Minimum Mean Square Error Research Articles

Novel deep neural network architecture fusion to simultaneously predict short-term and long-term energy consumption.

Energy is integral to the socio-economic development of every country. This development leads to a rapid increase in the demand for energy consumption. However, due to the constraints and costs associated with energy generation resources, it has become crucial for both energy generation companies and consumers to predict energy consumption well in advance. Forecasting energy needs through accurate predictions enables companies and customers to make informed decisions, enhancing the efficiency of both energy generation and consumption. In this context, energy generation companies and consumers seek a model capable of forecasting energy consumption both in the short term and the long term. Traditional models for energy prediction focus on either short-term or long-term accuracy, often failing to optimize both simultaneously. Therefore, this research proposes a novel hybrid model employing Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), and Bi-directional LSTM (Bi-LSTM) to simultaneously predict both short-term and long-term residential energy consumption with enhanced accuracy measures. The proposed model is capable of capturing complex temporal and spatial features to predict short-term and long-term energy consumption. CNNs discover patterns in data, LSTM identifies long-term dependencies and sequential patterns and Bi-LSTM identifies complex temporal relations within the data. Experimental evaluations expressed that the proposed model outperformed with a minimum Mean Square Error (MSE) of 0.00035 and Mean Absolute Error (MAE) of 0.0057. Additionally, the proposed hybrid model is compared with existing state-of-the-art models, demonstrating its superior performance in both short-term and long-term energy consumption predictions.

New comprehensive mean estimation using regression-cum-exponential type estimator: application with neutrosophic data

When the point estimator is used to estimate population parameters, it provides a single value. In such a scenario, the neutrosophic method is beneficial for estimating the parameters of interest in sampling theory as it yields interval estimates where the parameter value mainly originates. Neutrosophic statistics focuses on uncertain or imprecise data. In this article, we suggest a new enhanced neutrosophic class of estimators to estimate the population mean. The properties (bias and mean squared error) are derived from the first-degree approximation. The suggested estimators are useful when working with uncertain, unclear, neutrosophic-type data. The best possible values of the defining scalars characterizing constants and the minimum neutrosophic mean squared error (MSE) for the suggested estimators are determined for these ideal values. Neutrosophic estimators outperform their classical counterparts because the existing estimated interval includes the minimum MSE when estimating the population mean. We use a simulation study and a real dataset from the Islamabad Stock Exchange. Variations in parameter and estimator combinations are reflected in the MSE values. From the numerical results, the estimators , , and have substantially higher MSE values, suggesting more significant estimation error. The estimators (i=1, 2, 3, 4, and 5) show better accuracy performance with relatively minimum MSE values. The numerical outcome shows that the suggested classes of estimators perform well as compared to the existing estimators.

Can all variations within the unified mask-based beamformer framework achieve identical peak extraction performance?

This study investigates mask-based beamformers (BFs), which estimate filters for target sound extraction (TSE) using time-frequency masks. Although multiple mask-based BFs have been proposed, no consensus has been reached on which one offers the best target-extraction performance. Previously, we found that maximum signal-to-noise ratio and minimum mean square error (MSE) BFs can achieve the same extraction performance as the theoretical upper-bound performance, with each BF containing a different optimal mask. However, two issues remained unsolved: only two BFs were covered, excluding the minimum variance distortionless response BF; and ideal scaling (IS) was employed to ideally adjust the output scale, which is not applicable to realistic scenarios. To address these issues, this study proposes a unified framework for mask-based BFs comprising two processes: filter estimation that can cover all possible BFs and scaling applicable to realistic scenarios by employing a mask to generate a scaling reference. Based on the operators and covariance matrices used in BF formulas, all possible BFs can be classified into 12 variations, including two new ones. Optimal masks for both processes are obtained by minimizing the MSE between the target and BF output. The experimental results using the CHiME-4 dataset suggested that 1) all 12 variations can achieve the theoretical upper-bound performance, and 2) mask-based scaling can behave like IS, even when constraining the temporal mean of a non-negative mask to one. These results can be explained by considering the practical parameter count of the masks. These findings contribute to 1) designing a TSE system, 2) improving scaling accuracy through mask-based scaling, and 3) estimating the extraction performance of a BF.

