithm are chosen carefully. The Kalman filter is the optimum linear estimator (Bayesian) given the state and the measurement noise covariance matrices, but these matrices are not always known. This work considers the case where these matrices are not known, in the special cases that the Kalman filter reduces to the LMS. This results in an algorithm to select the step-size of the LMS algorithm with few priors. The optimum step size can be calculated using estimates of the probability density function (PDF) of the coefficient estimation error variance (qw ) and measurement noise variance (qv ). The PDFs can be estimated from the data using Bayes’ rule and assuming Gaussian reference and measurement noise signals. The resulting algorithm to determine qw and qv is a second small Kalman filter, and the outputs of this filter (means and covariances) are used to determine the expected value of the step.

Enhancement of LMS Convergence Rate with CLS-DFE for 5G Wireless Communication System

WiMAX physical layer implemented Orthogonal Frequency Division Multiple Access (OFDMA) as one of the medium to conduct data transmission. OFDMA suffers from Intersymbol Interference (ISI) which can distort efficiency of the signal transmitted. ISI emerges in the system because of multipath. Basic Cascaded Least Square (CLS) with Decision Feedback Equalizer (DFE) had been proposed in previous research to minimize ISI in wireless communication system. This research will improve CLS performance in terms of convergence. CLS is a cascaded of two adaptive algorithms which are Least Mean Square (LMS) and Recursive Least Square (RLS). Although basic LMS has low complexity than RLS and has been used widely in wireless environment, LMS is suffering in terms of convergence. Updated Normalized Least Mean Square (NLMS) with training rate applied in this research to overcome disadvantage in LMS algorithm. This research justified that training rate is an alternative method to improve CLS-DFE in wireless communication system.

A Study on Active Noise Reduction of Automobile Engine Compartment Based on Adaptive LMS Algorithm

The engine compartment is the main source of automobile noise. In this paper, based on the study of the noise characteristics of the engine compartment, the relationship model is established between engine speed and noise frequency, and an active noise reduction method is proposed based on the adaptive least mean square (LMS) algorithm. Because the adaptive change of the convergence factor is controlled by noise error, the method can reduce the steady-state error of the algorithm and improve the convergence speed of the algorithm. Through the analysis of single-channel active noise reduction control method, we deduced that this method can also realize multi-channel and multi-frequency point active noise reduction. Simulation and experimental results show that the convergence rate and steady-state error of the adaptive LMS algorithm are both taken into account in our method; the two-channel noise reduction experiment also shows that the total sound pressure level of channel one and channel two is reduced by 4.6 and 9.6 dB, respectively, which fully shows the feasibility of the multi-channel active noise reduction method based on the adaptive LMS algorithm.

Fast and Robust Variable-Step-Size LMS Algorithm for Adaptive Beamforming

Conventional least-mean-square (LMS) algorithm is one of the most popular algorithms, which is widely used for adaptive beamforming. But the performance of the LMS algorithm degrades significantly because the constant step size is not suitable for varying signal-to-noise ratio (SNR) scenarios. Although numerous variable-step-size LMS (VSS-LMS) algorithms were proposed to improve the performance of the LMS algorithm; however, most of these VSS-LMS algorithms are either computationally complex or not reliable in practical scenarios since they depend on many parameters that are not easy to tune manually. In this letter, a fast and robust VSS-LMS algorithm is proposed for adaptive beamforming. The VSS is obtained based on normalized sigmoid function, where the sigmoid function is calculated by using the mean of instantaneous error first and then normalized by the squared cumulative sum of instantaneous error and estimated signal power. The proposed algorithm can update the step size adaptively without tuning any parameter and outperform state-of-the-art algorithms with low computational complexity. The simulation results show better performance of the proposed algorithm.

Torque identification based on LMS adaptive delay inverse system method

In order to relieve the dependence of load estimation upon the prior knowledge of mechanical system, an adaptive delayed inverse model is proposed for identifying the torque time history based on adaptive delay inverse system identification method. The LMS (least mean square) algorithm was used to identify the inverse model of the rotating system, which instead of system characteristic matrix inversion in common determination methods and ill-posed problem is avoided consequently. The adaptive delayed inverse model was used to identify the time-domain torque by analyzing the angular acceleration response data of the working state. The single-point time-domain torque of the bare shaft was identified by the angular acceleration response in the case of noiseless interference. The simulation results illustrate that the recognition results of this method is satisfied. It is proved by the experiment that the method is also feasible to the shaft system with disk coupling. The proposed method can be applied in practical engineering as it is not necessary to grip the mathematical model and system parameters in advance.

