Mean Square Error Performance Research Articles

How well do ridge parameter estimators proposed so far perform in terms of normality, outlier detection, and MSE criteria?

Ridge regression is a commonly used prediction method in cases of multicollinearity among regressors in multiple linear regression model. In this study, the performances of 366 different estimators proposed in the literature for ridge parameter estimation were evaluated. The criteria of estimators’ ratio of generating outliers and the proportion of normality besides the Mean Square Error (MSE) criterion were used for diagnosing ridge parameter estimators. Besides, the effect of outliers and deviations from normality generated by the ridge parameter estimators on the MSE was revealed by Spearman’s Rho correlation analysis. To do so, a Monte Carlo simulation was designed for 2420 different cases, considering the simulation parameters comprehensively in terms of the number of regressors, sample size, collinearity level and error variances. The results revealed that some ridge parameter estimators recommended according to MSE criterion, do not perform well in terms of outlier generation and normality criteria. Significant inter-linear correlations were also found among the ridge parameter estimators’ MSE performance criterion, ratios of outlier generation criterion and normality criterion. Thus, it is suggested that an effective ridge parameter estimator should perform well in terms of outlier generation and normality criteria, as well as having small MSE value.

A stochastic scale conjugate neural network procedure for the SIRC epidemic delay differential system

In this study, a stochastic computing structure is provided for the numerical solutions of the SIRC epidemic delay differential model, i.e. SIRC-EDDM using the dynamics of the COVID-19. The design of the scale conjugate gradient (CG) neural networks (SCGNNs) is presented for the numerical treatment of SIRC-EDDM. The mathematical model is divided into susceptible S ( ρ ) , recovered R ( ρ ) , infected I ( ρ ) , and cross-immune C ( ρ ) , while the numerical performances have been provided into three different cases. The exactitude of the SCGNNs is perceived through the comparison of the accomplished and reference outcomes (Runge-Kutta scheme) and the negligible absolute error (AE) that are performed around 10−06 to 10−08 for each case of the SIRC-EDDM. The obtained results have been presented to reduce the mean square error (MSE) using the performances of train, validation, and test data. The neuron analysis is also performed that shows the AE by taking 14 neurons provide more accurateness as compared to 4 numbers of neurons. To check the proficiency of SCGNNs, the comprehensive studies are accessible using the error histograms (EHs) investigations, state transitions (STs) values, MSE performances, regression measures, and correlation.

On the conjugate symmetry and sparsity of the harmonic decomposition of parametric surfaces with the randomised Kaczmarz method

The downside of increasing the resolution of surface scanning devices is that the amount of acquired data makes the morphological analysis of the scanned surfaces computationally challenging. This limitation is circumvented by using scalable and non–memory–intensive harmonic expansions. In this paper, the projection of parametric surfaces onto disk and spherical harmonics bases is investigated, and three novel computationally efficient algorithms are proposed based on the randomised Kaczmarz (RK). To boost the computational performance and convergence of the root mean square error (RMSE) of the reconstructed surfaces we exploited the conjugate symmetry property of the harmonic basis functions. Further, the sparsity of the signals is used for estimating the projection coefficients from an undersampled surface. The first algorithm only takes into consideration the conjugate symmetry property for enhancing the convergence of the RMSE. The second algorithm endows the sparse version of the RK algorithm with the conjugate symmetry property. The third algorithm combines the previous two to further accelerate the convergence of the RMSE. The performance of the developed algorithms is tested on three surfaces where we demonstrate that they outperform conventional reconstruction techniques in terms of processing time with comparable precision.