An instructional emperor pigeon optimization (IEPO) based DeepEnrollNet for university student enrolment prediction and retention recommendation

Academic institutions face increasing challenges in predicting student enrollment and managing retention. A comprehensive strategy is required to track student progress, predict future course demand, and prevent student churn across various disciplines. Institutions need an effective method to predict student enrollment while addressing potential churn. The existing approaches are often inadequate in handling both numerical and textual data, limiting the ability to provide personalized retention strategies. We propose an innovative framework that combines deep learning with recommender systems for student enrollment prediction and churn prevention. The framework integrates advanced preprocessing techniques for both numeric and textual data. Feature extraction is performed with statistical measures for numeric data, and advanced text techniques like GloVe embeddings, Latent Dirichlet Allocation (LDA) for topic modeling, and SentiWordNet for sentiment analysis. A weighted feature fusion approach combines these features, and the optimal features are selected using the Pythagorean fuzzy AHP with a Hybrid Optimization approach, specifically the Instructional Emperor Pigeon Optimization (IEPO). The DeepEnrollNet model, a hybrid CNN-GRU-Attention QCNN architecture, is used for enrollment prediction, while Deep Q-Networks (DQN) are applied to generate actionable retention recommendations. This comprehensive methodology improves predictive accuracy for student enrolment and provides tailored strategies to enhance retention by addressing both text and numeric data in a unified framework. The DeepEnrollNet has the minimum MSE of 0.218978, MSRE of 0.216445, a NMSE of 0.232453, RMSE of 0.23213, and MAPE of 0.218754.

Stochastic analysis of frequency-domain adaptive filters

This study investigates the convergence behaviors of a family of frequency-domain adaptive filters (FDAFs) under both exact- and under-modeling situations. The stochastic analysis is conducted by transforming the frequency-domain equations into their time-domain counterparts. We discuss the transient and steady-state convergence behaviors of four FDAF versions, i.e., the constrained FDAFs with and without step-normalization, the unconstrained FDAFs with and without step-normalization, and we also present the upper bounds of step size for mean stability and mean-square stability. Starting from the expression for the steady-state mean weight vector, this study investigates whether the FDAFs can converge to unknown system impulse responses and optimum Wiener solutions. Moreover, we provide the closed-form minimum mean-square error (MMSE) that each FDAF can achieve. The difference between the current work and our previous one is threefold. First, the presented time-domain analysis is much easier to handle and has a more explicit physical meaning than that in the frequency domain. Second, we here consider an arbitrary overlap factor between consecutive blocks, while our previous analysis only focuses on 50% overlap. Third, the presented MMSE expressions and excess mean-square error (EMSE) approximations have not been given before. Simulations reveal high consistency between the experimental and theoretical results.

Handling Multicollinearity and Outliers: A Comparative Study of Some One and Two–Parameter Estimators Using Real-Life Data

It is evident that when data suffers the problem of multicollinearity, the traditional least square is incapacitated and unreliable. Hence, needs to use bias estimator such as Ridge estimator, Liu estimator among others. Also, presence of outliers is another treat and to tackle this challenge is the use of robust regression estimators which include M, MM, LTS, LMS, LAD, LQS and S estimators. However, the presence of the two anomalies may be inevitable. Several estimators have been combined to handle the problems simultaneously. Therefore, this study compared and contrasted some robust one and two-parameter estimators using some real-life data sets. Mean Square Error (MSE) was used as criterion to select the best estimator. Some of the robust estimators were found to be inconsistent in addressing the twin problems. However, across all the data set employed in the study, the results revealed that robust Modified Ridge Type (MRT) in M, MM and LTS did well using minimum MSE

