Minimum Mean Square Error Research Articles

New generalized class of estimators for estimation of finite population mean based on probability proportional to size sampling using two auxiliary variables: A simulation study.

This article aims to suggest a new generalized class of estimators based on probability proportional to size sampling using two auxiliary variables. The numerical expressions for the bias and mean squared error (MSE) are derived up to the first order of approximation. Four actual data sets are used to examine the performances of a new improved generalized class of estimators. From the results of real data sets, it is examined that the suggested estimator gives the minimum MSE and the percentage relative efficiency is higher than all existing estimators, which shows the importance of the new generalized class of estimators. To check the strength and generalizability of our proposed class of estimators, a simulation study is also accompanied. The consequence of the simulation study shows the worth of newly found proposed class estimators. Overall, we get to the conclusion that the proposed estimator outperforms as compared to all other estimators taken into account in this study.

Slepian Transform Based Detectors for HF Skywave Massive MIMO-OFDM Systems

In this paper, we investigate signal detection for high frequency (HF) skywave massive multiple-input multiple-output (MIMO) systems with orthogonal frequency division multiplexing (OFDM) modulation. We first introduce the beam based channel model for HF skywave massive MIMO-OFDM channels and show the relationship of sparse supports between the beam domain channel and the Fourier spectrum of the space domain channel. Based on the sparse beam domain channel, we propose a separate Slepian transform (SST) based detector, where a set of modulated Slepian sequences are designed independently for user terminals (UTs). Before the minimum mean-squared error (MMSE) detection, the Slepian transform is performed for each UT to reduce the dimension of the observation vector and the channel matrix, thus avoiding high dimensional matrices multiplications and inversions. Due to the sparsity of the beam domain channel, the Slepian transform of channel vectors can be efficiently implemented by low-dimensional matrix-vector multiplications. To further reduce the computational complexity, we propose a joint Slepian transform (JST) based detector, where a fixed set of modulated Slepian sequences are designed. As a result, Slepian transforms of the observation vector can be efficiently implemented using low-dimensional fast Fourier transform (FFT). Simulation results demonstrate the advantages of high performance and low complexity of proposed detectors.

Performance Analysis of Cell-Free Massive MIMO Network With Large-Scale-Fading Decoding and Low-Resolution ADCs

Concentrating on cell-free massive multiple-input multiple-output (MIMO) networks with low-resolution analog-to-digital converters (ADCs), we derive the theoretical achievable uplink spectral efficiency (SE) for the minimum mean-squared error (MMSE)-based large-scale fading decoding (LSFD). Moreover, we investigate the bit allocation (BA) among access points (APs) to maximize the asymptotic sum SE under the constraint of total ADC quantization bits. Simulation results confirm that our theoretical analysis is accurate and validate that the proposed BA technique is preferable to the random and fixed counterparts.

A Soft Sensor for Estimating Tire Cornering Properties for Intelligent Tires

Intelligent tire systems are promising solutions for achieving precise vehicle state estimations, localization, and motion control in the context of autonomous driving. Tire cornering properties, namely, lateral force, aligning moment, and pneumatic trail, are crucial factors that should be accurately estimated for vehicle dynamics control purposes. In this work, a soft sensor for estimating tire cornering properties based on intelligent tire and machine learning is developed. The intelligent tire system is based on a triaxial accelerometer mounted on the inner liner of the tire tread, which provides acceleration measurements from the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$</tex-math> </inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$y$</tex-math> </inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$</tex-math> </inline-formula> directions. Partial least squares and variable importance in the projection scores (PLS-VIP) are used in the feature extraction of the acceleration signals over the contact patch. A Gaussian process regression (GPR) model is trained to predict the cornering properties with confidence intervals under different input conditions. Based on the variances in the GPR predictions and minimum mean-square error criterion, a data fusion method for pneumatic trail estimation is proposed. It is demonstrated that the developed GPR models for cornering properties and the data fusion method for pneumatic trail estimation have satisfactory accuracy and reliability. The experimental results show that the soft sensor proposed in this work is a strong candidate for further applications in the development of vehicle state estimation and control algorithms.