A Nonredundant SVD-based Precoding Matrix for Blind Channel Estimation in CP-OFDM Systems Over Channels with Memory

In this paper, we investigate blind channel estimation in cyclic, prefixed orthogonal frequency division multiplexing (OFDM) systems using precoding matrices. Many studies show how the performance of bit error rate (BER) and mean square error of channel estimation are impacted by using a circulant matrix as a precoding matrix. We investigate a new structure for the precoding matrix in which the first row is generated by an exponentially decreasing equation along with the Toeplitz function and deploying singular value decomposition (SVD) to generate the final precoder matrix. This type of SVD-based precoding matrix has been presented and simulated under various circumstances. The resulting precoding matrix is employed in two different OFDM systems to estimate the channel frequency response vector up to scalar ambiguity. The proof of the precoding matrix full rank property is presented, along with other criteria that help with the development of various precoding matrices.

Channel-level Matching Knowledge Distillation for object detectors via MSE

Knowledge distillation (KD) has been widely used in different tasks as a practical model compression technique. Due to the poor performance of directly using Mean Square Error (MSE) between the intermediate features of the teacher and student, most feature-based detector distillation methods are primarily concerned with proposing diverse attention mechanisms and employing MSE to guide the student in learning critical information. However, the significance of MSE in detector distillation is often overlooked. To enhance the distillation performance of MSE and provide a novel perspective, we propose channel-level Matching Knowledge Distillation via MSE (MKD). The idea of MKD is simple but effective: based on the match or mismatch of student and teacher channel features in Feature Pyramid Networks (FPN), we divide channels at the same location in the FPN layers of the student and teacher into match channels and mismatch channels and then assign different weights to them to calculate the MSE-based distillation loss, which forces the student to distinguish the teacher’s channels and imitate the features of the corresponding channels to achieve better performance. We conduct extensive experiments on MS COCO and PASCAL VOC benchmarks to prove that MKD is superior to state-of-the-art distillation methods. For example, with a powerful RetinaNet-ResNeXt101 detector as the teacher, ResNet-50 based RetinaNet and RepPoints with our distillation method achieve 40.9% and 42.2% mAP on COCO2017, which are 3.5% and 3.6% higher than the baseline, respectively.

Development and validation of a deep learning model to predict axial length from ultra-wide field images.

To validate the feasibility of building a deep learning model to predict axial length (AL) for moderate to high myopic patients from ultra-wide field (UWF) images. This study included 6174 UWF images from 3134 myopic patients during 2014 to 2020 in Eye and ENT Hospital of Fudan University. Of 6174 images, 4939 were used for training, 617 for validation, and 618 for testing. The coefficient of determination (R2), mean absolute error (MAE), and mean squared error (MSE) were used for model performance evaluation. The model predicted AL with high accuracy. Evaluating performance of R2, MSE and MAE were 0.579, 1.419 and 0.9043, respectively. Prediction bias of 64.88% of the tests was under 1-mm error, 76.90% of tests was within the range of 5% error and 97.57% within 10% error. The prediction bias had a strong negative correlation with true AL values and showed significant difference between male and female (P < 0.001). Generated heatmaps demonstrated that the model focused on posterior atrophy changes in pathological fundus and peri-optic zone in normal fundus. In sex-specific models, R2, MSE, and MAE results of the female AL model were 0.411, 1.357, and 0.911 in female dataset and 0.343, 2.428, and 1.264 in male dataset. The corresponding metrics of male AL models were 0.216, 2.900, and 1.352 in male dataset and 0.083, 2.112, and 1.154 in female dataset. It is feasible to utilize deep learning models to predict AL for moderate to high myopic patients with UWF images.

Stress Intensity Factors for Pressurized Pipes with an Internal Crack: The Prediction Model Based on an Artificial Neural Network