Predictive Adaptive Filter for Reducing Total Harmonics Distortion in PV Systems

This paper presents a new method for reducing the total harmonic distortion (THD) of photovoltaic (PV) systems by using an adaptive filter based on a predictive model. Instead of reducing the produced THD at each stage of the PV system, a one-step process is implemented at the end stage. The connection topology of the adaptive filter is similar to normal active and passive filters. The main difference is its ability to adjust the filtering coefficients while others cannot. The proposed method is applied to a single-phase standalone PV system by adopting least mean square (LMS), normalized LMS (NLMS) and leaky LMS algorithms to verify the validity of the proposed method. Various values of filter length and step size are evaluated, and results indicate that the proposed method can reduce THD in the current signal of the PV system significantly by using all of the mentioned algorithms. Different step sizes and filter lengths directly influence the effectiveness of the THD reduction, with small step sizes and long filters being the most effective. Amongst the algorithms, NLMS reduces THD the most, and LMS reaches the peak current value the fastest.

Modified leaky LMS‐based control strategy for reliable operation of single‐stage three‐phase grid‐tied PV system

This study presents development of a modified leaky least mean square (MLLMS)-based control strategy for a single-stage three-phase grid-tied photovoltaic (PV) system. In the proposed MLLMS-based control scheme, the authors employ an incremental conductance maximum power point tracking algorithm for maximum power extraction, MLLMS algorithm for extraction of fundamental active and reactive components of the load current, delivering PV power to the grid, balancing the grid current and compensating harmonics of the connected loads at the point of common coupling. By virtue of a leakage factor and selection of sum of the exponential of the adaptation error in the cost function, the MLLMS algorithm overcomes the problems of drifting, low convergence and oscillations in weights encountered by some popular adaptive algorithms, e.g. least mean square (LMS) and least mean fourth (LMF) algorithms. The proposed control scheme is simulated in MATLAB/Simulink environment under different load and environmental conditions. Subsequently, the proposed control scheme is realised on a prototype grid-tied PV system developed in the laboratory. From both the simulation and experimental results, it is observed that the proposed MLLMS algorithm outperforms LMS and LMF algorithms in terms of mean square error, oscillation in weights and total harmonic distortions of the grid currents.

Adaptive Modified Versoria Zero Attraction Least Mean Square Algorithms

Low complexity and ease of implementation provided by zero-attraction-based least mean square (LMS) algorithms have made them popular candidates for sparse system identification. In this brief, a new sparsity aware norm based on a modified Versoria function is proposed, and utilized to develop a novel Versoria zero-attraction LMS (VZA-LMS) algorithm. Moreover, to make the proposed algorithm independent of the zero-attraction parameter, an adaptive zero attractor VZA-LMS (A-VZA-LMS) algorithm is also derived. The bound on learning rate, which ensures convergence in the mean and mean square sense, is derived. Computational complexity of the proposed algorithms are also compared with the existing zero-attraction-based LMS algorithms. Simulation results show that the proposed algorithms provide improved performance over the state-of-the-art algorithms.

Reweighted l p constraint LMS‐based adaptive sparse channel estimation for cooperative communication system

The issue of sparsity adaptive channel reconstruction in time-varying cooperative communication networks through the amplify-and-forward transmission scheme is studied. A new sparsity adaptive system identification method is proposed, namely reweighted l p norm ( 0 < p < 1 ) penalised least mean square (LMS) algorithm. The main idea of the algorithm is to add a l p norm penalty of sparsity into the cost function of the LMS algorithm. By doing so, the weight factor becomes a balance parameter of the associated l p norm adaptive sparse system identification. Subsequently, the steady state of the coefficient misalignment vector is derived theoretically, with a performance upper bounds provided which serve as a sufficient condition for the LMS channel estimation of the precise reweighted l p norm. With the upper bounds, the authors prove that the l p ( 0 < p < 1 ) norm sparsity inducing cost function is superior to the reweighted l 1 norm. An optimal selection of p for the l p norm problem is studied to recover various d sparse channel vectors. Several experiments verify that the simulation results agree well with the theoretical analysis, and thus demonstrate that the proposed algorithm has a better convergence speed and better steady-state behaviour than other LMS algorithms.

