Minimization Of Mean Square Error Research Articles

System estimation of the SOFCs using fractional-order social network search algorithm

In the preset study, a new identifier system has been proposed for optimal model estimation of Solid Oxide Fuel Cell (SOFC) stacks. To afford an appropriate identification system, the voltage-current profile of the system has been considered. The main idea is to minimize the Mean Squared Error (MSE) value between the actual output voltage of the stack and the output value achieved by the proposed model. Here, the MSE minimization has been established based on a new improved metaheuristic technique, called Fractional-order Social Network Search algorithm. The main advantage of the proposed technique is that it provides better trade-off between the global optimum and local optimum values. After system designing, it has been implemented to a studied case and its results are put in comparison with several latest techniques with considering two scenarios. One scenario with constant pressure and variable temperature and one other scenario with constant pressure and variable temperature. Final results indicate that the presented identification system provides satisfying results against the other compared methods in optimum system identification of the SOFCs.

QoS-Aware Hybrid Beamforming and DOA Estimation in Multi-Carrier Dual-Function Radar-Communication Systems

In this paper, the issues of transmit hybrid beamforming (HBF) design and direction-of-arrival (DOA) estimation in multi-carrier dual-function radar-communication (DFRC) systems, in consideration of quality-of-service (QoS) for multiple users (MUs), are investigated. In the designed system, communication symbols are embedded into radar pulse interval with multiple orthogonal waveforms, and the HBF is optimized to focus the transmit energy within the spatial sectors of interest by taking the QoS requirement for MUs into account. The problem involving these considerations is formulated as the minimization of mean squared error (MSE) between the achieved spatial spectrum and a desired one, subject to constraints of communication QoS, constant modulus, power and orthogonality. Accordingly, a consensus alternating direction method of multipliers (consensus-ADMM) framework based on weighted mean-square error minimization (WMMSE) is devised to tackle the resultant nonconvex problem. Further, the closed-form solutions of the primal variables are derived. Additionally, the MUltiple SIgnal Classification (MUSIC)-based DOA estimation with the designed HBF architecture is presented, and the corresponding Cramér-Rao bound is derived. Numerical simulations are performed to demonstrate the effectiveness of the proposed designs.

MSE-Based Joint Transceiver and Passive Beamforming Designs for Intelligent Reflecting Surface-Aided MIMO Systems

In this letter, novel schemes for joint transceiver and passive beamforming design in an intelligent reflecting surface (IRS)-aided multiple-input multiple-output (MIMO) system are developed. Specifically, active beamformer at the BS, passive beamfomer at the IRS, and receive filter at the user are jointly optimized based on two realistic mean square error (MSE) criteria for signal estimation: (i) total MSE minimization and (ii) maximum per-stream MSE minimization. To tackle these challenging nonconvex problems effectively, two efficient iterative algorithms are proposed for both MSE criteria, in which the receive filter, active and passive beamformers are designed in alternating manner through solving the corresponding convex subproblems, respectively. Numerical results demonstrate better performance of the proposed schemes compared to baseline schemes in terms of the MSE and error rate performance.

Training Optimization for Subarray-Based IRS-Assisted MIMO Communications

In this article, we investigate the training optimization for multiple-input–multiple-output (MIMO)-aided Internet of Things (IoTs) systems that employ subarray-based intelligent reflecting surface (IRS). In order to overcome the nonlinear relationship between two cascaded channel matrices, the IRS can be divided into a series of subarrays, for which only an equivalent cascaded channel matrix should be estimated in each subarray. Correspondingly, the training sequence should be divided into multiple segments. By sufficiently utilizing the available statistical channel state information (CSI), either mean-square error (MSE) minimization or mutual information (MUI) maximization can be taken as the performance metric for optimizing the training sequence. A variety of fairnesses among different subarray channel estimations has been taken into account. Furthermore, in order to reduce the hardware cost of the power amplifier, we propose a two-stage training sequence structure, including a fully digital filter and a constant modulus sequence. To further reduce computational complexity, various low-complexity water-filling solutions are proposed. Numerical results demonstrate the accuracy and efficiency of the proposed solutions.

