Mean Square Error Performance Research Articles

Robust Linear Transceiver Designs for Vector Parameter Estimation in MIMO Wireless Sensor Networks Under CSI Uncertainty

This work conceives the robust linear transceivers for the estimation of an unknown vector parameter in a coherent multiple access channel (MAC)-based multiple-input multiple-output (MIMO) multi-sensor network under imperfect channel state information (CSI) at the fusion center (FC). Both the popular stochastic (S-) and norm ball CSI uncertainty (N-CSIU) models are considered for robust design. The proposed techniques are based on two design criterion, the first being, minimizing the mean squared error (MSE) of the estimate at the FC subject to total network power or individual sensor power constraints. Second, minimizing the total power consumption in the network while meeting a predefined level of MSE performance. Furthermore, the framework for precoder and combiner optimization is based on results from majorization theory, which leads to non-iterative closed-form solutions for the transceivers. While the most general scenario with correlated parameters and arbitrary observation SNR is considered to begin with, scenarios with uncorrelated parameters and high observation SNR are also considered as special cases, which makes the analysis comprehensive. Simulation results are presented to demonstrate the efficacy of the proposed schemes.

Novel hybrid model based on echo state neural network applied to the prediction of stock price return volatility

The prediction of stock price return volatilities is important for financial companies and investors to help to measure and managing market risk and to support financial decision-making. The literature points out alternative prediction models - such as the widely used heterogeneous autoregressive (HAR) specification - which attempt to forecast realized volatilities accurately. However, recent variants of artificial neural networks, such as the echo state network (ESN), which is a recurrent neural network based on the reservoir computing paradigm, have the potential for improving time series prediction. This paper proposes a novel hybrid model that combines HAR specification, the ESN, and the particle swarm optimization (PSO) metaheuristic, named HAR-PSO-ESN, which combines the feature design of the HAR model with the prediction power of ESN, and the consistent PSO metaheuristic approach for hyperparameters tuning. The proposed model is benchmarked against existing specifications, such as autoregressive integrated moving average (ARIMA), HAR, multilayer perceptron (MLP), and ESN, in forecasting daily realized volatilities of three Nasdaq (National Association of Securities Dealers Automated Quotations) stocks, considering 1-day, 5-days, and 21-days ahead forecasting horizons. The predictions are evaluated in terms of r-squared and mean squared error performance metrics, and the statistical comparison is made through a Friedman test followed by a post-hoc Nemenyi test. Results show that the proposed HAR-PSO-ESN hybrid model produces more accurate predictions on most of the cases, with an average R2 (coefficient of determination) of 0.635, 0.510, and 0.298, an average mean squared error of 5.78 × 10−8, 5.78 × 10−8, and 1.16 × 10−7, for 1, 5, and 21 days ahead on the test set, respectively. The improvement is statistically significant with an average rank of 1.44 considering the three different datasets and forecasting horizons.

Event-triggered optimal Kalman consensus filter with upper bound of error covariance

In this paper, we present an event-triggered optimal Kalman consensus filter (EOKCF) for state estimation in distributed wireless sensor networks. The local message is exchanged only when the local estimation violates a predetermined Send-on-Delta (SoD) data transmission condition in order to reduce the amount of data transfer. The neighboring measurement and estimation information are integrated into the consensus filter, and a recursive upper bound of the error covariance is derived for uncertainties of interval communication from the event-based systems. The optimal Kalman gain and consensus gain matrices are obtained by minimizing the upper bound of state error covariance. The Crameˇr−−Rao lower bound (CRLB) of the state estimates is also introduced to measure the mean-square estimation error performance. The effectiveness of event-triggered communication protocol and the advantages of filtering performance of EOKCF are demonstrated using Monte Carlo simulations on a target tracking application in a distributed sensor network.