‐norm feature least mean square algorithm

In many practical applications, systems and signals show energy concentration in a few coefficients. This prior knowledge can often be incorporated into algorithms designed for tasks such as compressive sensing and system identification. This Letter proposes a new least mean square (LMS)-based algorithm that exploits the hidden sparsity of the system that the adaptive filter intends to estimate. The algorithm minimises the -norm of a linear transformation of the coefficient vector, using the minimum distortion principle. Simulation results demonstrate good performance of the proposed algorithm with respect to the LMS algorithm. In addition, a stochastic model of the advanced algorithm is proposed, which provides accurate mean-square deviation and mean-square error predictions.

Noise Reduction in RTL-SDR using Least Mean Square and Recursive Least Square

Noise reduction is an important process in a communication system, one of which is radio communication. In the process of broadcasting radio Frequency Modulation (FM) often encountered noise so that listeners find it difficult to understand the information provided. In the past, noise reduction used traditional filters that were only able to filter certain frequencies. However, for future technologies an adaptive filter is needed that can dynamically reduce noise effectively. Register Level-Software Defined Radio (RTL-SDR) can capture signals with a very wide frequency range but has a less clear sound quality. So it needs to be done noise reduction. In this study, two methods are used, namely Least Mean Square (LMS) and Recursive Least Square (RLS). The data used five radio stations in Malang. The results showed that the LMS algorithm is stable but has a slow convergence speed, whereas the RLS algorithm has poor stability but has a high convergence speed. From the test, it can be concluded that the performance of RLS is better than LMS for noise reduction in RTL-SDR. The best performance is the reduction of White Noise using RLS on the Oryza radio station with an Normalized Weight Differences (NWD) value of -13.93 dB.

Performance Enhancement of Coherent Optical OFDM System Using LMS Algorithm

Instability of the local oscillator causes phase noise – a phenomenon that is a disadvantage and is considered to be a major obstacle in the functioning of coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. An attempt has been made in this paper to reduce the effects of common phase errors generated by phase noise. In this paper, a least mean square (LMS) based algorithm is proposed for estimation of phase noise. Using this proposed algorithm, the major problem of phase ambiguity caused by cycle slip is avoided and the bit error rate is greatly improved. Further, there is no requirement for modifying the frame structure of OFDM using this algorithm. A CO-OFDM system with the 8-PSK technique is used to implement the algorithm concerned. Furthermore, the algorithm, using the 8-PSK modulation technique, is analyzed and compared with the existing QPSK technique and with other algorithms. The investigations reveal that 8-PSK outperforms existing LMS algorithms using other techniques and significantly reduces the bit error rate.

A variable step-size diffusion LMS algorithm with a quotient form

A new variable step-size strategy for the least mean square (LMS) algorithm is presented for distributed estimation in adaptive networks using the diffusion scheme. This approach utilizes the ratio of filtered and windowed versions of the squared instantaneous error for iteratively updating the step-size. The result is that the dependence of the update on the power of the error is reduced. The performance of the algorithm improves even though it is at the cost of added computational complexity. However, the increase in computational complexity can be minimized by careful manipulation of the update equation, resulting in an excellent performance-complexity trade-off. Complete theoretical analysis is presented for the proposed algorithm including stability, transient and steady-state analyses. Extensive experimental analysis is then done to show the performance of the proposed algorithm under various scenarios.