Federated Learning via Intelligent Reflecting Surface

Over-the-air computation (AirComp) based federated learning (FL) is capable of achieving fast model aggregation by exploiting the waveform superposition property of multiple-access channels. However, the model aggregation performance is severely limited by the unfavorable wireless propagation channels. In this paper, we propose to leverage intelligent reflecting surface (IRS) to achieve fast yet reliable model aggregation for AirComp-based FL. To optimize the learning performance, we present the convergence analysis of our proposed IRS-assisted AirComp-based FL system, based on which we propose to maximize the number of scheduled devices of each communication round under certain mean-squared error (MSE) requirements. To tackle the formulated highly-intractable problem, we propose a two-step optimization framework. Specifically, we induce the sparsity of device selection in the first step, followed by solving a series of MSE minimization problems to find the maximum feasible device set in the second step. We then propose an alternating optimization framework, supported by the difference-of-convex programming for low-rank optimization, to efficiently design the aggregation beamformers at the BS and phase shifts at the IRS. Simulation results demonstrate that our proposed algorithm and the deployment of an IRS can achieve a higher FL prediction accuracy than the baseline schemes.

Multiuser Uplink MIMO Communications Assisted by Multiple Reconfigurable Intelligent Surfaces

This letter focuses on the design of multiuser uplink multiple-input multiple-output (MIMO) communications assisted by multiple reconfigurable intelligent surfaces (RISs), where we consider both linear minimal mean-squared error (MMSE) and nonlinear MMSE-decision feedback equalization (DFE) receivers. The RISs, consisting of massive low-cost passive elements, can reflect the incident signals with either continuous or discrete phase shifts. Adopting the sum mean-squared error (MSE) minimization criterion, we jointly optimize the RIS phase shifts, the linear or nonlinear receiving matrices, and the source precoding matrices in iterative manner. Simulation results show that, when the signals in direct user-access point (AP) links suffer severe attenuation, the introduction of indirect user-RIS-AP links can significantly improve the system performance.

The Role of Correlation in the Performance of Massive MIMO Systems

Massive multiple-input multiple-output (m-MIMO) is considered as an essential technique to meet the high data rate requirements of future sixth generation (6G) wireless communications networks. The vast majority of m-MIMO research has assumed that the channels are uncorrelated. However, this assumption seems highly idealistic. Therefore, this study investigates the m-MIMO performance when the channels are correlated and the base station employs different antenna array topologies, namely the uniform linear array (ULA) and uniform rectangular array (URA). In addition, this study develops analyses of the mean square error (MSE) and the regularized zero-forcing (RZF) precoder under imperfect channel state information (CSI) and a realistic physical channel model. To this end, the MSE minimization and the spectral efficiency (SE) maximization are investigated. The results show that the SE is significantly degraded using the URA topology even when the RZF precoder is used. This is because the level of interference is significantly increased in the highly correlated channels even though the MSE is considerably minimized. This implies that using a URA topology with relatively high channel correlations would not be beneficial to the SE unless an interference management scheme is exploited.

A new imputation-based incomplete data-driven fuzzy modeling for accuracy improvement in ubiquitous computing applications

