Mean Square Error Performance Research Articles

Analytical Second-Order Extended Kalman Filter for Satellite Relative Orbit Estimation

This study considers a relative orbit estimation problem wherein an observing spacecraft navigates with respect to a target space object at a large separation distance (several kilometers) using only the bearing angles obtained by a single onboard camera. Generally, the extended Kalman filter (EKF), which is based on linear relative motion equations such as the Clohessy–Wiltshire equation, is used for the relative navigation of satellites. The EKF linearizes the estimation error around the current estimate and applies the Kalman filter equations to this linearized system. However, it has been shown that nonlinearities of the orbit determination problem can make the linearization assumption insufficient to represent the actual uncertainty. Therefore, an analytical second-order extended Kalman filter (ASEKF) for relative orbit estimation is proposed in this study. The ASEKF, to sequentially estimate the relative states of satellites and their associated uncertainties, is formulated based on a second-order analytic relative-motion equation under J2-perturbtation, which can overcome the deficiencies of existing approaches that mainly focus on applications in two-body, near-circular, and linearized orbit dynamics. Numerical results show that the proposed method provides superior robustness and mean-square error performance compared to linear estimators under the conditions considered.

A Bayesian regularization radial basis neural network novel procedure for the fractional economic and environmental system

The motive of current work is to design a novel radial basis Bayesian regularization neural network (RB-BRNN) for solving the nonlinear fractional economic and environmental system (FEES). A radial basis activation function in the hidden layers is applied by taking 20 numbers of neurons. The mathematical FEES is presented in three classes, named as cost of control accomplishment, manufacturing elements competence and technical exclusion’s diagnostics cost. A reference dataset is obtained using the Adams numerical results to reduce the mean square error (MSE) by taking the data for training 70%, while 15% is used for both testing and validation. The negligible absolute error values and comparison of the solutions develop the worth of computing RB-BRNN in order to solve the nonlinear dynamics of the FEES. Error diagrams, regression values, and the MSE performances are implemented to assess the precision of the designed solver.

Method for remaining useful life prediction of rolling bearings based on deep reinforcement learning.

In contemporary industrial systems, the prediction of remaining useful life (RUL) is recognized as a valuable maintenance strategy for health management due to its ability to monitor equipment operational status in real time and ensure the safety of industrial production. Current studies have largely concentrated on deep learning (DL) techniques, leading to a shortage of RUL prediction methods that utilize deep reinforcement learning (DRL). To further enhance application and research, this paper introduces a novel approach to RUL prediction based on DRL, specifically using a combination of Convolutional Neural Network-Bidirectional Long Short-Term Memory Network (CNN-BiLSTM) and the Deep Deterministic Policy Gradient (DDPG) algorithm. The proposed method reframes the conventional task of estimating RUL as a Markov decision process (MDP), effectively integrating the feature extraction capabilities of DL with the decision-making abilities of DRL. Initially, a hybrid CNN-BiLSTM is employed to establish an agent that can extract degradation features from raw signals. Subsequently, the DDPG algorithm within DRL is leveraged to develop the RUL prediction mechanism, completing the MDP by defining appropriate action spaces and reward functions. The agent, through repeated trials and optimization, learns to map the current operational state of the rolling bearing to its remaining service life. Validation analysis was performed on the intelligent maintenance systems (IMS) bearing dataset. The findings suggest that the DRL-based approach outperforms the current methodologies, demonstrating a superior performance in root mean square error (MSE) and MSE metrics. The predicted outcomes align more closely with the actual lifespan values.