On Low-Complexity MMSE Channel Estimation for OCDM Systems

In this letter, we first present a time-domain model for pilot-assisted MMSE channel estimation in the orthogonal chirp division multiplexing (OCDM) systems. Then by proposing a pilot selection criterion, the complexity of MMSE channel estimation is reduced by the simplification of matrix inversion. Meanwhile, we prove that the criterion can lead to the optimal mean square error (MSE) performance. Furthermore, based on the criterion, by adopting the Zadoff-Chu sequences as pilots and presenting a split-and-decomposition algorithm, we propose a low-complexity channel estimator for OCDM. The complexity of the proposed estimator is <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (Nlog\frac L2), while the estimator in existing literature for OCDM is <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (NlogN), where L is the channel length and N is the number of subcarriers. Numerical results are provided to verify the performance of the proposed algorithm over frequency-selective Rayleigh fading channels. It turns out that the proposed estimator can significantly reduce the computational complexity without any MSE performance loss.

Morphology extraction of fetal electrocardiogram by slow-fast LSTM network

Fetal electrocardiogram (FECG) morphology plays an essential role in the early diagnosis of fetal health conditions. However, it is intractable to extract the clean morphology of FECG signals, which are usually contaminated by maternal ECG (MECG) and various noises. To extract the clean morphology of FECG signals from non-invasive abdominal ECG records, a high-performance and high-efficient two-stage slow-fast long short-term memory (SFLSTM) based architecture is proposed. The MECG elimination and the FECG enhancement are realized by the elaborately designed slow LSTM and fast LSTM to filter out the MECG and the residual noise components. Qualitative and quantitative experiments are conducted on the records from two public datasets. The experimental results reveal that our designed scheme achieves the best performance in kSQI, signal-to-noise ratio (SNR), and root mean square error (RMSE). The MECG elimination and the FECG enhancement improve SNR by 3.09 and 1.81 dB, respectively. The proposed fast LSTM reduces computation cost by approximately 50%, without any degradation in performance. Our method may leverage non-invasive FECG monitoring for the early detection of fetal heart diseases.

Probability-Constrained robust estimation for a random parameter with stochastic model uncertainties

This paper investigates the problem of estimating a random parameter in a linear observation model when the transformation matrix suffers stochastic uncertainties. In practice, the uncertainties can be either the bounded uncertainties or the Gaussian uncertainties. The existing minimax robust estimation method is only applicable to the bounded uncertainties, and minimizes the worst-case mean squared error (MSE) over the region of uncertainties, irrespective of the probability of such worst-case scenario, so it tends to be overly conservative. A probability-constrained (PC) robust linear estimation method is proposed in this paper to minimize the MSE with a guaranteed probability, which can handle bounded uncertainties as well as Gaussian uncertainties. However, the formulated problem is not analytically tractable due to the unspecified distribution of the uncertainties, so two approximate PC robust estimators are derived by tackling two upper bounds of the original optimization problem and converting them to semidefinite programming problems with the safe tractable approximation techniques. The comparative analysis reveals that there is a tradeoff between the MSE performance and computation complexity in the proposed two PC estimators. The Monte Carlo simulations are used to corroborate the theoretical results, which demonstrate that the proposed PC estimators are robust to the uncertainties compared to the nominal linear minimum mean squared error (LMMSE) estimator and the nominal best linear unbiased estimator (BLUE), and are less conservative compared to the traditional minimax robust estimator.

Bandwidth constrained distributed estimation for wireless sensor networks

The focus of this paper is power constrained in wireless sensor networks. We purpose an adaptive transmit power levels based on sensors noise variance and channel conditions. We also investigate its impact on energy saving. First, the measurement results of the sensors are quantized into discrete messages. Second, the quantized data are transmitted to the fusion center where a final estimate is generated. The optimal transmit power levels for each sensor is determined by the sensor noise levels and channels conditions from sensor to the fusion center. The goal is minimized the total transmitting power, while ensuring a given Mean Squared Error (MSE) performance. The sensor will be active when the measurement results of the sensors have low noises variances and the condition of the channel between the sensor and the FC is good and if the conditions are otherwise the sensor is not active with the aim of saving power. For the remaining active sensors, their optimal transmit power levels are determined jointly by individual channels gain, local observation noise variance sensor and the targeted MSE performance. Numerical examples show that an adaptive power levels achieves significantly smaller MSE than uniform power levels for the same average power consumption.