Minimum Mean Square Error Receiver for Multipath Detection in Non-Orthogonal Multiple Access

Non-orthogonal multiple access (NOMA) is a promising technique for next-generation wireless communications. NOMA witnesses performance degradation due to multi access and multipath interferences in dispersive channel. Therefore, power domain cyclic spread multiple access (PDCSMA), a NOMA variant, has been presented recently to minimize the multipath fading effect. The performance of the PDCSMA is limited due to the noise enhancement during multipath detection. Therefore, this paper proposes a novel minimum mean square error (MMSE) based interference minimization technique for the PDCSMA. The proposed technique acts on received signal matched to each path to minimize multipath interference and the effective noise power due to channel dispersion. Unlike the decorrelator employed in the current PDCSMA, the proposed technique enhances the diversity while suppressing the noise enhancement, which is evident from simulation results.

Compressive strength prediction of fiber-reinforced recycled aggregate concrete based on optimization algorithms

With the growing emphasis on sustainable development in the construction industry, fiber-reinforced recycled aggregate concrete (BFRC) has attracted considerable attention due to its superior mechanical properties and environmental benefits. However, accurately predicting the compressive strength of BFRC remains a challenge because of the complex interaction between recycled aggregates and fiber reinforcement. This study introduces an innovative predictive framework that combines the XGBoost machine learning algorithm with advanced optimization algorithms, including the Seagull Optimization Algorithm (SOA), Tunicate Swarm Algorithm (TSA), and Mayfly Algorithm (MA). The unique integration of these algorithms not only improves predictive accuracy but also optimizes model performance by enhancing parameter tuning capabilities. Experimental results demonstrated that the TSA-XGBoost model achieved an exceptional R2 of 0.9847 and a minimum mean square error (MSE) of 0.255958, outperforming other models in predicting BFRC’s compressive strength. This novel predictive approach offers an efficient and accurate tool for assessing BFRC’s mechanical performance in practical applications, thus supporting its broader adoption in sustainable construction.

Deep Neural Network-Based Channel Estimation Scheme in Massive MIMO Systems

Channel estimation is one of the most essential technologies of wireless communication, as well as necessary indicators to measure the system’s quality. In recent years, the combination of channel estimation and deep learning techniques has raised wide attention and become one of the most popular research directions of machine learning applications in the wireless communication area. However, in wireless communication systems such as massive MIMO, it’s too complicated to take traditional channel estimation methods with shortcomings like insufficient precision or increased cost. With the combination of deep neural networks (DDN) and the least squares (LS) method, this paper focuses on the deep learning-based channel estimation for massive MIMO systems. Compared with traditional algorithms such as LS or minimum mean-square error method, the loss function of the results is significantly reduced while simulating for the same analog channel. The problem of lack of precision has been improved efficiently and the performance has been improved substantially, which can prove the adequacy of the design of the channel estimator.

A Feed-Forward Back-Propagation Neural Network Approach for Integration of Electric Vehicles into Vehicle-to-Grid (V2G) to Predict State of Charge for Lithium-Ion Batteries

The accurate prediction and efficient management of the State of Charge (SoC) of electric vehicle (EV) batteries are critical challenges in the integration of vehicle-to-grid (V2G) systems within multi-energy microgrid (MMO) models. Inaccurate SoC estimation can lead to inefficiencies, increased costs, and potential disruptions in power generation. This paper addresses the problem of optimizing SoC estimation to enhance the reliability and efficiency of V2G scheduling and MMO coordination. In this work, we develop a Feed-Forward Back-Propagation Network (FFBPN) using MATLAB 2024 software, employing the Levenberg–Marquardt algorithm and varying the number of hidden neurons to achieve better performance; performance was measured by the maximum coefficient of determination (R2) and the minimum mean squared error (MSE). Utilizing the NASA Prognostics Center of Excellence (PCoE) dataset, we validate the model’s capability to accurately predict the life cycle of EV batteries. Our proposed FFBPN model demonstrates superior performance compared to existing methods from the literature, offering significant implications for future V2G system developments. The comparison between training, validation, and testing phases underscores the model’s validity and precisely identifies the characteristic curves of FFBPN, showcasing its potential to enhance profitability, efficiency, production, energy savings, and minimize environmental impact.