Purpose In real-world decision-making, high accuracy data analysis is essential in a ubiquitous environment. However, we encounter missing data while collecting user-related data information because of various privacy concerns on account of a user. This paper aims to deal with incomplete data for fuzzy model identification, a new method of parameter estimation of a Takagi–Sugeno model in the presence of missing features. Design/methodology/approach In this work, authors proposed a three-fold approach for fuzzy model identification in which imputation-based linear interpolation technique is used to estimate missing features of the data, and then fuzzy c-means clustering is used for determining optimal number of rules and for the determination of parameters of membership functions of the fuzzy model. Finally, the optimization of the all antecedent and consequent parameters along with the width of the antecedent (Gaussian) membership function is done by gradient descent algorithm based on the minimization of root mean square error. Findings The proposed method is tested on two well-known simulation examples as well as on a real data set, and the performance is compared with some traditional methods. The result analysis and statistical analysis show that the proposed model has achieved a considerable improvement in accuracy in the presence of varying degree of data incompleteness. Originality/value The proposed method works well for fuzzy model identification method, a new method of parameter estimation of a Takagi–Sugeno model in the presence of missing features with varying degree of missing data as compared to some well-known methods.

Particular properties of estimation of partial capacitances of insulation of three core power cables by applying aggregate measurements

This paper presents a description of specific properties of determining the values of partial capacitances of insulation gaps in power cables with paper insulation for various ways of forming and solving the system of linear algebraic equations. Possible ways of inspection the insulation of three core power cables for the estimation of values of partial capacitances by applying aggregate measurements which are based on various ways of connection of emittance meter to tested sample of power cable are given. Estimation of partial capacitances by the direct solution of a system of linear algebraic equations, by minimizing the root mean square error of solving an overdetermined system of equations by the least squares method, as well as by finding a normal solution of an indefinite system of equations by the pseudo-inverse matrix, is also considered. It is shown that minimization of the root mean square error by the least squares method and the direct solution of system of equations show quite similar results for the case of estimation of partial capacitances by means of aggregate measurements, at the same time the solution of an indefinite system of equations by the method of a pseudo-inverted matrix allows to reproduce rather accurately only 3 out of 6 values of partial capacitances. The uneven effect of frequency on the electrical capacitance of the insulation gaps between the cores of the power cable and between its cores and the sheath is shown. It was proposed to use the frequency dependence of the electrical capacitance of insulation gaps as an informative parameter about the technical state of insulating gaps between the cores of the power cable and between its cores and its sheath.
 
 Keywords: root mean square error; least squares method; system of linear algebraic equations; dielectric losses; dielectric permittivity.

Hybrid Beamforming for Multi-Carrier Dual-Function Radar-Communication System

This paper investigates a hybrid beamforming design for dual-function radar-communication (DFRC) systems. Comparing with fully digital beamforming, much less radio frequency (RF) chains are needed and hence, both hardware cost and energy consumption can be reduced. The hybrid transmit/receive beamformers are designed by maximizing the sum-rate under constraints of power as well as similarity between the designed beamformer and the reference one that has good beampattern property. Particularly, both single-user and multi-user scenarios are addressed by introducing different hybrid beamforming designs. For the single-user case, we devise an alternating optimization method under the alternating direction method of multipliers (ADMM) framework. For the multi-user scenario, we introduce a two-stage procedure based on weighted mean-square error minimization (WMMSE). Numerical simulations are provided to demonstrate the effectiveness of the proposed schemes.

Revealing and evaluating the influence of filters position in cascaded filter: application on the ECG de-noising performance disparity

In this paper, a new optimization on windowing technique based on finite impulse response (FIR) filters is proposed for revealing and evaluating the Influence of filters position in cascaded filter tested on the ECG signal de-noising. baseline wander (BLW), power line interference (PLI) and electromyography (EMG) noises are getting removed. The performance of the adopted method is evaluated on the PTB diagnostic database. Subsequently, the comparisons are based on signal to noise ratio (SNR) improvement and mean square error (MSE) minimization. Where the Rectangular, and Kaiser windows have been used for the more potent performances. The disparity average (DA) of SNR values is detected; in both Kaiser and Rectangular windows are assessed by ±0.38046dB and ±0.70278dB respectively, while the MSE values were constant. The excellent configuration or filters position (H-B-L) of the filtration system is selected according to high measurements of SNR and low MSE too, to de-noise the ECG signals. First of all, this applied approach has led to 31.30 dB SNR improvement with MSE minimization of 26. 43%. This means that there is a significant contribution to improving the field of filtration.

