Fractional Least Mean Square Research Articles

IMPROVING 5G NETWORK PERFORMANCE WITH MIMO TECHNOLOGY USING BEAMFORMING ALGORITHM

The advent of 5G technology aims to revolutionize wireless communication by providing significantly higher data rates, ultra- reliable low latency, and enhanced connectivity. However, optimizing 5G network performance remains a challenging task, particularly in terms of Bit Error Rate (BER) and spectral efficiency. Multiple-Input Multiple-Output (MIMO) technology, coupled with beamforming algorithms, offers a promising solution to these challenges. This study investigates the application of the Fractional Least Mean Square (FLMS) algorithm for beamforming in MIMO systems to improve BER and spectral efficiency in 5G networks. The primary problem addressed is the need for effective interference mitigation and signal enhancement in densely populated environments, which traditional methods struggle to handle. The proposed method utilizes the FLMS algorithm to dynamically adjust the beamforming weights, thereby optimizing the signal reception quality. The algorithm's fractional nature allows for finer adjustments and better adaptation to varying channel conditions compared to conventional LMS algorithms. Simulation results show the efficacy of the proposed method. Specifically, the implementation of the FLMS algorithm in a 4x4 MIMO system shows a reduction in BER by 30% and an improvement in spectral efficiency by 25% compared to traditional beamforming techniques. These numerical values highlight the potential of FLMS in enhancing 5G network performance, making it a viable approach for future wireless communication systems.

Self correction fractional least mean square algorithm for application in digital beamforming.

Fractional order algorithms demonstrate superior efficacy in signal processing while retaining the same level of implementation simplicity as traditional algorithms. The self-adjusting dual-stage fractional order least mean square algorithm, denoted as LFLMS, is developed to expedite convergence, improve precision, and incurring only a slight increase in computational complexity. The initial segment employs the least mean square (LMS), succeeded by the fractional LMS (FLMS) approach in the subsequent stage. The latter multiplies the LMS output, with a replica of the steering vector (Ŕ) of the intended signal. Mathematical convergence analysis and the mathematical derivation of the proposed approach are provided. Its weight adjustment integrates the conventional integer ordered gradient with a fractional-ordered. Its effectiveness is gauged through the minimization of mean square error (MSE), and thorough comparisons with alternative methods are conducted across various parameters in simulations. Simulation results underscore the superior performance of LFLMS. Notably, the convergence rate of LFLMS surpasses that of LMS by 59%, accompanied by a 49% improvement in MSE relative to LMS. So it is concluded that the LFLMS approach is a suitable choice for next generation wireless networks, including Internet of Things, 6G, radars and satellite communication.

F-LMS Adaptive Filter Based Control Algorithm With Power Management Strategy for Grid Integrated Rooftop SPV-BES System

The power quality performance of a grid-integrated rooftop solar photovoltaic (SPV) system is significantly affected by the local nonlinear loads. Further, during peak solar insolation and load demand, the SPV system experiences overvoltage and undervoltage at its point of interconnection. Both these issues infringe the IEEE std. 519 and 1547. Therefore, this paper presents a fractional least mean square (F-LMS) based control with the power management strategy (PMS) for the SPV-battery energy storage (BES) system. This presented control uses the SPV system's power converter to compensate load currents locally. By this means, the grid voltages and currents remain distortion-free. The introduced F-LMS algorithm is used as a pre-filter for load current. It estimates the load current fundamental component more accurately and swiftly than the existing LMS method. The designed PMS supervises the SPV array generation, BES power, and grid power to cater to both over and undervoltage issues and keeps the PIC voltage amplitude within the IEEE std. 1547 limits. In addition, this work enables the autonomous operation of SPV system during grid disruption, enhancing power resilience. The efficacy of the introduced work is experimentally verified.

Shuffled Shepherd Squirrel Optimization and Fractional LMS Model for In-Network Aggregation in Wireless Sensor Network

The wireless sensor network (WSN) is commonly based on small node collaboration. These nodes are specified by wireless communication, low price, and energy consumption. Moreover, the WSN can be utilized to compute pressure, temperature, as well as monitoring health, military supervision, and so on. A variety of WSN applications need to gather data from sensor nodes based on sink. In this paper, shuffled shepherd squirrel optimization (SSSOA) technique is devised for in-network aggregation in WSN. Here, the path is formulated from source node to destination through routing process, and source node broadcasts a packet concurrently to destination. The WSN is initiated, and the suitable cluster head (CH) is selected from all nodes. Consequently, CH is selected based on the developed shuffled shepherd squirrel optimization (SSSOA) method.