Deep Residual Learning-Assisted Channel Estimation in Ambient Backscatter Communications

Channel estimation is a challenging problem for realizing efficient ambient backscatter communication (AmBC) systems. In this letter, channel estimation in AmBC is modeled as a denoising problem and a convolutional neural network-based deep residual learning denoiser (CRLD) is developed to directly recover the channel coefficients from the received noisy pilot signals. To simultaneously exploit the spatial and temporal features of the pilot signals, a novel three-dimension (3D) denoising block is specifically designed to facilitate denoising in CRLD. In addition, we provide theoretical analysis to characterize the properties of the proposed CRLD. Simulation results demonstrate that the performance of the proposed method approaches the performance of the optimal minimum mean square error (MMSE) estimator with perfect statistical channel correlation matrix.

Hybrid Beamforming for Massive MIMO Over-the-Air Computation

Over-the-air computation (AirComp) has been recognized as a promising technique in Internet-of-Things (IoT) networks for fast data aggregation from a large number of wireless devices. However, the computation accuracy of AirComp highly depends on the devices with the worst channels condition, which degrades severely when the number of devices becomes large. To address this issue, we exploit the massive multiple-input multiple-output (MIMO) with hybrid beamforming, in order to enhance the computational accuracy of AirComp in a cost-effective manner. In particular, we consider the scenario with a large number of multi-antenna devices simultaneously sending data to an access point (AP) equipped with massive antennas for functional computation over the air. Under this setup, we jointly optimize the transmit digital beamforming at the wireless devices and the receive hybrid beamforming at the AP, with the objective of minimizing the computational mean-squared error (MSE) subject to the individual transmit power constraints at the wireless devices. To solve the non-convex hybrid beamforming design optimization problem, we propose an alternating-optimization-based approach, in which the transmit digital beamforming and the receive analog and digital beamforming are optimized in an alternating manner. In particular, we propose two computationally efficient algorithms to handle the challenging receive analog beamforming problem, by exploiting the techniques of successive convex approximation (SCA) and coordinate descent (CD), respectively. It is shown that for the special case with a fully-digital receiver at the AP, the achieved MSE of the massive MIMO AirComp system is inversely proportional to the number of receive antennas. Furthermore, numerical results show that the proposed hybrid beamforming design substantially enhances the computation MSE performance as compared to other benchmark schemes, while the SCA-based algorithm performs closely to the performance upper bound achieved by the fully-digital beamforming.

Robust Time-Varying Parameter Proportionate Affine-Projection-Like Algorithm for Sparse System Identification

Due to its low computational burden, the affine-projection-like (APL) adaptive filtering algorithm has been extensively studied for colored signal input. Recently, a robust APL algorithm was designed by adopting the M-estimate cost function in impulsive noise environment; however, its convergence rate is very slow for sparse system identification. This paper proposed a proportionate APL M-estimate (PAPLM) algorithm, which is derived by using the proportionate matrix to heighten the convergence rate. To maintain good steady-state performance of the PAPLM algorithm, a time-varying parameter PAPLM (TV-PAPLM) algorithm is proposed, which uses a modified exponential function to adjust the time-varying parameter according to the ratio of the mean square score function to the system noise variance. Moreover, the steady-state excess mean-square error performance of PAPLM algorithm is analyzed and obtained in detail. Simulation results reveal that the proposed PAPLM and TV-PAPLM algorithms achieve fast convergence rate and good steady-state performance in sparse system identification.

