Minimum Mean Square Error Research Articles

Performance analysis of linear detection for uplink massive MIMO system based on spectral and energy efficiency with Rayleigh fading channels in 3D plotting pattern

AbstractMassive multiple‐input multiple‐output (MIMO) is a critical component of 5G cellular networks, which utilizes large numbers of antennas at both the transmitter and receiver to enhance throughput and radiated energy efficiency. Various linear detection techniques are employed with massive MIMO to counteract path loss and interference, and maximize throughput. The first aim of this paper is to analyse the performance of uplink massive MIMO system for different linear detection techniques including: Maximum ratio combining (MRC), zero‐forcing (ZF), regularized ZF (RZF) and minimum mean squared error (MMSE) over Rayleigh channel model. The second aim is to jointly investigate the optimal values of signal‐to‐noise ratio (SNR), the number of antennas M and the number of users K for maximizing the spectral efficiency (SE) and energy efficiency (EE) through simulation using MATLAB and 3D plotting patterns. The obtained results show that the best SE and EE are achieved by uplink massive MIMO setup while using optimal values of SNR, M and K. It is observed that MMSE achieved the best performance. However, it requires estimation of average SNR at BS. Therefore, the best choice is ZF or RZF without any need for SNR estimation.

Massive MIMO Communication With Intelligent Reflecting Surface

This paper studies the feasibility of deploying intelligent reflecting surfaces (IRSs) in massive multiple input multiple-output (MIMO) systems to improve the performance of users in the service dead zone. One question of paramount importance is as follows: if the overhead of channel training and the computational complexity of algorithm design arising from the huge number of IRS reflecting elements and base station (BS) antennas have to be controlled, can we provide reasonable performance to the users with weak direct channels? This paper provides an affirm answer to this question. Specifically, to reduce the channel training overhead, we consider an appealing protocol for the uplink communication in the IRS-assisted massive MIMO systems. Under this protocol, the IRS reflection coefficients are optimized based on the channel covariance matrices, which are generally fixed for many coherence blocks, to boost the long-term performance. Then, given the IRS reflecting coefficients, the BS beamforming vectors are designed in each coherence block based on the effective channel of each user, which is the superposition of its direct and reflected user-IRS-BS channels, to improve the instantaneous performance. Since merely the user effective channels are estimated in each coherence block, the training overhead of this protocol is the same as that in the legacy wireless systems without IRSs. Moreover, in the asymptotic regime that the numbers of IRS elements and BS antennas both go to infinity with a fixed ratio, we manage to first characterize the minimum mean-squared error (MMSE) estimators of the user effective channels and then quantify the closed-form user achievable rates as functions of channel covariance matrices with channel training overhead and estimation error taken into account. Interestingly, it is shown that the properties of channel hardening and favorable propagation still hold for the user effective channels, and satisfactory user rates are thus achievable even if simple BS beamforming solutions, e.g., maximal-ratio combining, are employed. Finally, thanks to the rate characterization, we design a low-complexity algorithm to optimize the IRS reflection coefficients based on channel covariance matrices.

An intelligent shell game optimization based energy consumption analytics model for smart metering data

Smart metering is a hot research topic and has gained significant attention since the electromechanical metering is not reliable and requires more energy and time. All the existing methods are focused only on how to deal with data rather than how to do efficiently. Prediction of electricity consumption is essential to gain intelligence to the smart gird. Precise electricity prediction allows a service provided in resource planning and also controlling actions for the demand and supply balancing. The users are beneficial from the smart metering solution by effective interpretation of their energy utilization, and labelling them to efficiently handle the utilization cost. With this motivation, the paper presents intelligent energy consumption analytics using smart metering data (ECA-SMD) model to determine the utilization of energy. The presented ECA-SMD model involves three major processes namely data pre-processing, feature extraction, classification, and parameter optimization. The presented ECA-SMD model uses Extreme Learning Machine (ELM) based classification to determine the optimum class labels. Besides, shell game optimization (SGO) algorithm is applied for tuning the parameters involved in the ELM and boosts the classification efficiency. The efficacy of the ECA-SMD model is validated using an extensive set of smart metering data and the results are investigated based on accuracy and mean square error (MSE). The proposed model exhibited supremacy with the maximum accuracy of 65.917 % and minimum MSE of 0.096.