Design of auxiliary model based normalized fractional gradient algorithm for nonlinear output-error systems

A new avenue of fractional calculus applications has emerged that investigates the design of fractional gradient based novel iterative methods for analyzing fractals and nonlinear dynamics in solving engineering and applied sciences problems. The most discussed algorithm in this regard is fractional least mean square (FLMS) algorithm. This study presents an auxiliary model based normalized variable initial value FLMS (AM-NVIV-FLMS) algorithm for input nonlinear output error (INOE) system identification. First, NVIV-FLMS is presented to automatically tune the learning rate parameter of VIV-FLMS and then the AM-NVIV-FLMS is introduced by incorporating the auxiliary model idea that replaces the unknown values of the information vector with the output of auxiliary model. The proposed AM-NVIV-FLMS scheme is accurate, convergent, robust and reliable for INOE system identification. Simulation results validate the significance and efficacy of the proposed scheme.

Comments on “Design of momentum fractional LMS for Hammerstein nonlinear system identification with application to electrically stimulated muscle model”

The purpose of this article is to discuss some aspects of the convergence analysis performed in the paper (Design of momentum fractional LMS for Hammerstein nonlinear system identification with application to electrically stimulated muscle model, Eur Phys J Plus 134: 407, 2019). It is highlighted that the way the authors prove convergence suffers a lack of correct and valid mathematical justifications.

Fractional LMS and NLMS Algorithms for Line Echo Cancellation

In long haul communication environments, speech data transmission is severely affected by echoes. This phenomenon results in high bit errors as well as in degraded and annoying performance. Traditionally these problems, including hybrid and acoustic echoes, have been controlled through the use of echo suppressors. These suppressors were subsequently replaced by line echo cancellers using adaptive Finite Impulse Response filters. Fractional calculus has been applied successfully for fixed filtering with constant coefficients and in discrete time adaptive filtering that adjusts the weights according to the environment. This paper presents the Fractional Least Mean Square (FLMS) and Fractional Normalized LMS (FNLMS) algorithms for application in echo cancellation. Moreover, the performances of the FLMS and FNLMS are compared with those provided by the standard LMS, NLMS and Block Discrete Fourier Transform solutions. The mean square error criterion is used as the performance comparison criterion for two types of voice signals namely real and synthetic. The simulation results show a performance improvement of about 50% over the traditional counterparts.

Design of multi innovation fractional LMS algorithm for parameter estimation of input nonlinear control autoregressive systems

The development of procedures based on fractional calculus is an emerging research area. This paper presents a new perspective regarding the fractional least mean square (FLMS) adaptive algorithm, called multi innovation FLMS (MIFLMS). We verify that the iterative parameter adaptation mechanism of the FLMS uses merely the current error value (scalar innovation). The MIFLMS expands the scalar innovation into a vector innovation (error vector) by considering data over a fixed window at each iteration. Therefore, the MIFLMS yields better convergence speed than the standard FLMS by increasing the length of innovation vector. The superior performance of the MIFLMS is verified through parameter identification problem of input nonlinear systems. The statistical performance indices based on multiple independent trials confirm the consistent accuracy and reliability of the proposed scheme.

Design of momentum fractional LMS for Hammerstein nonlinear system identification with application to electrically stimulated muscle model

Fractional calculus extends the scope of adaptive algorithms supporting the design of novel fractional methods that outperform standard strategies in various applications arising in applied physics and engineering. In this study, a momentum fractional least-mean-square (M-FLMS) algorithm for nonlinear system identification using a first and fractional-order gradient information is proposed. The M-FLMS avoids being trapped in local minima and provides faster convergence than the standard FLMS. The convergence and complexity analysis of the M-FLMS are given along with simulation results of a benchmark nonlinear system identification problem. The M-FLMS accuracy is verified through a parameter estimation problem for a nonlinear Hammerstein structure, modeling an electrically stimulated muscle (ESM) for rehabilitation of paralyzed muscles. The proposed method is studied in detail for different levels of noise variance, fractional orders and proportion of gradients used in the current update.

Design of sign fractional optimization paradigms for parameter estimation of nonlinear Hammerstein systems

Fractional calculus plays a fundamental role in understanding the physics of nonlinear systems due to its heritage of uncertainty, nonlocality and complexity. In this study, novel sign fractional least mean square (F-LMS) algorithms are designed for ease in hardware implementation by applying sign function to input data and estimation error corresponding to first and fractional-order derivative terms in weight update mechanism of the standard F-LMS method. Theoretical expressions are derived for proposed sign F-LMS and its variants; strength of methods for different fractional orders is evaluated numerically through computer simulations for parameter estimation problem based on nonlinear Hammerstein system for low and high signal–noise variations. Comparison of the results from true parameters of the model illustrates the worth of the scheme in terms of accuracy, convergence and robustness. The stability and viability of design methodologies are examined through statistical observations on sufficiently large number of independent runs through mean square deviation and Nash–Sutcliffe efficiency performance indices.