Joint Channel and Phase Noise Estimation and Data Detection for GFDM

Generalized frequency division multiplexing (GFDM), an enabler of beyond-5G wireless networks, can be critically impaired due to radio frequency (RF) phase noise. However, joint channel estimation and phase noise compensation for GFDM systems have not been addressed before. Hence, we tackle this problem. To this end, we propose an iterative algorithm for joint channel and phase noise estimation and two algorithms for joint data detection and phase noise compensation. These algorithms use linear and non-linear least-squares (NLS) methods and employ block-type and comb-type pilots. The complexity of these algorithms is also analyzed. Moreover, to reduce their complexity, interpolation techniques are deployed to decrease the number of unknowns. We also analyze the signal-to-interference-plus noise ratio (SINR) and sum-rate of GFDM contaminated with phase noise. Furthermore, the accuracy of the channel and phase noise estimates is established via Cramer-Rao lower bounds (CRLBs). The simulation results illustrate that the mean-squared error (MSE) performance of the proposed joint channel and phase noise estimator reaches the CRLB. Moreover, the proposed joint data symbol detection and phase noise compensation algorithms nearly eliminate the impacts of phase noise in GFDM systems.

Coupled Regularized Sample Covariance Matrix Estimator for Multiple Classes

The estimation of covariance matrices of multiple classes with limited training data is a difficult problem. The sample covariance matrix (SCM) is known to perform poorly when the number of variables is large compared to the available number of samples. In order to reduce the mean squared error (MSE) of the SCM, regularized (shrinkage) SCM estimators are often used. In this work, we consider regularized SCM (RSCM) estimators for multiclass problems that couple together two different target matrices for regularization: the pooled (average) SCM of the classes and the scaled identity matrix. Regularization toward the pooled SCM is beneficial when the population covariances are similar, whereas regularization toward the identity matrix guarantees that the estimators are positive definite. We derive the MSE optimal tuning parameters for the estimators as well as propose a method for their estimation under the assumption that the class populations follow (unspecified) elliptical distributions with finite fourth-order moments. The MSE performance of the proposed coupled RSCMs are evaluated with simulations and in a regularized discriminant analysis (RDA) classification set-up on real data. The results based on three different real data sets indicate comparable performance to cross-validation but with a significant speed-up in computation time.

Standard errors of risk and performance estimators for serially dependent returns

In this paper, a new method for computing the standard errors (SEs) of returns-based risk and performance estimators for serially dependent returns is developed. The method uses both the fact that any such estimator can be represented as the mean of returns that are transformed using the estimator’s influence function (IF), and the fact that the variance of such a sum can be estimated by estimating the zero-frequency value of the spectral density of the IF transformed returns. The spectral density is estimated by fitting a polynomial to the periodogram using a generalized linear model for exponential distributions, with elastic net regularization. We study the use of the new SEs method with and without prewhitening. Applications to computing the SE of Sharpe ratio (SR) estimators for a collection of hedge funds, whose returns have varying degrees of serial dependence, show that the new methods are a considerable improvement on SE methods based on assumed independent and identically distributed returns, and that the prewhitening version performs better than the one without prewhitening. Monte Carlo simulations are conducted to study (i) the mean-squared error performance of the SE methods for a number of commonly used risk and performance estimators for first-order autoregression and GARCH(1,1) returns models; and (ii) the SR confidence interval error rate performance for first-order autoregression models with normal and t-distribution innovations. The results show that our new method is a considerable improvement on both earlier frequency domain methods and the Newey–West heteroscedasticity and autocorrelation consistent (HAC) SE method.