Channel estimation for OFDM-based indoor broadband power line communication systems

State-of-the-art indoor broadband power line communications (PLC) systems use orthogonal frequency division multiplexing (OFDM) signals with constellations up to 10 bits/symbol, which makes channel estimation a key aspect. This paper focuses on the initial channel estimation used in the payload, which might be further adapted by means of a decision-directed strategy. This initial estimate has to be computed on a per-frame basis and can be accomplished from the preamble, the header symbol (assuming that it has been correctly decoded) or from a combination of both. This work proposes simple channel estimation techniques for this problem and derives their most appropriate parameters. They are compared with the linear minimum mean squared-error (LMMSE) estimator and others commonly used in wireless scenarios by considering both their performance and computational complexity. The factors limiting the performance of the estimators based on the preamble and the header symbols are analyzed and the implications of the differences between PLC and wireless channels, such as the absence of fading, in the design of estimation techniques that require knowledge of the channel statistics are discussed. A performance analysis of the considered techniques is accomplished in a set of 171 measured indoor PLC channels. Obtained results indicate that estimators from the header perform better than those based on the preamble symbols and we provide a computationally simple estimator that gives nearly optimum performance by combining estimates from both the preamble and the header symbols.

A Best Linear Empirical Bayes Method for High-Dimensional Covariance Matrix Estimation

Covariance matrix estimation plays a significant role in both in the theory and practice of portfolio analysis and risk management. This paper deals with the available data prior to developing a factor model to enhance covariance matrix estimation. Our work has two main outcomes. First, for a general linear model with unknown prior parameters, a class of best linear empirical Bayes estimators is established through two kinds of architectures to improve the estimation accuracy by utilizing additional data prior. The theoretical results indicate two key points: the proposed estimators are equivalent to the linear minimum mean-square error estimator when complete or sufficient partial data prior are provided; and the proposed estimators perform better than the optimal weighted least squares method, which ignores the data prior in each situation. Second, the proposed estimators are used for calculating a high-dimensional covariance matrix through factor models. The numerical example and the simulation results verify the effectiveness of our methods.

An improved fast adaptive complex approximation message passing algorithm

To solve the problem of reconstructing complex sparse signals from linear measurements of additive white Gaussian noise (AWGN) under the condition of unknown sparse signal distribution, this paper proposes a fast adaptive complex approximate message passing (CAMP) algorithm with significantly reduced mean square error and adaptive to parameter selection. First, we establish a complex sparse signal distribution model. Secondly, the unknown parameters of the distribution model are estimated in each iteration, and the estimated values are used as prior information to obtain the complex shrinkage function with minimum mean square error (MMSE). Finally, an improved fast adaptive CAMP algorithm is obtained by combining the updated shrinkage function with the CAMP. The algorithm has the advantages of fast convergence, low computational complexity, small mean square error, and good robustness. Theoretical analysis and simulation verify the effectiveness of the proposed algorithm.

AWOA: An Advanced Whale Optimization Algorithm for Signal Detection in Underwater Magnetic Induction Multi-Input–Multi-Output Systems

With the increasing exploitation and use of marine resources, the limitations of acoustic, optical, and radio frequency technologies for underwater communications have become increasingly apparent. Magnetic induction (MI) is a new communication technology that enables wireless data transmission via magnetic field coupling between transmitting and receiving coils. MI offers advantages such as channel stability, small antenna size, and no multi-path loss. Multi-input–multi-output (MIMO) is a multi-antenna technology that significantly increases system capacity and spectrum utilization without increasing bandwidth. The whale optimization algorithm (WOA) is a well-known bio-inspired algorithm that mimics the hunting behavior of whales to optimize swarm intelligence. This paper proposes a model for an underwater MIMO communication system based on magnetic induction. We then construct a signal detection algorithm for MI-MIMO systems using the advanced whale optimization algorithm (AWOA) and conduct simulation experiments to compare the performance and complexity of three standard signal detection algorithms: zero-forcing (ZF), minimum mean square error (MMSE), and maximum likelihood (ML). The experimental results show that AWOA achieves suboptimal results, as its bit error rate (BER) is close to that of the ML algorithm. Furthermore, the complexity of AWOA is comparable to that of the MMSE strategy. This work supports the development of a high-performance MI-based underwater communication system.