A new computing paradigm for the optimization of parameters in adaptive beamforming using fractional processing

The use of fractional calculus based novel adaptive algorithms to solve various applied physics and engineering problems is an emerging area of research. In the present study, the parameter estimation problem in adaptive beamforming is explored through the fractional least mean square (FrLMS) adaptive algorithm. The FrLMS algorithm uses the concept of the fractional order gradient in addition to the standard integer order gradient calculation in the recursive parameter update mechanism of optimization. The unknown parameters of adaptive beamforming networks are effectively estimated using FrLMS for various scenarios based on the number of antenna elements in a uniform linear array, the number of interference signals, the signal to noise ratios (SNRs) as well as fractional orders. A comparative study of the proposed FrLMS with standard LMS for different scenarios of adaptive beamforming shows the quality of the design scheme in terms of accuracy, convergence, robustness and stability.

A hierarchical fractional LMS prediction method for data reduction in a wireless sensor network

A network of sensor nodes forms WSN, where the nodes observe the environment and transfer the sensed data to the sink node. Constraints on various resources, like energy, bandwidth, and memory, are usual in WSN, which the researchers attempt to solve. This paper presents a transmission technique with data reduction using Hierarchical Fractional Least-Mean-Square (HFLMS), in WSN. The proposed HFLMS filter is a prediction method that attempts to predict the sensed data based on an error estimate. The filter design of HFLMS extends Hierarchical Least-Mean-Square (HLMS) by modifying its weight update using Fractional Calculus (FC). The proposed adaptive filter reduces energy constraints in WSN by allowing the sensor nodes to transmit only the required data to the sink. Thus, HFLMS with integrated FC prolongs the lifespan of the network preserving the energy. Two evaluation parameters, energy and prediction error, are utilized to measure the performance of the algorithm. The experimental results performed using two datasets from UCI machine learning, show that HFLMS has better results than the existing without prediction, LMS, and HLMS techniques, with the energy of 0.1202 at 500th round and minimum prediction error of 0.0253.

Design of normalized fractional adaptive algorithms for parameter estimation of control autoregressive autoregressive systems

• Fractional adaptive algorithms are designed for parameter estimation of CARAR systems. • Algorithms remain convergent for all noise and fractional order variations. • Accuracy of proposed fractional strategies is better than for standard methods. • Proposed algorithms can be exploited to solve complex and stiff control problems. • Proposed normalized fractional algorithms have comparable computational requirements. In this paper, strength of fractional adaptive signal processing is exploited for parameter identification of control autoregressive autoregressive (CARAR) systems using normalized version of fractional least mean square (FLMS) and its recently introduced modification of type 1 and 2. The adaptation performance of the proposed normalized FLMS methods is compared with standard counterparts for CARAR identification model by taking different noise levels as well as fractional orders. The results of the statistical analyses are used to validate the consistency of the proposed normalized fractional adaptive methodologies in terms of convergence, accuracy and robustness. The reliability and effectiveness of the design schemes is further validated through consistently approaching the desired identification parameters based on performance metrics of mean square error, variance account for and Nash–Sutcliffe efficiency.

QRS detection using adaptive filters: A comparative study

Electrocardiogram (ECG) is one of the most important physiological signals of human body, which contains important clinical information about the heart. Monitoring of ECG signal is done through QRS detection. In this paper, an improved QRS detection algorithm, based on adaptive filtering principle, has been designed. Enumeration of the effectiveness of various LMS variants used in adaptive filtering based QRS detection algorithm has been done through fidelity parameters like sensitivity and positive predictivity. Whole family of LMS algorithm has been implemented for comparison. Sign-sign LMS, sign error LMS, basic LMS and normalized LMS are re-implemented, while variable leaky LMS, variable step-size LMS, leaky LMS, recursive least squares (RLS), and fractional LMS are novel combination presented in this paper. After analysis of the obtained results, performance of leaky-LMS algorithm is found to be the best with sensitivity, positive predictivity, and processing time of 99.68%, 99.84%, and 0.45s respectively. Reported results are tested and evaluated over MIT/BIH arrhythmia database. Presented study also concludes that the performance of most of the variants gets affected due to low SNR but the Leaky LMS performs better even under heavy noise conditions.