Evaluating SEM Model Fit with Small Degrees of Freedom

Research has revealed that the performance of root mean square error of approximation (RMSEA) in assessing structural equation models with small degrees of freedom (df) is suboptimal, often resulting in the rejection of correctly specified or closely fitted models. This study investigates the performance of standardized root mean square residual (SRMR) and comparative fit index (CFI) in small df models with various levels of factor loadings, sample sizes, and model misspecifications. We find that, in comparison with RMSEA, population SRMR and CFI are less susceptible to the effects of df. In small df models, the sample SRMR and CFI could provide more useful information to differentiate models with various levels of misfit. The confidence intervals and p-values of a close fit were generally accurate for all three fit indices. We recommend researchers use caution when interpreting RMSEA for models with small df and to rely more on SRMR and CFI.

Retrieval of the Soil Salinity From Sentinel-1 Dual-Polarized SAR Data Based on Deep Neural Network Regression

Soil salinity is a significant environmental indicator, directly reflecting the land quality and its productivity. In this work, dual-polarized synthetic aperture radar (PolSAR) data were exploited to retrieve the soil salinity in saline-affected fields based on the deep neural network (DNN) theory. Two polarimetric features gotten from Cloude polarization decomposition, together with six other features, were calculated and selected from ten features according to the feature importance. The DNN regression model for soil salinity (DNNR-S) based on one-dimensional convolutional neural network, quantifying the relationship between the eight feature parameters and soil salinity, was established to retrieve the soil salinity in northeastern China. Compared with other five traditional machine learning regression methods [logistic regression (LOR), random forest regression (RFR), support vector regression (SVR), decision tree regression (DTR), and multilayer perceptron regression (MPR)], DNNR-S is the best-performing model with the performance of root mean square error (RMSE) &#x003D; 0.28, mean absolute error (MAE) &#x003D; 0.21, and <inline-formula> <tex-math notation="LaTeX">$r = 0.74$ </tex-math></inline-formula>. Using the proposed model, the soil salinity was retrieved, and 52.37&#x0025; was found to be affected by salinization which was in general agreement with the government report. Due to the training criteria in the proposed model, it was a little more computationally intensive than all the others, but the DNNR-S had the advantage of easy spread to other study areas.

Application-Based Coexistence of Different Waveforms on Non-Orthogonal Multiple Access

In the study, the coexistence of different waveform structures on the same resource element is studied under the theory of non-orthogonal multiple access (NOMA). This study introduces a paradigm-shift on NOMA towards the application-centric waveform coexistence. Throughout this article, the coexistence of different waveforms is explained with two specific use cases, which are power-balanced NOMA and joint radar-sensing and communication with NOMA. For the first use case, block error rate (BLER) performance in the power-balanced regime for two user is improved compared to conventional NOMA transmission with the same waveform. For the joint radar-sensing and communication aspect, the superiority of proposed NOMA scheme over orthogonal frequency division multiplexing (OFDM) joint radar-communication (JRC) scheme is demonstrated regarding radar ambiguity, channel estimation mean-square error (MSE) and bit-error rate (BER) performances. In addition, some of the previous works in the literature are reviewed regarding waveform coexistence in a non-orthogonal manner. However, the concept is not limited to these use cases. With the rapid development of wireless technology, next-generation wireless systems are proposed to be flexible and hybrid, having different kinds of capabilities such as sensing, security, intelligence, control, and computing. Therefore, the concept of different waveforms’ coexistence to meet these concerns are becoming impressive for researchers.