During pipeline operation, internal cracks may occur. The severity around the crack tip can be quantified by the stress intensity factor (KI), which is a linear–elastic fracture mechanics parameter. For pressurized pipes featuring infinitely long internal surface cracks, KI can be interpolated from a function considering pressure, geometry, and crack size, as presented in API 579-1/ASME FFS-1. To enhance KI prediction accuracy, an artificial neural network (ANN) model was developed for such pressurized pipes. Predictions from the ANN model and API 579-1/ASME FFS-1 were compared with precise finite element analysis (FEA). The ANN model with an eight-neuron sub-layer outperformed others, displaying the lowest mean squared error (MSE) and minimal validation discrepancies. Nonlinear validation data improved both MSE and testing performance compared to uniform validation. The ANN model accurately predicted normalized KI, with differences of 2.2% or lower when compared to FEA results. Conversely, API 579-1/ASME FFS-1′s bilinear interpolation predicted inaccurately, exhibiting disparities of up to 4.3% within the linear zone and 24% within the nonlinearity zone. Additionally, the ANN model effectively forecasted the critical crack size (aC), differing by 0.59% from FEA, while API 579-1/ASME FFS-1′s bilinear interpolation underestimated aC by 4.13%. In summary, the developed ANN model offers accurate forecasts of normalized KI and critical crack size for pressurized pipes, providing valuable insights for structural assessments in critical engineering applications.

Transceiver Beamforming for Over-the-Air Computation in Massive MIMO Systems

This paper investigates the transmitter and receiver beamforming (TB and RB) for over-the-air computation (AirComp) in massive multiple-inputs and multiple-outputs (MIMO) systems. First, we propose a two-phase hybrid beamforming algorithm to design TB and hybrid RB. In the first phase, we adopt a projected gradient descent with momentum (PGDM) algorithm to search for the optimal fully-digital TB matrices. Compared with the benchmarks on the mean square error (MSE) performances, PGDM can achieve up to 5 dB gain in signal-to-noise ratio (SNR) with less algorithm execution time when fully-digital RB is assumed. In the second phase, we plug the TB matrices obtained in PGDM as well as the optimal baseband RB (BBRB) matrix into the MSE objective, and adopt gradient descent to search for the optimal radio-frequency RB (RFRB) matrix. Compared with the state-of-the-arts, the proposed two-phase algorithm reduces up to 30% of the algorithm execution time and 18% of the MSE. Second, we propose a statistical TB algorithm to reduce the communication overheads, in which TB completely depends on statistical channel state information (CSI) and thus does not rely on the feedback from the base station (BS). We prove that orthonormal matrices are asymptotically optimal for statistical TB when uncorrelated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rayleigh</i> channels are assumed and the number of receiving antennas approaches to infinity. For correlated channels, experimental results show that the proposed statistical TB can achieve about 5 dB gain in SNR compared with orthonormal matrices in terms of the MSE performance. Third, a large scale system analysis is made in this paper. As the number of the receiving antennas approaches to infinity, asymptotically optimal choices for TB and RB are provided, and upper bounds of MSE are derived in terms of the number of clients and receiving antennas. For hybrid RB, an upper bound of the squared distance between the optimal hybrid RB and the optimal fully-digital RB is also derived.

Multiple Signal Classification Based Joint Communication and Sensing System

Joint communication and sensing (JCS) has become a promising technology for mobile networks because of its higher spectrum and energy efficiency. Up to now, the prevalent fast Fourier transform (FFT)-based sensing method for mobile JCS networks is on-grid based, and the grid interval determines the resolution. Because the mobile network usually has limited consecutive OFDM symbols in a downlink (DL) time slot, the sensing accuracy is restricted by the limited resolution, especially for velocity estimation. In this paper, we propose a multiple signal classification (MUSIC)-based JCS system that can achieve higher sensing accuracy for the angle of arrival, range, and velocity estimation, compared with the traditional FFT-based JCS method. We further propose a JCS channel state information (CSI) enhancement method by leveraging the JCS sensing results. Finally, we derive a theoretical lower bound for sensing mean square error (MSE) by using perturbation analysis. Simulation results show that in terms of the sensing MSE performance, the proposed MUSIC-based JCS outperforms the FFT-based one by more than 20 dB. Moreover, the bit error rate (BER) of communication demodulation using the proposed JCS CSI enhancement method is significantly reduced compared with communication using the originally estimated CSI.