A sliding-window approximation-based fractional adaptive strategy for Hammerstein nonlinear ARMAX systems

This paper presents a sliding-window approximation-based fractional least mean square (FLMS) algorithm for parameter estimation of Hammerstein nonlinear autoregressive moving average system with exogenous noise. The FLMS algorithm available in the literature makes use of data available at the current iteration only (or memory-less algorithm). This results in poor convergence rate of the algorithm, and the presence of immeasurable noise terms in the information vector makes identification a difficult task. The sliding-window approximation-based fractional LMS (SW-FLMS) algorithm uses not only the current data but also the past data at each iteration. The proposed algorithm uses sliding-window approximation of the expectation where the length of data used by SW-FLMS algorithm determines the size of sliding window. Moreover, a variable convergence approach is also proposed for fast convergence of SW-FLMS algorithm. Compared with the standard FLMS algorithm, the proposed SW-FLMS algorithms can converge at a fast rate to highly accurate parameter estimates. Estimation accuracy and convergence rate of the standard FLMS algorithm and proposed methods are evaluated for 200 independent runs. Simulation results confirm that performance of standard FLMS algorithm can be improved by the use of proposed modifications.

Comments on “Design of fractional adaptive strategy for input nonlinear Box–Jenkins systems”

This note points out some errors in the identification model and implementation issues of adaptive strategies presented by Chaudhary and Raja for estimation of input nonlinear Box–Jenkins (INBJ) systems (Chaudhary and Raja, 2015 [1]). This note proves that identification model presented in above mentioned paper is incorrect and in stepwise manner suggests some suitable corrections. Authors claim to propose two algorithms for INBJ systems in above mentioned paper: fractional least mean square (F-LMS) algorithm and auxiliary model fractional least mean square (AM-FLMS) algorithm. AM-FLMS algorithm is not presented in this paper, but results of this algorithm are provided. The adaptive algorithms presented by authors are not implementable due to the presence of unknown noise terms in information vector. Authors have ignored these critical issues. Finally, corrections on the basis of established techniques are also mentioned that solve the problems in the above mentioned paper.

Adaptive filtering algorithms for channel equalization in wireless communication

The major problem in today’ wireless communications is time dispersion and inter symbol interference. To combat these issues various adaptive equalization techniques are used. In literature state of art algorithms of adaptive equalization will be studied in detail, however the utmost goal of these algorithms is to attain high convergence rate, less complexity and least error. In this paper a comparison between least mean square algorithm and fractional least mean square algorithm is presented and experimentally proved that the rate of convergence is high in case of fractional least mean square algorithm. Also it is observed that LMS algorithm has better performance for random signals and fractional LMS has proved very efficiently in case of deterministic signals. These both algorithms are implemented in MATLAB and eight channels with different tap weights are used but in this paper only selected are presented.

Design of modified fractional adaptive strategies for Hammerstein nonlinear control autoregressive systems

In this study, modified fractional least mean square (FrLMS) algorithms are formulated for parameter estimation of Hammerstein nonlinear control autoregressive system (HNCAR) by exploiting the fractional calculus concepts in weight adaptation mechanism of the algorithm. In modified FrLMS (MFrLMS) of first kind, forgetting factor is applied to exploit the strength of both standard LMS and FrLMS algorithms. The MFrLMS algorithm of second kind is based on single fractional weight adaptation term in cost function for finding the optimal values instead of considering both fractional and first derivative terms as in FrLMS approach. Performance analysis of the proposed methods are carried out on the basis of optimization ability to the true values of HNCAR system, and comparison is made in terms of accuracy, convergence and complexity. Reliability and effectiveness of the proposed scheme is validated through performance indices based on mean square error, variance account for and Nash Sutcliffe efficiency for sufficient large number of independent runs.

Design of fractional adaptive strategy for input nonlinear Box–Jenkins systems

In this study, the strength of fractional signal processing is exploited in designing fractional adaptive algorithms for parameter estimation of input nonlinear Box–Jenkins (INBJ) systems. The idea is to develop fractional least mean square (F-LMS) and auxiliary model F-LMS (AM-FLMS) algorithms with three values of fractional order to adopt the variables of INBJ system for different scenarios based on noise and step size variations. The comparative study of the proposed results is made with true values of the system, as well as, with the results of Volterra and Kernel LMS adaptive algorithms in order to establish the correctness of the design scheme. The accuracy and convergence of the proposed scheme is analyzed on large data set generated through statistical analysis based on sufficient number of independent runs of the algorithm and result in term of performance measures established the worth of the scheme.

Adaptive strategies for parameter estimation of Box–Jenkins systems

This study presents a novel application of fractional adaptive algorithms for parameter identification of Box–Jenkins (BJ) systems. The idea is to adapt the unknown parameter vector of the BJ system by the fractional least mean square (FLMS) algorithm for three different values of the fractional order and then to compare the estimated results with state of the art Volterra least mean square and kernel least mean square adaptive algorithms to validate and verify the correctness of the design scheme. The reliability and effectiveness of the proposed scheme is analysed through the results of the statistical analysis based on sufficient large number of independent runs and it is found that the proposed FLMS algorithm provides consistently accurate and convergent results for BJ systems under different scenarios.