Low-Complexity Convolutional Neural Network for Channel Estimation

This paper presents a deep learning algorithm for channel estimation in 5G New Radio (NR). The classical approach that uses neural networks for channel estimation requires more than one stage to obtain the full channel matrix. First, the channel has to be constructed by the received reference signal, and then, the precision is improved. In contrast, to reduce the computational cost, the proposed neural network method generates the channel matrix from the information captured from a few subcarriers along the slot. This information is extrapolated by applying the Least Square technique only on the Demodulation Reference Signal (DMRS). The received DMRS placed in the grid can be seen as a 2D low-resolution image and it is processed to generate the full channel matrix. To reduce complexity in the hardware implementation, the convolutional neural network (CNN) structure is selected. This solution is analyzed comparing the Mean Square Error (MSE) and the computational cost with other deep learning-based channel estimation, as well as the traditional channel estimation methods. It is demonstrated that the proposed neural network delivers substantial complexity savings and favorable error performance. It reduces the computational cost by an order of magnitude, and it has a maximum error discrepancy of 0.018 at 5 dB compared to Minimum Mean Square Error (MMSE) channel estimation.

The INS/GPS integrated navigation based on autonomous underwater vehicle using modified extended Kalman filter

Ensuring highhtab accuracy and robustness remains a paramount concern in the realm of underwater positioning and navigation research. This paper proposes a filtering algorithm grounded in Inertial Measurement Unit/Global Positioning System (INS/GPS) integrated navigation to effectively address the challenges posed by non-Gaussian noise, stemming from outliers and measurement inaccuracies. Currently, most filtering algorithms are developed based on the criteria of minimum mean square error (MMSE) or maximum entropy criteria (MCC). To address the challenge of handling complex non-Gaussian noises, this paper uses the Minimum Error Entropy Criterion (MEE) and Extended Kalman Filter (EKF) with Kernel Risk-Sensitive Loss (KRSL) instead of MMSE or MCC to develop an online filtering algorithm with a recursive process, and adjusts the kernel size of MEE within a reasonable range by constructing an adaptive factor to deal with outliers generated during measurement and excessive convergence caused by the inapplicability of the kernel size. Through extensive target tracking simulations and surface Autonomous Underwater Vehicle (AUV) localization experiments, results demonstrate the efficacy of the proposed algorithm. Notably, the algorithm optimizes kernel sizes for different types of noises, ensuring robust state estimation and rapid convergence without compromising filtering accuracy.

Exploring the spatial effects influencing the EGFR/ERK pathway dynamics with machine learning surrogate models

The fate of cells is regulated by biochemical reactions taking place inside of them, known as intracellular pathways. Cells display a variety of characteristics related to their shape, structure and contained fluid, which influences the diffusion of proteins and their interactions. To gain insights into the spatial effects shaping intracellular regulation, we apply machine learning (ML) to explore a previously developed spatial model of the epidermal growth factor receptor (EGFR) signaling. The model describes the reactions between molecular species inside of cells following the transient activation of EGF receptors. To train our ML models, we conduct 10,000 numerical simulations in parallel where we calculate the cumulative activation of molecules and transcription factors under various conditions such as different diffusion speeds, inactivation rates, and cell structures. We take advantage of the low computational cost of ML algorithms to investigate the effects of cell and nucleus sizes, the diffusion speed of proteins, and the inactivation rate of the Ras molecules on the activation strength of transcription factors. Our results suggest that the predictions by both neural networks and random forests yielded minimal mean square error (MSEs), while linear generalized models displayed a significantly larger MSE. The exploration of the surrogate models has shown that smaller cell and nucleus radii as well, larger diffusion coefficients, and reduced inactivation rates increase the activation of transcription factors. These results are confirmed by numerical simulations. Our ML algorithms can be readily incorporated within multiscale models of tumor growth to embed the spatial effects regulating intracellular pathways, enabling the use of complex cell models within multiscale models while reducing the computational cost.