A Single Objective Crow Search for Modelling of Horizontal Flexible Plate Structure

The magnificent features of flexible plate structure, including lightweight and high-speed response, resulted in additional market demand, especially in the automotive and manufacturing industries. Nevertheless, the structure may incur structural damage and performance degradation when the system encounters excessive vibration. Therefore, a system identification approach utilising a metaheuristic algorithm via crow search to develop a horizontal flexible plate (HFP) model for vibration control is introduced in this paper. Crow search (CS) is a modern algorithm inspired by a crow’s intellectual operation to store additional food and memorise the food storage location. In this study, CS is employed to optimise the objective function, which is the mean squared error for accomplishing a precise predicted model in replicating the dynamic response of the actual structure. Hence, the preliminary action for modelling using this approach is designing and fabricating an HFP rig for experimentally gathering the real input-output vibration data. After that, the mathematical modelling utilising the CS algorithm was implemented using a parametric model structure. Finally, the best-fit model is chosen for the representation of the HFP based on the lowest mean squared error, correlation test within a 95% confidence level and stability in a pole-zero plot. The simulation result reveals that the CS algorithm with a second-order estimated model accomplished a minimum MSE of 1.1168 × 10-5, an unbiased correlation test and excellent stability for the HFP structure.

Downlink Spectral Efficiency of Massive MIMO Systems with Mutual Coupling

Massive multiple-input multiple-output (MIMO) is a profitable technique to greatly boost spectral efficiency, which has been embraced by the fifth-generation (5G) and sixth-generation (6G) mobile communication systems. By exploiting appropriate downlink precoding algorithms, base stations (BSs) equipped with a large number of antennas are able to provide service to multiple users as well as several cells at the same time and frequency. However, the mutual coupling effect due to the compact antenna array gives misleading results in massive MIMO communication systems. In this paper, we focus on the mutual coupling effect for massive MIMO systems with maximal ratio transmission (MRT), zero-forcing (ZF), regularize ZF (RZF), and minimum mean square error (MMSE) precoding to solve the mutual coupling problem. Additionally, we construct the closed-form expressions of the spectral efficiency (SE) to evaluate the effect of mutual coupling on system performance. Simulation results validate the effectiveness of the proposed mutual coupling effect assessment method and demonstrate the significant impacts of mutual coupling on massive MIMO system performance.

Innovation-based stealthy attack against distributed state estimation over sensor networks

This paper presents a new design of an innovation-based stealthy attack strategy against distributed state estimation over a sensor network. In the absence of network attack, an optimal distributed minimum mean-square error (MMSE) estimator is developed by fusing the interaction measurements from neighboring nodes in the sensor network. Also, the boundedness of distributed estimation covariance is discussed over a regionally observable sensor network, which weakens the requirement for local observability of each sensor. Then, a stealthy attack framework embedded with an adjustable parameter is proposed, under which the attack strategy is to maximize the distributed estimation covariance. Sufficient conditions on the boundedness of the compromised covariance are derived, and the tradeoff between attack stealthiness and attack effects is determined. Finally, numerical examples are shown to verify the developed techniques.

Deep learning-enabled broadband full-Stokes polarimeter with a portable fiber optical spectrometer.