Bayesian denoising of structured sources and its implications on learning-based denoising

Abstract Denoising a stationary process $(X_{i})_{i \in \mathbb{Z}}$ corrupted by additive white Gaussian noise $(Z_{i})_{i \in \mathbb{Z}}$ is a classic, well-studied and fundamental problem in information theory and statistical signal processing. However, finding theoretically founded computationally efficient denoising methods applicable to general sources is still an open problem. In the Bayesian set-up where the source distribution is known, a minimum mean square error (MMSE) denoiser estimates $X^{n}$ from noisy measurements $Y^{n}$ as $\hat{X}^{n}=\mathrm{E}[X^{n}|Y^{n}]$. However, for general sources, computing $\mathrm{E}[X^{n}|Y^{n}]$ is computationally very challenging, if not infeasible. In this paper, starting from a Bayesian set-up, a novel denoising method, namely, quantized maximum a posteriori (Q-MAP) denoiser is proposed and its asymptotic performance is analysed. Both for memoryless sources, and for structured first-order Markov sources, it is shown that, asymptotically, as $\sigma _{z}^{2} $ (noise variance) converges to zero, ${1\over \sigma _{z}^{2}} \mathrm{E}[(X_{i}-\hat{X}^{\mathrm{QMAP}}_{i})^{2}]$ converges to the information dimension of the source. For the studied memoryless sources, this limit is known to be optimal. A key advantage of the Q-MAP denoiser, unlike an MMSE denoiser, is that it highlights the key properties of the source distribution that are to be used in its denoising. This key property leads to a new learning-based denoising approach that is applicable to generic structured sources. Using ImageNet database for training, initial simulation results exploring the performance of such a learning-based denoiser in image denoising are presented.

End-to-end DVB-S2X system design with DL-based channel estimation over satellite fading channels at Ka-band

Satellite channels suffer from heavy fading due to the atmospheric impairments at high frequencies. Therefore, channel estimation is essential for coherent detection and demodulation in satellite-coded systems. The conventional minimum mean square error (MMSE) estimator (the theoretical upper bound) requires a priori knowledge about the channel statistics which is not feasible to obtain in a real transmission. Also, it suffers from high complexity. However, deep learning (DL) estimators do not require any information about the channel statistics. Therefore, in this paper, two DL-based channel estimators are proposed for digital and video broadcasting second generation extension (DVB-S2X) system with less complexity than the MMSE estimator. In particular, the bidirectional long-short term memory (BLSTM) and the gated recurrent unit (GRU) are adopted in our proposed estimators which are termed as DLBLSTM and DLGRU, respectively. The proposed estimators evaluated over two satellite fading channels; one with heavy fading and the other with low fading. Moreover, these estimators are compared with the conventional estimators, the least square (LS) and the MMSE, in terms of the normalized mean square error (NMSE) and the bit error rate (BER). Simulation results show that the proposed DL-based estimators have better performance than the LS estimator and the DLBLSTM has better performance than the DLGRU estimator in terms of NMSE and BER with both satellite channels.

BER analysis of an optimum MIMO linear receiver in optical SDM systems with mode-dependent loss.

Multiple-input multiple-output (MIMO) receivers designed to optimize the minimum mean square error (MMSE) are a common choice in coherent optical communication systems based on spatial division multiplexing (SDM). This kind of receivers naturally integrate both MIMO equalization and matched filtering functions. However, when the optical channel exhibits significant mode-dependent loss (MDL) and/or mode-dependent gain (MDG), the impact of inter-symbol interference (ISI) and crosstalk that arise, even using an ideal MIMO MMSE linear receiver, is barely analyzed. Moreover, due to the random nature of the MDL/MDG model, the resulting ISI, crosstalk, and bit error rate (BER) also become random variables and, hence the system performance is more unpredictable. In this paper, we first evaluate the residual distortion (ISI and crosstalk) after the MIMO receiver and then we study the validity of assuming it as an additional Gaussian noise term independent of the channel noise. Next, the probability density distribution (PDF) of the BER is analyzed, from both an analytical perspective and numerical simulations. For the latter, we use a single-carrier 2-PAM (pulse amplitude modulation) system, with pulse shaping, and the MIMO MMSE receiver implementation by means of a MIMO fractionally-spaced equalizer (FSE). We carry out simulations of the system under different conditions of MDL/MDG level and signal to noise ratio (SNR), measured at the receiver input. Additionally, we address possible fits of the BER PDF to known closed-form distributions, among which the Generalized Extreme Value (GEV) family of distributions is selected, and polynomial functions are proposed that relate the system parameters with the GEV PDF parameters. Finally, we present contour maps of BER according to a giving target of system outage probability (OP) that depend on the MDL/MDG and SNR conditions.