Research on time series prediction of hybrid intelligent systems based on deep learning

Power forecasting plays a crucial role in the operation of smart grid system, which is indispensable for making the operation plan of power system, improving economic efficiency and ensuring the quality of power supply. In order to enhance the accuracy of power load forecasting, a hybrid intelligent power load forecasting system is proposed in this paper. The system first preprocesses the raw data using Savitzky-Golay smoothing technology to eliminate noise and improve data quality. Then, a long and short term memory network with attention mechanism is used to enhance the generalization ability of the model. In addition, in order to further improve the prediction performance, an improved genetic algorithm is integrated to optimize the model parameters. Finally, a data set is used to verify the proposed prediction method. In terms of short-term forecasting ability of experiment of the testing data set, compared with LSTM model, the proposed method shows superior performance in root mean square error and mean absolute error indicators, with root mean square error reduced by 18.7 % and mean absolute error reduced by 26.2 %. In terms of long-term prediction ability of experiment of the testing data set, compared with GBRT model, the proposed method reduces root mean square error and mean absolute error by 24.8 % and 30.7 %, respectively. The experimental results show that compared with the existing benchmark algorithm, the proposed method is significantly improved in two key indexes of prediction accuracy, which proves its effectiveness and superiority in power load prediction.

Estimation of sea surface salinity from MODIS-Aqua data in the northern South China Sea

Sea Surface Salinity (SSS) is a key variable in physical oceanography and biogeochemical research. Microwave remote sensing technology has been used to monitor SSS in open ocean areas. However, the limited spatial resolution and suboptimal precision exhibited by microwave remote sensing derived SSS data have led to the omission of crucial oceanic information, consequently constraining its utilization. In this study, an artificial neural network (ANN) model for the regional SSS inversion was constructed utilizing in situ SSS measurements in the northern South China Sea and remote sensing sea surface temperature and reflectance at wavelengths of 412, 443, 488, 555 and 667 nm derived from MODIS-Aqua satellite Level 2 data. The model showed a good performance of root mean square error (RMSE) of 0.32 and 0.34 for the model training and testing datasets, with mean bias (MB) of 0 and 0.01, and correlation coefficients (R2) reaching 0.93. The model validation indicated that the ANN model reproduced the spatial distribution of SSS highly consistent with the measured SSS (RMSE = 2.75, MB = −1.67, R2 = 0.95), demonstrating its strong applicability in the NSCS. In contrast to other local SSS inversion models, our ANN model clearly showed the fine-scale SSS feature under the intrusion of Pearl River plume near to Dongsha Island with the help of anticyclonic-cyclonic eddies. This prediction closely aligned with the observations from the Soil Moisture Active Passive SSS dataset. The ANN model was applied to MODIS-Aqua data to generate the monthly SSS from 2003 to 2022. A decreasing SSS trend in SSS of 0.02 psu y−1 during 2005–2013 and 2017–2020 and a slightly increasing SSS trend of 0.01 psu y−1 from 2013 to 2017 were observed. Further analysis shows the low-frequency variability of SSS is significantly correlated with the Pacific Decadal Oscillation.

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.

Intelligent PID Controller Based on Neural Network for AI-Driven Control Quadcopter UAV

Unmanned Aerial Vehicle (UAV), specifically a quadcopter is publicly popular which it provides services in different applications such as aerial delivery, aerial photography, military, weather forecasting and more examples to date. A Proportional-Integral-Derivative (PID) controller is one of the control techniques that can provide stabilization and reliable trajectory tracking. However, proper PID gains are needed to ensure a stable flight and it should be hybridized or improved to increase the robustness, reliability, and stabilization during flight. In this paper, an intelligent PID controller using neural network is proposed based on Levenberg-Marquardt feedforward neural network training method. The PID gains are initialized using different ranges according to the optimal gains generated by Particle Swarm Optimization, and this contributes towards a good training performance using Mean Square Error (MSE) evaluation. The trained network takes desired output and references as input data to calculate the required combination of PID gains as the output. The including of the response characteristics as the input data for the network, together with reference, error, and control input is the significance of the work. The performance of this work is presented using MSE performances, attitudes and altitude stabilization, and trajectory tracking reliability through error index performances. The simulation results graphically prove that the proposed controller provides better stability with reduced overshoot and settling times. Disturbance rejection is also enhanced by 1.7% compared to manual tuned PID controller. The reliability of the proposed controller highlights avenues for further exploration in AI-driven control strategies for quadcopter systems.

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.