Beamforming Techniques for Over-the-Air Computation in MIMO IoT Networks

In this paper, a novel beamforming technique is proposed as the over-the-air computation (AirComp) framework in a multiple-input multiple-output (MIMO) Internet-of-things (IoT) network consisting of multiple IoT sensors (STAs) and a single access point (AP). We assume that each IoT device has the channel state information (CSI) from itself to the AP and the AP has the global CSI of all IoT devices. We consider the mean squared error (MSE), which represents the reliability of function computation, as a performance metric. In short, each IoT device exploits maximum-ratio transmission (MRT) as a transmit beamforming technique to improve MSE performance by taking full advantage of multiple transmit antennae. Moreover, for the receive beamforming, we first consider a receive antenna selection (RAS) technique as the simplest beamforming method at the AP. Then, a semi-definite relaxation (SDR) method and a successive convex approximation (SCA) algorithm are considered and compared with each other in terms of MSE. Finally, we propose a novel two-step beamforming algorithm to further improve the MSE performance of the aforementioned techniques. We have numerically verified through computer simulations that the proposed framework has an improved MSE performance of about 6dB compared to the conventional single-input multiple-output (SIMO) AirComp, even with only two transmit antennae, and the modified MRT outperforms the other transmit beamforming techniques. Furthermore, the proposed receive beamforming technique, a two-step algorithm, shows the best performance in terms of MSE compared to prior studies.

Realistic Channel Estimation of IEEE 802.11af Systems in TV White Space

This work investigates the realistic performance of IEEE 802.11af systems released for the efficient spectrum utilization of TV white space (TVWS). These systems are operated over many contiguous or non-contiguous channels based on the TVWS frequency band availability. Accordingly, we consider realistic channel estimation for TVWS system and analyze the corresponding system performance of linear minimum mean square error (LMMSE) and orthogonal matching pursuit (OMP) algorithms. While LMMSE estimates channel path gains assuming perfectly known tap delay locations, OMP estimates both channel path gains and delays. Owing to the realistic implementation and estimating the full channel state information (CSI) of sparse channels, we mainly assess the OMP performance together with the LMMSE estimation for comparison in terms of channel reconstruction and symbol detection errors. To address the channel estimation performance, Bayesian Cramer-Rao bound is derived theoretically for both perfect and imperfect CSI, and confirmed with the simulations. Simulation results demonstrate that the realistic OMP-based symbol detection performance is found to be only 1–2 dB inferior compared to the near-optimal LMMSE-based estimation with known delays in low and medium signal-to-noise-ratio regions, where communication mainly occurs in practice. In addition, the effects of channel multipath number, channel resolution and operation modes on the system performance are studied for different scenarios. The results of this work are important for the practical implementation of IEEE 802.11af-based systems.

Robust Design for Intelligent Reflecting Surfaces Assisted MISO Systems

In this work, we study the statistically robust beamforming design for an intelligent reflecting surfaces (IRS) assisted multiple-input single-output (MISO) wireless system under imperfect channel state information (CSI), where the channel estimation errors are assumed to be additive Gaussian. We aim at jointly optimizing the transmit/receive beamformers and IRS phase shifts to minimize the average mean squared error (MSE) at the user. In particular, to tackle the non-convex optimization problem, an efficient algorithm is developed by capitalizing on alternating optimization and majorization-minimization techniques. Simulation results show that the proposed scheme achieves robust MSE performance in the presence of CSI error, and substantially outperforms conventional non-robust methods.

OFDM-IDMA Sistemi İçin Genetik Algoritmaya Dayalı Biyo-İlhamlı Pilot Dizayn Yaklaşımı

It is well known that the efficiency of a channel estimator employing the strategy of comb-type pilot placement can be controlled by adjusting the positions of pilot tones. In this paper, by considering this situation, in order to maximize the estimation precision of the least squares (LS) algorithm utilized as a channel estimator in orthogonal frequency division multiplexing – interleave division multiple access (OFDM-IDMA) scheme, the genetic algorithm (GA) possessing a wide range of uses due to its powerful problem solving capability was utilized in the optimization of pilot positions. Besides, the computational load of mean square error (MSE) which is used as the objective function of GA was avoided by employing its upper bound during the optimization process. The upper bound of MSE was achieved by utilizing the Gershgorin disc theorem. In the simulations, the suggested pilot arrangement strategy based on the GA was compared to the conventional techniques like equispaced and random pilot placements in point of two criteria known as bit error rate (BER) and MSE. Simulation results put forth that GA-based pilot design strategy establishes a very clear superiority over the other considered methods by providing significant MSE and BER performances.