Hybrid Multi-Channel EEG Filtering Method for Ocular and Muscular Artifact Removal Based on the 3D Spline Interpolation Technique

Abstract The present work develops a novel hybrid method for ocular and muscular artifact removal from electroencephalography (EEG) signals, EFICA-TQWT. It is a combination of efficient fast independent component analysis (EFICA) method with the tunable Q-factor wavelet transform (TQWT). The main contribution of this paper is to apply the 3D interpolation method in the filtering system. Three EEG datasets are used in this work, two healthy and one epileptic. The choice of subjects for each dataset is made with the help of an expert in physiology. The selection criterion adopted is the presence of muscular and ocular artifacts in the processed recordings. First, a noisy channel automatic classification is performed by the support vector machine (SVM) with radial basis function in order to delete the signal(s) corresponding to the noisiest channel(s) from each EEG recording. The results of the automatic classification by the SVM were compared with those found by the expert’s classification. An accuracy of 97.45%, a sensitivity of 86.66% and a 100% specificity are provided by the SVM classification. The hybrid method of artifact removal will be applied on the rest of the EEG channels of international 10/20 system for each subject. Then, a reconstruction of the eliminated channel signal(s) will be performed in order to obtain a well-filtered signal. The proposed filtering process is evaluated by calculating the mean squared error (MSE) and the signal to noise ratio (SNR). Both for the healthy and pathological EEG datasets, a comparative study of the proposed method (EFICA-TQWT) and other filtering techniques (Fast-ICA, DWT, TQWT and EFICA) is generated. The EFICA-TQWT method gave the best results with a minimum of MSE and a maximum of SNR, more particularly in the case of the application of the 3D interpolation method. Besides, in order to optimize the computing time of the proposed system, a parallel implementation of this filtering system is developed based on graphical processing units using compute unified device architecture.

Kernel Entropy Based Extended Kalman Filter for GPS Navigation Processing

This paper investigates the kernel entropy based extended Kalman filter (EKF) as the navigation processor for the Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS). The algorithm is effective for dealing with non-Gaussian errors or heavy-tailed (or impulsive) interference errors, such as the multipath. The kernel minimum error entropy (MEE) and maximum correntropy criterion (MCC) based filtering for satellite navigation system is involved for dealing with non-Gaussian errors or heavy-tailed interference errors or outliers of the GPS. The standard EKF method is derived based on minimization of mean square error (MSE) and is optimal only under Gaussian assumption in case the system models are precisely established. The GPS navigation algorithm based on kernel entropy related principles, including the MEE criterion and the MCC will be performed, which is utilized not only for the time-varying adaptation but the outlier type of interference errors. The kernel entropy based design is a new approach using information from higher-order signal statistics. In information theoretic learning (ITL), the entropy principle based measure uses information from higher-order signal statistics and captures more statistical information as compared to MSE. To improve the performance under non-Gaussian environments, the proposed filter which adopts the MEE/MCC as the optimization criterion instead of using the minimum mean square error (MMSE) is utilized for mitigation of the heavy-tailed type of multipath errors. Performance assessment will be carried out to show the effectiveness of the proposed approach for positioning improvement in GPS navigation processing.