RIS-Aided MIMO Systems With Hardware Impairments: Robust Beamforming Design and Analysis

Reconfigurable intelligent surface (RIS) has been anticipated to be a novel cost-effective technology to improve the performance of future wireless systems. In this paper, we investigate a practical RIS-aided multiple-input-multiple-output (MIMO) system in the presence of transceiver hardware impairments, RIS phase noise and imperfect channel state information (CSI). Joint design of the MIMO transceiver and RIS reflection matrix to minimize the total average mean-square-error (MSE) of all data streams is particularly considered. This joint design problem is non-convex and challenging to solve due to the newly considered practical imperfections. To tackle the issue, we first analyze the total average MSE by incorporating the impacts of the above system imperfections. Then, in order to handle the tightly coupled optimization variables and non-convex NP-hard constraints, an efficient iterative algorithm based on alternating optimization (AO) framework is proposed with guaranteed convergence, where each subproblem admits a closed-form optimal solution by leveraging the majorization-minimization (MM) technique. Moreover, via exploiting the special structure of the unit-modulus constraints, we propose a modified Riemannian gradient ascent (RGA) algorithm for the discrete RIS phase shift optimization. Furthermore, the optimality of the proposed algorithm is validated under line-of-sight (LoS) channel conditions, and the irreducible MSE floor effect induced by imperfections of both hardware and CSI is also revealed in the high signal-to-noise ratio (SNR) regime. Numerical results show the superior MSE performance of our proposed algorithm over the adopted benchmark schemes, and demonstrate that increasing the number of RIS elements is not always beneficial under the above system imperfections.

Artificial Neural Network Based Prediction of Long-Term Electric Field Strength Level Emitted by 2G/3G/4G Base Station

Accurate predictions of radio frequency electromagnetic field (RF-EMF) levels can help implement measures to reduce exposure and check regulatory compliance. Therefore, this study aims to predict the RF-EMF levels in the medium using an artificial neural network (ANN). The work was conducted at Ondokuz Mayis University, Kurupelit Campus, where the measurement location has line-of-sight to the base stations. Band selective measurements were also performed to assess the contribution of 2G/3G/4G services to the total RF-EMF level, which was found to be the highest among all services within the total band. Long-term RF-EMF measurements were carried out for 35 days within the frequencies of 100 kHz to 3 GHz. Then, an ANN model with Levenberg–Marquardt (LM) and Bayesian Regulation (BR) algorithms was proposed, which utilized inputs from real-time RF-EMF measurements. The performance of the models was assessed in terms of mean squared error (MSE) and regression performance. The average MSE and regression performances of the models were similar, with the lowest testing MSEs of 2.78 × 10−3 and 3.76 × 10−3 for LM and BR methods, respectively. The analysis of the models showed that the proposed models help to predict the RF-EMF level in the medium with up to 99% accuracy.

A surrogate modeling method for distributed land surface hydrological models based on deep learning

Surrogate modelling methods have been used to estimate spatially distributed parameters of land surface hydrological models due to their computational efficiency. However, traditional surrogate techniques have trouble in modelling high-dimensional input–output maps. In addition, their applications to a distributed model over large spatial and temporal domains are very unlikely to produce consistent spatial pattern and dynamic relationship of model input and output, leading to unbalanced model performance across different spatiotemporal domains. To address these issues, we employ a deep autoregressive neural network to construct an accurate and reliable surrogate system of distributed dynamic model outputs. The network uses a deep convolutional encoder-decoder architecture to take full advantage of the deep convolutional layers in high-dimensional image processing and spatial feature extraction. Moreover, the autoregressive strategy makes the network good at handling dynamic relationship between the time-varying model input and output. We apply this deep learning (DL) network to building a surrogate model of the Variable Infiltration Capacity (VIC) model simulated soil moisture over the Huaihe river basin of China. The results show that the adopted deep autoregressive neural network can provide an accurate surrogate model of the high-dimensional dynamic relationship between 15 input fields and 1 output field, each covering 408 grids, over multiple years. This surrogate model significantly outperforms the popular long short-term memory (LSTM) model, achieving an average mean squared error (MSE) of 0.26 and an average R2 of 0.76 using the test datasets. The surrogate's MSE and R2 performance represents an average improvement of 43% and 33%, respectively, compared to the LSTM model. In addition, it shows better spatial performance than the LSTM model, demonstrating its superior performance in approximating spatial patterns of VIC simulated soil moisture. The accuracy of this surrogate method and its ability to handle high-dimensional data is promising for advancing parameter uncertainty quantification of distributed land surface hydrological models, which usually have high dimensionality due to the large number of variables involved, including distributed parameters, input forcing variables, and output variables.