Signal detection of M-MIMO-orthogonal time frequency space modulation using hybrid algorithms: ZFE + MMSE and ZFE + MF

Orthogonal Time Frequency Space (OTFS) modulation, coupled with Massive Multiple Input Multiple Output (Massive-MIMO) technology, presents a promising avenue for enhancing the efficiency and reliability of fifth-generation (5G) and beyond fifth-generation (B5G) systems. OTFS modulation offers robust communication in high-mobility environments by converting signals into the delay-Doppler domain, ensuring better performance over fading channels. MIMO enhances wireless networks by using large antenna arrays to boost capacity, spectral efficiency, and reliability, making both technologies vital for next-generation radio systems. In this study, we explore the detection of (8 × 8, 16 × 16, 64 × 64, and 256 × 256) Massive-MIMO-OTFS signals utilizing two prominent detection algorithms: zero forcing equalization (ZFE) with matched filter (MF) known as (ZFE + MF) and Zero Forcing with minimum mean square error (MMSE) known as (ZFE + MMSE). The combination of Massive MIMO and OTFS offers improved spectral efficiency, robustness against fading, and enhanced spatial multiplexing capabilities. The parameters such as bit error rate (BER) and power spectral density (PSD) are analyzed and estimated for the proposed hybrid and conventional algorithms. The proposed algorithms obtained the SNR and PSD gain of 3.2 dB, 3.2 dB, 4.8 dB, and 6.1 dB gain, respectively, for 8 × 8, 16 × 16, 64 × 54, and 256 × 256 MIMO systems. Further, the PSD gain of -390 is obtained for the 256 × 256 system, resulting in high spectral efficiency.

Deep learning aided underwater acoustic OFDM receivers: Model-driven or data-driven?

The Underwater Acoustic (UWA) channel is bandwidth-constrained and experiences doubly selective fading. It is challenging to acquire perfect channel knowledge for Orthogonal Frequency Division Multiplexing (OFDM) communications using a finite number of pilots. On the other hand, Deep Learning (DL) approaches have been very successful in wireless OFDM communications. However, whether they will work underwater is still a mystery. For the first time, this paper compares two categories of DL-based UWA OFDM receivers: the Data-Driven (DD) method, which performs as an end-to-end black box, and the Model-Driven (MD) method, also known as the model-based data-driven method, which combines DL and expert OFDM receiver knowledge. The encoder-decoder framework and Convolutional Neural Network (CNN) structure are employed to establish the DD receiver. On the other hand, an unfolding-based Minimum Mean Square Error (MMSE) structure is adopted for the MD receiver. We analyze the characteristics of different receivers by Monte Carlo simulations under diverse communications conditions and propose a strategy for selecting a proper receiver under different communication scenarios. Field trials in the pool and sea are also conducted to verify the feasibility and advantages of the DL receivers. It is observed that DL receivers perform better than conventional receivers in terms of bit error rate.