Joint Collaboration and Compression Design for Random Signal Detection in Wireless Sensor Networks

In this work, we propose a joint collaboration-compression framework for sequential estimation of a random vector parameter in a resource constrained wireless sensor network (WSN). Specifically, we propose a framework where the local sensors first collaborate (via a collaboration matrix) with each other. Then a subset of sensors selected to communicate with the FC linearly compress their observations before transmission. We design near-optimal collaboration and linear compression strategies under power constraints via alternating minimization of the sequential minimum mean square error. We show that the objective function for collaboration design can be non-convex depending on the network topology. We reformulate and solve the collaboration design problem using quadratically constrained quadratic program (QCQP). Moreover, the compression design problem is also formulated as a QCQP. We propose two versions of compression design, one centralized where the compression strategies are derived at the FC and the other decentralized, where the local sensors compute their individual compression matrices independently. It is noted that the design of decentralized compression strategy is a non-convex problem. We obtain a near-optimal solution by using the bisection method. In contrast to the one-shot estimator, our proposed algorithm is capable of handling dynamic system parameters such as channel gains and energy constraints. Importantly, we show that the proposed methods can also be used for estimating time-varying random vector parameters. Finally, numerical results are provided to demonstrate the effectiveness of the proposed framework.

Joint Collaboration and Compression Design for Distributed Sequential Estimation in a Wireless Sensor Network

In this work, we propose a joint collaboration-compression framework for sequential estimation of a random vector parameter in a resource constrained wireless sensor network (WSN). Specifically, we propose a framework where the local sensors first collaborate (via a collaboration matrix) with each other. Then a subset of sensors selected to communicate with the FC linearly compress their observations before transmission. We design near-optimal collaboration and linear compression strategies under power constraints via alternating minimization of the sequential minimum mean square error. The objective function for collaboration design is generally non-convex. We establish correspondence between the sparse collaboration matrix and the non-sparse vector consisting of the nonzero elements of the collaboration matrix. Then, we reformulate and solve the collaboration design problem using quadratically constrained quadratic program (QCQP). The compression design problem is solved using the same methodology. We propose two versions of compression design, one centralized scheme where the compression strategies are derived at the FC and decentralized, where the local sensors compute their individual compression strategies independently. Importantly, we show that the proposed methods can also be used for estimating time-varying random vector parameters. Finally, numerical results are provided to demonstrate the effectiveness of the proposed framework.

Sum Rate Maximization Versus MSE Minimization in FDD Massive MIMO Systems With Short Coherence Time

The increasing demand for higher data rates motivates the exploration of advanced techniques for future wireless networks. To this end, massive multiple-input multiple-output (mMIMO) is envisioned as the most essential technique to meet this demand. However, the expansion of the number of antennas in mMIMO systems with short coherence time makes the downlink channel estimation (DCE) overhead potentially overwhelming. As such, the number of training sequence (TS) needs to be significantly reduced. However, reducing the number of TS reduces the mean-squared error (MSE) accuracy significantly and to date it is not clear to what extend can this TS reduction affects the achievable sum rate performance. Therefore, this paper develops a low complexity and tractable TS solution for DCE and establishes an analytical framework for the optimum TS. Furthermore, the tradeoff between the achievable sum rate maximization criteria and the MSE minimization criteria is investigated. This investigation is essential to characterize the optimum TS length and the actual performance of mMIMO systems when the channel exhibits a limited coherence time. To this end, the statistical structure of mMIMO channels is exploited. In addition, this paper utilizes a random matrix theory (RMT) method to characterize the downlink achievable sum rate and MSE in a closed-form. This paper shows that maximizing the downlink sum rate criterion is more important than minimizing the MSE of the SINR only, which is typically considered in the conventional MIMO systems and/or in the time division duplex (TDD) mMIMO systems. The results demonstrate that a feasible downlink achievable sum rate can be achieved in an frequency division duplex (FDD) mMIMO system. This finding is necessary to extend the benefit of mMIMO systems to high frequency bands such as millimeter-wave (mmWave) and Terahertz (THZ) communications.