Pixel-Wise Attention Residual Network for Super-Resolution of Optical Remote Sensing Images

The deep-learning-based image super-resolution opens a new direction for the remote sensing field to reconstruct further information and details from captured images. However, most current SR works try to improve the performance by increasing the complexity of the model, which results in significant computational costs and memory consumption. In this paper, we propose a lightweight model named pixel-wise attention residual network for optical remote sensor images, which can effectively solve the super-resolution task of multi-satellite images. The proposed method consists of three modules: the feature extraction module, feature fusion module, and feature mapping module. First, the feature extraction module is responsible for extracting the deep features from the input spatial bands with different spatial resolutions. Second, the feature fusion module with the pixel-wise attention mechanism generates weight coefficients for each pixel on the feature map and fully fuses the deep feature information. Third, the feature mapping module is aimed to maintain the fidelity of the spectrum by adding the fused residual feature map directly to the up-sampled low-resolution images. Compared with existing deep-learning-based methods, the major advantage of our method is that for the first time, the pixel-wise attention mechanism is incorporated in the task of super-resolution fusion of remote sensing images, which effectively improved the performance of the fusion network. The accuracy assessment results show that our method achieved superior performance of the root mean square error, signal-to–reconstruction ratio error, universal image quality index, and peak signal noise ratio compared to competing approaches. The improvements in the signal-to-reconstruction ratio error and peak signal noise ratio are significant, with a respective increase of 0.15 and 0.629 dB for Sentinel-2 data, and 0.196 and 1 dB for Landsat data.

An Information-Theoretic Branch-and-Prune Algorithm for Discrete Phase Optimization of RIS in Massive MIMO

In this paper, we consider passive RIS-assisted multi-user communication between wireless nodes to improve the blocked line-of-sight (LOS) link performance. The wireless nodes are assumed to be equipped with Massive Multiple-Input Multiple-Output antennas, hybrid precoder, combiner, and low-resolution analog-to-digital converters (ADCs). We first derive the expression for the Cramer-Rao lower bound (CRLB) of the Mean Squared Error (MSE) of the received and combined signal at the intended receiver under interference. By appropriate design of the hybrid precoder, combiner, and RIS phase settings, it can be shown that the MSE achieves the CRLB. We further show that minimizing the MSE w.r.t. the phase settings of the RIS is equivalent to maximizing the throughput and energy efficiency of the system. We then propose a novel Information-Directed Branch-and-Prune (IDBP) algorithm to derive the phase settings of the RIS. We, for the first time in the literature, use an information-theoretic measure to decide on the pruning rules in a tree-search algorithm to arrive at the RIS phase-setting solution, which is vastly different compared to the traditional branch-and-bound algorithm that uses bounds of the cost function to define the pruning rules. In addition, we provide the theoretical guarantees of the near-optimality of the RIS phase-setting solution thus obtained using the Asymptotic Equipartition property. This also ensures near-optimal throughput and MSE performance.