An Automated Sparse Channel Estimation Framework for MU‐MIMO‐OFDM System With Adaptive Extreme Learning and Heuristic Mechanism

ABSTRACTCompressed sensing is used for channel estimation in Multiple Input Multiple Output‐Orthogonal Frequency Division Multiplexing (MIMO‐OFDM) systems, but large‐scale networks face challenges regarding the antenna elements and spatial non‐stationarities. To enhance spectral efficiency in Multi User‐MIMO (MU‐MIMO) systems, essential signals are collected by Quadrature Phase Shift Keying (QPSK) in the transformer phase. Further, the modulated signals are provided to the “Pulse Shaping Algorithm (PSA)” for neglecting the inter‐symbol interference rate along with inter‐carrier interference. Subsequently, in the transmitter phase, the “Inverse Fast Fourier Transforms (IFFT)” technique is performed to map the symbols and then provide the signal to the receiver side. The spare channel is validated using a semi‐blind sparse algorithm, with parameters tuned using the Opposition Mud Ring Algorithm (OMRA). Then, the estimated sparse channel values are used for generating the new data, and the Adaptive Extreme Learning Model (AELM) is trained to predict the spare channel outcome. The main objective is to reduce the Minimum Mean Square Error (MMSE) in the channel. Thus, the spare channel outcome is predicted automatically using the AELM. Then, diverse evaluations are executed in the suggested spare channel estimation approach over the different mechanisms to observe their effectualness rate.

Generalized spatial modulation detector assisted by reconfigurable intelligent surface based on deep learning

Reconfigurable Intelligent Surface (RIS) is regarded as a cutting-edge technology for the development of future wireless communication networks with improved frequency efficiency and reduced energy consumption. This paper proposes an architecture by combining RIS with Generalized Spatial Modulation (GSM) and then presents a Multi-Residual Deep Neural Network (MR-DNN) scheme, where the active antennas and their transmitted constellation symbols are detected by sub-DNNs in the detection block. Simulation results demonstrate that the proposed MR-DNN detection algorithm performs considerably better than the traditional Zero-Forcing (ZF) and the Minimum Mean Squared Error (MMSE) detection algorithms in terms of Bit Error Rate (BER). Moreover, the MR-DNN detection algorithm has less time complexity than the traditional detection algorithms.

Unified ISAC Pareto Boundary Based on Mutual Information and Minimum Mean-Square Error Estimation

Unified ISAC Pareto Boundary Based on Mutual Information and Minimum Mean-Square Error Estimation

Gaussian Particle Filtering for Nonlinear Systems With Heavy-Tailed Noises: A Progressive Transform-Based Approach.

The Gaussian particle filter (GPF) is a type of particle filter that employs the Gaussian filter approximation as the proposal distribution. However, the linearization errors are introduced during the calculation of the proposal distribution. In this article, a progressive transform-based GPF (PT-GPF) is proposed to solve this problem. First, a progressive transformation is applied to the measurement model to circumvent the necessity of linearization in the calculation of the proposal distribution, thereby ensuring the generation of optimal Gaussian proposal distributions in sense of linear minimum mean-square error (LMMSE). Second, to mitigate the potential impact of outliers, a supplementary screening process is employed to enhance the Monte Carlo approximation of the posterior probability density function. Finally, simulations of a target tracking example demonstrate the effectiveness and superiority of the proposed method.

Bayesian quantum phase estimation with fixed photon states

We consider a two-mode bosonic state with fixed photon number n∈N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n \\in \\mathbb {N}$$\\end{document}, whose upper and lower modes pick up a phase ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} and -ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\\phi $$\\end{document}, respectively. We compute the optimal Fock coefficients of the input state, such that the mean square error (MSE) for estimating ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} is minimized, while the minimum MSE is always attainable by a measurement. Our setting is Bayesian, i.e., we consider ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} to be a random variable that follows a prior probability distribution function (PDF). Initially, we consider the flat prior PDF and we discuss the well-known fact that the MSE is not an informative tool for estimating a phase when the variance of the prior PDF is large. Therefore, we move on to study truncated versions of the flat prior in both single-shot and adaptive approaches. For our adaptive technique, we consider n=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=1$$\\end{document} and truncated prior PDFs. Each subsequent step utilizes as prior PDF the posterior probability of the previous step, and at the same time we update the optimal state and optimal measurement.