Portable fiber optical spectrometers (PFOSs) have been widely used in the contemporary industrial and agricultural production and life due its low cost and small volume. PFOSs mainly combine one fiber to guide light and one optical spectrometer to detect spectra. In this work, we demonstrate that PFOSs can work as a broadband full-Stokes polarimeter through slightly bending the fiber several times and establishing the mapping relationship between the Stokes parameters S^ and the bending-dependent light intensities I^, i.e., S^=f(I^). The different bending geometries bring different birefringence effects and reflection effects that change the polarization state of the out-going light. In the meanwhile, the grating owns a polarization-depended diffraction efficiency especially for the asymmetric illumination geometry that introduces an extrinsic chiroptical effect, which is sensitive to both the linear and spin components of light. The minimum mean squared error (MSE) can reach to smaller than 1% for S1, S2, and S3 at 810 nm, and the averaged MSE in the wave band from 440 nm to 840 nm is smaller than 2.5%, where the working wavelength can be easily extended to arbitrary wave band by applying PFOSs with proper parameters. Our findings provide a convenient and practical method for detecting full-Stokes parameters.

Self-interference cancellation in underwater acoustic communications systems using orthogonal pilots in IBFD

This paper proposes a Self-interference (SI) cancellation system model of Underwater acoustic (UWA) communication for in-band full-duplex (IBFD) technology. The SI channel is separated from the Far channel by exploiting a concurrently orthogonal pilot channel estimation technique using two orthogonal frequency-division multiplexing (OFDM) blocks to establish orthogonality between them based on a unitary matrix. Compared to the half-duplex channel estimator, the mean squared error (MSE) and the bit error rate (BER) provided strong evidence for the efficiency of the proposed SI cancellation. Since full-duplex systems are more efficient than half-duplex ones, the proposed approach might be seen as a viable option for them. The proposed method proved effective when used with a fixed full-duplex (FD) position and FD shifting of up to 4°. Different channel lengths and distances are adopted to evaluate the proposed method. Initial findings indicate that MSE for the SI channel minimum mean-square error (MMSE) estimator at 20 dB is 0.118 · 10−3, for fixed FD. In addition, this paper presents a geometry channel model for the Far channel in the IBFD underwater communication system that describes the propagation delay of the multipath reflection. The simulation results for the multipath propagation delay spread are similar to the traditional results, with the delay spread of the suggested model reaching (79 ms), which is close to the Bellhop simulator result (78 ms).

Performance prediction of a clean coal power plant via machine learning and deep learning techniques

Computer simulation of energy resources has led to significant achievements in the interdisciplinary fields of energy and environment. Apart from renewable resources, fossil-fuel power generation plants can be made cleaner to satisfy the future climate targets while keeping secure and stable grid. Clean coal power plants are still among the dominant options for power generation, which are committed through energy-efficient operation, carbon capture and storage, or combination of both strategies. On the other hand, machine learning and deep learning techniques have a leading integrity in the field of simulation. This paper presents accurate models of a cleaner coal-fired supercritical (SC) unit using two types of artificial neural network, which are Elman neural network (ENN) and generalized regression neural network (GRNN). The models newly embed higher coverage range and more accurate results than previously published models. Each subsystem of the models has been structured as a multi-input single-output (MISO) component to predict the behavior of significant variables in the plant, mainly the supercritical pressure in MPa, the steam temperature in °C and the production in MW. Those variables have been intentionally selected as they are clear indicators for the energy-efficient and cleaner production. Simulation results of four sets of data have indicated satisfactory performance of both models with a bit higher superiority of the GRNN that has given negligible or zero Mean Squared Error (MSE) for all outputs, whereas the minimum MSE of the deep ENN is 3.131 × 10−3.

Quantum-Inspired Multi-Parameter Adaptive Bayesian Estimation for Sensing and Imaging