Evaluation of orthogonal frequency‐division multiple‐access systems in the presence of carrier frequency offset using wireless images transmission

AbstractOrthogonal Frequency‐Division Multiple‐Access (OFDMA) is used in different recent wireless communication systems. However, it is susceptible to carrier frequency offset (CFO) which effects the orthogonality between subcarriers and causes inter‐carrier interference (ICI) and multiple access interference (MAI). The aim of this paper is to analyze the impact of the CFOs on the performance of Discrete Sine Transform (DST) DST‐OFDMA, Discrete Cosine Transform (DCT) DCT‐OFDMA and Discrete Fourier Transform (DFT) DFT‐OFDMA systems and to evaluate them with different modulation schemes and different subcarriers mapping schemes over vehicular A and Stanford University Interim (SUI) 3 channels. Transmission of image over the wireless system is performed to analyze and investigate the performance in terms of the Peak Signal‐to‐Noise Ratio (PSNR), and the Mean Square Error (MSE). Through the evaluation, with CFO compensation, without CFO, and without CFO compensation cases are considered. In this work, Joint Minimum Mean Square Error (JMMSE) equalization and CFO compensation technique is used. It is noted that when the QPSK scheme and the SUI3 channel model are used then the DCT‐OFDMA system provides better MSE and PSNR performances than other systems for the JMMSE compensation technique.

Channel Estimation With Hybrid Reconfigurable Intelligent Metasurfaces

Reconfigurable Intelligent Surfaces (RISs) are envisioned to play a key role in future wireless communications, enabling programmable radio propagation environments. They are usually considered as almost passive planar structures that operate as adjustable reflectors, giving rise to a multitude of implementation challenges, including the inherent difficulty in estimating the underlying wireless channels. In this paper, we focus on the recently conceived concept of Hybrid Reconfigurable Intelligent Surfaces (HRISs), which do not solely reflect the impinging waveform in a controllable fashion, but are also capable of sensing and processing an adjustable portion of it. We first present implementation details for this metasurface architecture and propose a convenient mathematical model for characterizing its dual operation. As an indicative application of HRISs in wireless communications, we formulate the individual channel estimation problem for the uplink of a multi-user HRIS-empowered communication system. Considering first a noise-free setting, we theoretically quantify the advantage of HRISs in notably reducing the amount of pilots needed for channel estimation, as compared to the case of purely reflective RISs. We then present closed-form expressions for the Mean-Squared Error (MSE) performance in estimating the individual channels at the HRISs and the base station for the noisy model. Based on these derivations, we propose an automatic differentiation-based first-order optimization approach to efficiently determine the HRIS phase and power splitting configurations for minimizing the weighted sum-MSE performance. Our numerical evaluations demonstrate that HRISs do not only enable the estimation of the individual channels in HRIS-empowered communication systems, but also improve the ability to recover the cascaded channel, as compared to existing methods using passive and reflective RISs.

Pilot Optimization and Channel Estimation for Two-Way Relaying Network Aided by IRS With Finite Discrete Phase Shifters

In this paper, we investigate the problem of pilot optimization and channel estimation of two-way relaying network (TWRN) aided by an intelligent reflecting surface (IRS) with finite discrete phase shifters. In a TWRN, there exists a challenging problem that the two cascading channels from User1-to-IRS-to-relay and User2-to-IRS-to-relay and two direct channels from User1-to-relay and User2-to-relay interfere with each other. Via smartly designing the initial phase shifts of IRS and pilot pattern, the two cascading channels are separated over only four pilot sequences by using simple arithmetic operations like addition and subtraction. Then, the least-squares estimator is adopted to estimate the two cascading channels and two direct channels. The corresponding sum mean square errors (MSE) of channel estimators are derived. By minimizing Sum-MSE, the optimal phase shift matrix of IRS is proved. Then, two special matrices Hadamard and discrete Fourier transform (DFT) matrix are shown to be two optimal training matrices for IRS. Furthermore, the IRS with discrete finite phase shifters is taken into account. The Hadamard matrix requires only one-bit phase shifters to achieve the optimal Sum-MSE performance for specific numbers of IRS elements. Using theoretical derivation and numerical simulations, we find that 3 or 4-bit phase shifters are sufficient for IRS to achieve a negligible MSE performance loss for any number.