DL-Based OTFS Signal Detection in Presence of Hardware Impairments

Orthogonal time frequency space (OTFS) modulation is an emerging technique for next-generation communication due to its robustness to the doubly dispersive channels under high mobility scenarios. We have designed and analyzed a deep learning (DL)-based OTFS system (DL-OTFS) in the presence of hardware impairments (HI) such as in-phase and quadrature-phase (IQ) component mismatch and DC offset. Further, data augmentation is also considered for the proposed DL-OTFS to enhance the system performance. Numerical results show that the DL-OTFS model can efficiently learn the input and output relation and leads to improved bit error rate (BER) performance than the conventional message passing and minimum mean square error (MMSE)-based receiver with and without HI.

Optimal monitoring and attack detection of networks modeled by Bayesian attack graphs

Early attack detection is essential to ensure the security of complex networks, especially those in critical infrastructures. This is particularly crucial in networks with multi-stage attacks, where multiple nodes are connected to external sources, through which attacks could enter and quickly spread to other network elements. Bayesian attack graphs (BAGs) are powerful models for security risk assessment and mitigation in complex networks, which provide the probabilistic model of attackers’ behavior and attack progression in the network. Most attack detection techniques developed for BAGs rely on the assumption that network compromises will be detected through routine monitoring, which is unrealistic given the ever-growing complexity of threats. This paper derives the optimal minimum mean square error (MMSE) attack detection and monitoring policy for the most general form of BAGs. By exploiting the structure of BAGs and their partial and imperfect monitoring capacity, the proposed detection policy achieves the MMSE optimality possible only for linear-Gaussian state space models using Kalman filtering. An adaptive resource monitoring policy is also introduced for monitoring nodes if the expected predictive error exceeds a user-defined value. Exact and efficient matrix-form computations of the proposed policies are provided, and their high performance is demonstrated in terms of the accuracy of attack detection and the most efficient use of available resources using synthetic Bayesian attack graphs with different topologies.

Channel Estimation and Turbo Equalization for Coded OTFS and OFDM: A Comparison

In this letter, we study joint channel estimation and turbo equalization for coded orthogonal time frequency space (OTFS) and orthogonal frequency division multiplexing (OFDM). To the best of our knowledge, this is the first study that compares performance of OTFS and OFDM coded systems using the state-of-the-art message passing (MP) and soft minimum mean square error (MMSE) equalizers, under imperfect channel estimation. We show that the commonly used threshold-based channel estimator incurs noticeable performance loss for OTFS. Hence, we propose a basis expansion model (BEM) channel estimation technique for OTFS, which improves performance of the threshold-based channel estimator and yields a superior performance to OFDM when using small modulations of BPSK and QPSK. Our work also reveals that OTFS can perform inferior to OFDM as the modulation order increases. This is due to the increased 2D detection complexity of OTFS.

Temperature behavior modeling based on resilient BPNN for a GaAs pHEMT high gain MMIC PA

AbstractAs the key component of transceiver, power amplifier (PA) plays an extremely important role in wireless communication system. In order to accurately characterize the performance variation of PA at any temperature, the temperature behavior of a gallium arsenide (GaAs) pseudomorphic high electron mobility transistor (pHEMT) high gain monolithic microwave integrated circuit (MMIC) PA is modeled in this paper. In this modeling, the resilient back propagation neural network (BPNN) is utilized to do the temperature behavior modeling for this PA. The investigation shows that the minimum mean square error (MSE) of the prediction results is 4.9607 × 10−4, which implies that it is feasible to use this modeling method to characterize the temperature behavior of PA. This modeling not only theoretically overcomes the problem of slow convergence speed of BPNN, but also solves the limitation of experimental devices and time setting. It will provide a more convenient guidance for test engineers.