It is well known in Bayesian estimation theory that the conditional estimator attains the minimum mean squared error (MMSE) for estimating a scalar parameter of interest. In quantum, e.g., optical and atomic, imaging and sensing tasks the user has access to the quantum state that encodes the parameter. The choice of a measurement operator, i.e. a positive-operator valued measure (POVM), leads to a measurement outcome on which the aforesaid classical MMSE estimator is employed. Personick found the optimum POVM that attains the MMSE= over all possible physically allowable measurements and the resulting MMSE [1]. This result from 1971 is less-widely known than the quantum Fisher information (QFI), which lower bounds the variance of an unbiased estimator over all measurements without considering any prior probability. For multi-parameter estimation, in quantum Fisher estimation theory the inverse of the QFI matrix provides an operator lower bound on the covariance of an unbiased estimator, and this bound is understood in the positive semidefinite sense. However, there has been little work on quantifying the quantum limits and measurement designs, for multi-parameter quantum estimation in a Bayesian setting. In this work, we build upon Personick's result to construct a Bayesian adaptive (greedy) measurement scheme for multiparameter estimation. We illustrate our proposed measurement scheme with the application of localizing a cluster of point emitters in a highly sub-Rayleigh angular field-of-view, an important problem in fluorescence microscopy and astronomy. Our algorithm translates to a multi-spatial-mode transformation prior to a photon-detection array, with electro-optic feedback to adapt the mode sorter. We show that this receiver performs superior to quantum-noise-limited focal-plane direct imaging.

Modified entropy based least square channel estimation technique for 5G massive multiple input multiple output universal filtered multicarrier systems

These days’ Massive multiple input multiple output (mMIMO) systems have become popular because of their enhanced data transmission rates, robustness against multipath fading, enhanced spectral efficacy, and ability to communicate with a more significant number of users with immense coverage. The critical challenge of the mMIMO systems is precisely replenishing the channel state information (CSI), along with the synchronization between receiver and transmitter. The CSI has recovered with the help of various channel estimation (CE) techniques. This paper presents a modified entropy-based least square CE technique for 5G mMIMO-UFMC systems. The proposed CE technique performance is novel and better than the Least Square (LS) and minimum mean square error (MMSE) CE techniques. The proposed CE technique was evaluated using MATLAB, and its performance results are shown in the simulation. The performance results of the proposed CE are evaluated based on the mean square error (MSE) and bit error rate (BER) of the obtained signal. The executed results prove that the proposed CE is efficient compared to conventional CE methods. The performance of the MCM techniques with respect to the proposed CE is also presented in this paper. This paper also explains the analytical assessment of the LS, MMSE, and MELS CE techniques. The results show that at high values of SNR, the proposed algorithm outperforms the LS and MMSE for both BER and MSE.

Deep Learning for Super-Resolution Channel Estimation in Reconfigurable Intelligent Surface Aided Systems

Reconfigurable intelligent surface (RIS) enables the configuration of the propagation environment. Channel estimation is an essential task in realizing the RIS-aided communication system. A RIS-aided multi-user multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) communication system involves cascaded channels with high dimensions and sophisticated statistics. Thus, implementing the optimal minimum mean square error (MMSE) with the integration computation is infeasible in practice. To accurately estimate channels with high accuracy in a RIS-aided multi-user MIMO-OFDM system, we model the channel state information (CSI) estimation as an image super-resolution (SR) problem to recover and denoise the channel matrix. Particularly, a convolutional neural network based on a super-resolution convolutional neural network (SRCNN) and denoising convolutional neural network (DnCNN), named SRDnNet, is then proposed. By taking estimated channels at pilot positions as a low-resolution image, the enhanced SRCNN can fully exploit the features of inputs to learn a suitable interpolation method and generate the coarse estimation of the channel matrix. The denoising model DnCNN with an element-wise subtraction structure can exploit features of the additive noise and recover channel coefficients from the coarse channel matrix. The simulation results demonstrate the effectiveness and excellent performance of the proposed SRDnNet.

Underwater VLC channel estimation based on Kalman filtering for direct current optical- and asymmetrically clipping optical- orthogonal frequency division multiplexing techniques