Improvement of LMS adaptive noise canceller using uniform Poly-phase digital filter bank

&lt;span&gt;This paper presents the Least Mean Square (LMS) noise canceller using uniform poly-phase digital filter bank to improve the noise can-cellation process. Analysis filter bank is used to decompose the full-band distorted input signal into sub-band signals. Decomposition the full-band input distorted signal into sub-band signals based on the fact that the signal to noise ratio (S/N) is inversely proportional to the signal bandwidth. Each sub-band signal is fed to individual LMS algorithm to produce the optimal sub-band output. Synthesis filter bank is used to compose the optimal sub-band outputs to produce the final optimal full-band output. In this paper, m-band uniform Discrete Fourier Transform (DFT) digital filter bank has been used because its computational complexity is much smaller than the direct implementation of digital filter bank. The simulation results show that the proposed method provides the efficient performance with less and smooth error signal as compared to conventional LMS noise canceller.&lt;/span&gt;

Combination of fractional FLANN filters for solving the Van der Pol-Duffing oscillator

Functional link artificial neural network (FLANN) has received much attention due to its wide applicability. The Van der Pol-Duffing oscillator (VdPDO)-based nonlinear systems, which own complex dynamical behaviors, identification of such nonlinear model is vital. This paper exploits the nonlocality of fractional calculus, aiming to enhance the identification accuracy of the VdPDO-based nonlinear systems. The proposed combined FEM-LMS (CFEM-LMS) algorithm, which is based on the FLANN structure, convexly combines the least mean square (LMS) algorithm and the newly proposed fractional-order error modified LMS (FEM-LMS) algorithm. The CFEM-LMS algorithm has improved performance and can dynamically adapt to the nonlinearity of the system. As an added contribution, a novel mixing parameter adaptation criterion is proposed for performance improvement. Extensive simulation results in the context of VdPDO-based nonlinear system identification demonstrate the superiority of the proposed algorithm as compare to state-of-the-art approaches.

Mitigation of Multipath Effects Based on a Robust Fractional Order Bidirectional Least Mean Square (FOBLMS) Beamforming Algorithm for GPS Receivers

Consideration on positioning and location services among the public has been increasing in the recent years with their applications in most of the anticipating milieus such as automobile navigation system etc. This insists for a development of high recitation global navigation satellite system such as global positioning system (GPS). Multipath effects, interference, signal jamming etc. are the major sources of error influencing the performance of the GPS receiver. Literature presents many of the multipath mitigation techniques. Among them, adaptive processing technology based beamforming algorithms appears a viable solution for multipath mitigation. The least mean square (LMS) beamforming algorithms were sensitive to dynamic environments thus affecting the accuracy of GPS. In this paper, an adaptive beamforming algorithm called fractional order bidirectional least mean square (FOBLMS) algorithm is proposed to mitigate the multipath effects and to conceal the jammer signal in a GPS receiver. The FOBLMS is an integration of the fractional calculus and bidirectional least mean square algorithm. The effectiveness of the proposed algorithm is validated using the bit error rate and experimentation gain results over the existing beamforming algorithms. Experimental results demonstrated that the performance of the proposed beamforming algorithm is better than LMS algorithm with maximal relative antenna gain of 28.92 dB, 32.84 dB for two and four element antenna arrays at − 60° and 10°, direction of arrivals respectively. The outcome of this work would be useful for developing a robust technique for multipath mitigation in GPS receivers.

Adaptive Array Design using Least Mean Square Algorithm

This paper presents the designing and testing of an 8-element linear array for Adaptive Antenna applications using the Least Mean Square (LMS) algorithm towards improving the directive gain of the array. A conventional patch antenna is optimized to operate at 2.35 GHz (4G applications) and this design is extended up to 8 elements using CST Microwave Studio parameterization. The S-parameters, Return Loss, Gain and VSWR of the antenna array are studied for the 2, 4, and 8 elements adaptive array. The simulation results are validated on the hardware setup and found closely matching with the experimental results. The resulting eight-element antenna array geometry is optimized with a coaxial feeding technique. This geometry appears promising in improving the gain from 6.13 to 23.5 dBi for a single element to eight elements respectively. Further, the LMS algorithm is used to compute the optimal complex weights considering different angles for desired User (60o and 30o) and Interferer (10o and 15o) during MATLAB simulation and then these optimal weights are fed to antenna elements using CST for beam steering in a different direction. Maximas are obtained at 54o and 28o when nulls are at 10o and 15o using CST software which is closely matching with MATLAB results.