Suitable pilot search method for channel estimation in underwater acoustic OFDM systems

The underwater environment poses challenges to the Underwater Acoustic OFDM (UWA-OFDM) system, causing the tendency of lacking pilots to recover the channel impulse response (CIR). Our previous research (pilot enrichment estimator) supplemented potential pilots based on the distance to the nearest constellation point below a fixed threshold T. However, this does not guarantee that the extracted pilots have sufficiently good quality. Therefore, this article presents a suitable pilot search (SPS) method with the flexible threshold T and second minimum mean square error (MMSE) estimation to improve channel estimation effectiveness in UWA-OFDM systems. Our approach is compared to the MMSE and PE methods across various criteria, such as pilot spacing and different modulators. The experiments demonstrate that the SPS estimator performs better than the MMSE and PE techniques regarding bit error rate (BER).

Neutrosophic ratio-type exponential estimators for estimation of population mean

The current work is one step in filling a large void in the research left by the advent of neutrosophic Statistics (NS), a philosophized variant of classical statistics (CS). The philosophy of NS deals with techniques for investigating data that is ambiguous, hazy, or uncertain. The traditional techniques of estimation utilizing auxiliary information work under specific determinate data, which in the case of neutrosophic data may lead to mistakes (over/ under-estimation). This study presents a generalized neutrosophic ratio-type exponential estimator (NRTEE) for estimating location parameters and achieving the lowest mean square error (MSE) possible for interval neutrosophic data (IND). The offered NRTEE helps to deal with the uncertainty and ambiguity of data. Unlike typical estimators, its findings are not single-valued but rather in interval form, which reduces the possibility of over-or under-estimation caused by single crisp outcomes and also increases the likelihood of the parameter dwelling in the interval. It improves the efficiency of the estimator since we have an estimated interval that contains the unknown value of the population mean with a minimal MSE. The suggested NRTEE’s efficiency is further addressed by utilizing real-life IND of temperature and simulations. A comparison is also performed to establish the superiority of the proposed estimator over the traditional estimators. The limits are calculated and discussed in cases when our suggested estimator is always efficient. The suggested estimator is the most efficient of all estimators and outperformed all others on both IND and classical data.

Optimizing Nonlinear Distortion and Interference in MC-CDMA Receivers Employing Deep Neural Networks

Systems that employ multicarrier code division multiple access, commonly known as MC-CDMA, produce outstanding results in terms of both the performance of the system as a whole and the efficiency with which it uses the spectrum. However, multiple access strategies are susceptible to interference despite their high spectrum efficiency. This work aims to reduce multiple access interference (MAI) by developing an MC-CDMA receiver. When MC-CDMA deteriorates nonlinearly, standard receivers, namely, zero forcing (ZF), maximal ratio combining (MRC), minimum mean square error (MMSE), and equal gain combining (EGC), are unable to cancel MAI. Neural network (NN) receivers are a better option due to their nonlinear nature. Based on the simulation results, the suggested deep neural network- (DNN-)based schemes outperform the current baselines in terms of error handling and usability. This research explores the viability and effectiveness of a DNN-based receiver designed for MC-CDMA with nonlinearity degradations. The focus of this research is on MC-CDMA.

Instant decompression‐induced swell drying of banana: Machine learning and swarm intelligence embedded modeling and process optimization

AbstractA novel approach of instant decompression‐induced swell drying also known as instant controlled pressure drop‐hot air dried (ICPD‐HAD) process was applied for the process performance and quality enhancement of dried banana slices. Using a hybrid approach of particle swarm embedded methodology, the process parameters treatment pressure (TP), treatment time (TT), and duration of decompressed State (DDS) were optimized for various responses including drying time (DT), browning index (BI), rehydration ratio (RR), and total antioxidant activity (TAA). The optimized process conditions were found to be 0.1 MPa of TP, 25 s of TT, and 12 s of DDS for a minimum DT of 225 min and, maximum BI, RR, and TAA, of 6.20%, 3.40%, and 98.78% respectively. The results also demonstrated that the dried banana samples produced by the ICPD‐HAD method exhibited superior quality in terms of minimal DT and BI and maximum TAA and RR compared to those produced by the vacuum and hot air drying techniques. Microstructural investigation demonstrating the superiority of ICPD‐induced samples provided additional evidence for the minimum DT requirement. Furthermore, the use of an artificial neural network was employed to investigate the drying kinetics of the novel instant decompression‐induced swell drying process. With R2 greater than 0.99 and a minimum mean square error (MSE) of 0.000131, the 2‐4‐1 artificial neural network (ANN) architecture performed admirably as a means of optimal simulation and robust control of the drying process.Practical applicationsInstant decompression‐induced swell drying also known as ICPD‐HAD process is a novel approach for the drying of banana sample with enhanced process performance and quality attires. It is common for banana drying to cause loss of total antioxidant activity and other important functional properties like color and texture. This issue can be solved and process performance can be enhanced with less energy use by employing an innovative swell drying technique triggered by instant decompression. Therefore, the dried banana samples made using this cutting‐edge technique will be advantageous from a health point of view. This method can be used by the food manufacturing sector to produce dried bananas of a higher quality and greater consumer acceptance.