In this paper, we suppose an underwater optical wireless communication (UOWC) system, where the communication utilizes visible light communication for its advantages as wide spectrum, high data rate and high accuracy. The novelty of this paper is focused on improving the channel estimation between transmitter and receiver, where using Kalman Filter (KF) for channel estimation in UOWCs achieves the best results as compared to other traditional channel estimation methods. The scenario of this paper is summarized in transmitting data from transmitter to receiver via underwater harbor and coastal channels. Two channel models are utilized: weighted double gamma functions (WDGF) and a combination of exponential and arbitrary power function (CEAPF). The modulation technique used is optical orthogonal frequency division multiplexing with two kinds: direct current optical orthogonal frequency division multiplexing (DCO-OFDM) and asymmetrically clipping optical orthogonal frequency division multiplexing (ACO-OFDM). Three different techniques are used for channel estimation: Least Square (LS), minimum mean square error (MMSE), and KF. The simulation results reveal that the ACO-OFDM modulation technique with CEAPF channel modeling using KF achieves the lowest bit error rate (BER) compared to other channel estimation methods. The improvement percentage at BER = 10−1 is 13.3% for ACO-OFDM over DCO-OFDM with CEAPF in coastal water and is is 9.3% for WDGF. This indicates that CEAPF performs about 4% better than WDGF for ACO-OFDM than DCO-OFDM in terms of channel estimation.

Reference Signal Design and Power Optimization for Energy-Efficient 5G V2X Integrated Sensing and Communications

Recently, the development of integrated sensing and communications (ISAC) has attracted great attention. In this paper, the reference signal (RS) in 5G vehicle-to-everything (V2X) communications is leveraged for radar sensing. Particularly, the scattered RS design is adopted under the constraints of communication channel estimation and radar sensing ambiguity functions. To quantify the influence of RS design on channel estimation, the minimum mean square error (MMSE) via two-dimensional Wiener filter is derived in a closed-form for doubly-selective communication channel. The RS spacing and power allocation for RS and each data subcarrier are further jointly optimized to minimize the transmission power, while satisfying the requirements of communication data rate and radar sensing signal to noise ratio (SNR), which results in a mixed-integer non-linear programming (MINLP) problem. To address this problem, the successive convex approximation (SCA) based method is first developed to achieve a suboptimal solution. Next, we show that if the RS spacing is given, the optimal power allocation among RS and each data subcarrier can be achieved by solving three subproblems sequentially via (reverse) water-filling algorithms. Extensive simulations are carried out to validate the effectiveness of our proposed design. Compared to the existing subcarrier-wise RS design with uniform power allocation for data subcarriers, our design can reduce the power consumption by up to 12 dB.

Sensing-Aided Uplink Channel Estimation for Joint Communication and Sensing

The joint communication and sensing (JCAS) technique has drawn great attention due to its high spectrum efficiency by using the same transmit signal for both communication and sensing. Exploiting the correlation between the uplink (UL) channel and the sensing results, we propose a sensing-aided Kalman filter (SAKF)-based channel state information (CSI) estimation method for UL JCAS, which exploits the angle-of-arrival (AoA) estimation to improve the CSI estimation accuracy. A Kalman filter (KF)-based CSI enhancement method is proposed to refine the least-square CSI estimation by exploiting the estimated AoA as the prior information. Simulation results show that the bit error rates (BER) of UL communication using the proposed SAKF-based CSI estimation method approach those using the minimum mean square error (MMSE) method, while at significantly reduced complexity.

Weber’s Law of perception is a consequence of resolving the intensity of natural scintillating light and sound with the least possible error

Efficient resolution of natural light and sound intensity is essential for organisms, systems and machines that rely on visual and auditory sensory perception to survive or function effectively in their environment. This resolution obeys Weber’s Law when the smallest resolvable change, a just-noticeable-difference, grows in direct proportion to the stimulus. Here, Weber’s Law is found to be a consequence of attaining the theoretical minimum mean-square error possible, the Cramer–Rao lower bound, in resolving the intensity of naturally scintillating light and sound. The finding is based on statistics from thousands of measurements of naturally scintillating environmental light and sound signals. Remarkably, just-noticeable-differences in light and sound intensity measured over decades of psychophysical experiments with artificial sources are also found to approximately attain the respective Cramer–Rao lower bounds. Human intensity resolution is in this way optimally adapted to the natural scintillation of light and sound. Pattern recognition by simple matched-filter correlation between measured and hypothetical images cancels natural scintillation. For intensity perception obeying Weber’s Law, this is found to be advantageous and statistically optimal because perceived scintillation is independent of the underlying signal pattern. A small visual patch change or acoustic signature truncation is shown to be lost in natural signal-dependent fluctuations if perception with constant intensity resolution is attempted.