Energy Efficiency and Spectral Efficiency Tradeoff in RIS-Aided Multiuser MIMO Uplink Transmission

The emergence of reconfigurable intelligent surfaces (RISs) enables us to establish programmable radio wave propagation that caters for wireless communications, via employing low-cost passive reflecting units. This work studies the non-trivial tradeoff between energy efficiency (EE) and spectral efficiency (SE) in multiuser multiple-input multiple-output (MIMO) uplink communications aided by a RIS equipped with discrete phase shifters. For reducing the required signaling overhead and energy consumption, our transmission strategy design is based on the partial channel state information (CSI), including the statistical CSI between the RIS and user terminals (UTs) and the instantaneous CSI between the RIS and the base station. To investigate the EE-SE tradeoff, we develop a framework for the joint optimization of UTs' transmit precoding and RIS reflective beamforming to maximize a performance metric called resource efficiency (RE). For the design of UT's precoding, it is simplified into the design of UTs' transmit powers with the aid of the closed-form solutions of UTs' optimal transmit directions. To avoid the high complexity in computing the nested integrals involved in the expectations, we derive an asymptotic deterministic objective expression. For the design of the RIS phases, an iterative mean-square error minimization approach is proposed via capitalizing on the homotopy, accelerated projected gradient, and majorization-minimization methods. Numerical results illustrate the effectiveness and rapid convergence rate of our proposed optimization framework.

Three-Dimensional Shape Detection for Non Uniform Reflective Objects: Combination of Color Light Projection and Camera’s Exposure Adjustment

For non uniform reflective objects, a new three-dimensional (3-D) shape detection method that combines color light projection with camera exposure adjustment is proposed. First, the intensity of the projected fringes is set to maximum. Second, we combine red, green and blue light projection with the camera exposure adjustment to obtain fringe sequences with different intensity and contrast. Finally, the optimal set of fringes is extracted from raw fringes, and used for 3-D shape reconstruction. Experimental results show that the method can successfully reconstruct the 3-D shape of the specular and colored objects with minimum of MSE (mean square error) 0.125 mm.

Application of Artificial Neural Network Over Nickel-Based Catalyst for Combined Steam-Carbon Dioxide of Methane Reforming (CSDRM).

The application of artificial neural network (ANN) for modeling, combined steam-carbon dioxide reforming of methane over nickel-based catalysts, was investigated. The artificial neural network model consisted of a 3-layer feed forward network, with hyperbolic tangent function. The number of hidden neurons is optimized by minimization of mean square error and maximization of R² (R square, coefficient of determination) and set of 8 neurons. With feed ratio, flow rate, and temperature as independent variables, methane, carbon dioxide conversion, and H₂/CO ratio, were measured using artificial neural network. Coefficient of determination (R²) values of 0.9997, 0.9962, and 0.9985 obtained, and MAE (Mean Absolute Error), MSE (Mean Squared Error), RMSE (Root Mean Squared Error), and MAPE (Mean Absolute Percentage Error) showed low value. This study indicates ANN can successfully model a highly nonlinear process and function.

Development of statistical estimators for speech enhancement using multi-objective grey wolf optimizer

Statistical Estimation using the SNR uncertainty technique is one of the effective Speech Enhancement (SE) algorithms. In this method, the Gain function plays a crucial role and it depends on the proper selection of the smoothing and threshold constants. In the literature, the values of these constants have been optimized by considering a single objective function of maximization of speech quality for a specific noise condition. But in practice, the noise magnitude varies and one set of optimized parameters cannot always provide consistent performance. In this paper, this problem has been addressed and solved in three steps. The first step is multi-objective optimization to find the best set of values of smoothing and threshold constants at different noise levels by considering the objectives of maximization of speech quality, intelligibility, and minimization of mean square error. The second step is the classification of the noisy speech into four SNR levels such as 0 dB, 5 dB, 10 dB, and 15 dB by using appropriate audio features. The values obtained in steps one and two are stored and in the third step, when the unknown noisy speech signal is to be enhanced the best-chosen values of the smoothing and threshold constants are selected for this task. Finally, the performance of the proposed method is evaluated in two different speech datasets. Then, comparative performance and statistical analysis are carried out using six other standard SE algorithms and it is demonstrated that the proposed approach provides superior performance than others.