IoMT-Enabled Real-Time Blood Glucose Prediction With Deep Learning and Edge Computing

Blood glucose (BG) prediction is essential to the success of glycemic control in type 1 diabetes (T1D) management. Empowered by the recent development of the Internet of Medical Things (IoMT), continuous glucose monitoring (CGM) and deep learning technologies have been demonstrated to achieve the state of the art in BG prediction. However, it is challenging to implement such algorithms in actual clinical settings to provide persistent decision support due to the high demand for computational resources, while smartphone-based implementations are limited by short battery life and require users to carry the device. In this work, we propose a new deep learning model using an attention-based evidential recurrent neural network and design an IoMT-enabled wearable device to implement the embedded model, which comprises a low-cost and low-power system on a chip to perform Bluetooth connectivity and edge computing for real-time BG prediction and predictive hypoglycemia detection. In addition, we developed a smartphone app to visualize BG trajectories and predictions, and desktop and cloud platforms to backup data and fine-tune models. The embedded model was evaluated on three clinical data sets including 47 T1D subjects. The proposed model achieved superior performance of root mean square error (RMSE), mean absolute error, and glucose-specific RMSE, and obtained the best accuracy for hypoglycemia detection when compared with a group of machine learning baseline methods. Moreover, we performed hardware-in-the-loop in silico trials with ten virtual T1D adults to test the whole IoMT system with predictive low-glucose management, which significantly reduced hypoglycemia and improved BG control.

Bayesian Over-the-Air Computation

As an important piece of the multi-tier computing architecture for future wireless networks, over-the-air computation (OAC) enables efficient function computation in multiple-access edge computing, where a fusion center aims to compute a function of the data distributed at edge devices. Existing OAC relies exclusively on the maximum likelihood (ML) estimation at the fusion center to recover the arithmetic sum of the transmitted signals from different devices. ML estimation, however, is much susceptible to noise. In particular, in the misaligned OAC where there are channel misalignments among received signals, ML estimation suffers from severe error propagation and noise enhancement. To address these challenges, this paper puts forth a Bayesian approach by letting each edge device transmit two pieces of statistical information to the fusion center such that Bayesian estimators can be devised to tackle the misalignments. Numerical and simulation results verify that, 1) For the aligned and synchronous OAC, our linear minimum mean squared error (LMMSE) estimator significantly outperforms the ML estimator. In the low signal-to-noise ratio (SNR) regime, the LMMSE estimator reduces the mean squared error (MSE) by at least 6 dB; in the high SNR regime, the LMMSE estimator lowers the error floor of MSE by 86.4%; 2) For the asynchronous OAC, our LMMSE and sum-product maximum a posteriori (SP-MAP) estimators are on an equal footing in terms of the MSE performance, and are significantly better than the ML estimator. Moreover, the SP-MAP estimator is computationally efficient, the complexity of which grows linearly with the packet length.

DNoiseNet: Deep learning-based feedback active noise control in various noisy environments

The use of active noise control/cancelation (ANC) has increased because of the availability of efficient circuits and computational power. However, most ANC systems are based on traditional linear filters with limited efficiency due to the highly nonlinear and nonstationary nature of various noises. This paper proposes an advanced deep learning–based feedback ANC named DNoiseNet that overcomes the limitations of traditional ANCs and addresses primary and secondary path effects, including acoustic delay. Mathematical operators (i.e., atrous convolution, pointwise convolution, nonlinear activation filters, and recurrent neural networks) learn multilevel temporal features under different noises in various environments, such as construction sites, vehicle interiors, and airplane cockpits. Due to the nature of feedback control using a single error sensor, an estimation of the reference noise signal must be regenerated. In this paper, a multilayer perceptron (MLP) neural network–based secondary path estimator is also proposed to improve the performance of DNoiseNet. In extensive parametric and comparative studies, the DNoiseNet with the MLP secondary path estimator exhibited the best performance in root mean square error and noise attenuation metrics.