Spatially correlated channel estimation for RIS‐assisted MIMO systems with correlated gaussian perturbation

AbstractThis paper studies the problem of spatially correlated channel estimation for reconfigurable intelligent surface (RIS)‐assisted multiple‐input multiple‐output (MIMO) systems with arbitrarily correlated Gaussian perturbation. In particular, composite RIS channel estimation is first explored based on minimum mean square error (MMSE) method, and optimal training sequence design of pilots with MSE minimization. Applying the Kronecker‐structured model, correlated composite RIS‐related channels and correlated Gaussian perturbation are then characterized. The optimal training sequence structure and spatial training power allocation conditions are derived, and the choice of the optimal training sequence length is also analyzed. Finally, numerical results are provided to assess the performance of the proposed estimate method under different training sequence structures, the optimal length of the training sequence, and information statistics. Extensive numerical results show that the proposed estimate method has supreme performance compared to state of‐the‐art baseline methods (e.g. maximum likelihood and two‐sided linear channel estimation methods).

Shrinkage estimation for square of location parameter of the exponential distribution with known coefficient of variation

Shrinkage estimation has become a basic tool in the computational analysis of high-dimensional data. Historically and conceptually a key development toward this was the discovery of the inadmissibility of the usual estimator of a multivariate normal mean. This study explores the problem of estimating the square of location parameter of an exponential distribution when the coefficient of variation is known without error. Several estimators have been proposed with their properties. The best unbiased estimator as well least minimum mean square error (MMSE) estimator has been identified among several estimators. Numerical illustrations are given in the support of the present study.

Bi‐directional LSTM based channel estimation in 5G massive MIMO OFDM systems over TDL‐C model with Rayleigh fading distribution

SummaryIn this work, a deep learning (DL)‐based massive multiple‐input multiple‐output (mMIMO) orthogonal frequency division multiplexing (OFDM) system is investigated over the tapped delay line type C (TDL‐C) model with a Rayleigh fading distribution at frequencies ranging from 0.5 to 100 GHz. The proposed bi‐directional long short‐term memory (Bi‐LSTM) channel state information (CSI) estimator uses online learning during training and offline learning during the practical implementation phase. The design of the estimator takes into account situations in which prior knowledge of channel statistics is limited and targets excellent performance, even with limited pilot symbols (PS). Three separate loss functions (mean square logarithmic error [MSLE], Huber, and Kullback–Leibler Distance [KLD]) are assessed in three classification layers. The symbol error rate (SER) and outage probability performance of the proposed estimator are evaluated using a number of optimization techniques, such as stochastic gradient descent (SGD), momentum, and the adaptive gradient (AdaGrad) algorithm. The Bi‐LSTM‐based CSI estimator is trained considering a specific number of PS. It can be readily seen that by incorporating a cyclic prefix (CP), the system becomes more resilient to channel impairments, resulting in a lower SER. Simulations show that the SGD optimization approach and Huber loss function‐trained Bi‐LSTM‐based CSI estimator have the lowest SER and very high estimation accuracy. By using deep neural networks (DNNs), the Bi‐LSTM method for CSI estimation achieves a superior channel capacity (in bps/Hz) at 10 dB than long short‐term memory (LSTM) and other conventional CSI estimators, such as minimum mean square error (MMSE) and least squares (LS). The simulation results validate the analytical results in the study.

Deep Learning Peephole LSTM Neural Network-Based Channel State Estimators for OFDM 5G and Beyond Networks

This study uses deep learning (DL) techniques for pilot-based channel estimation in orthogonal frequency division multiplexing (OFDM). Conventional channel estimators in pilot-symbol-aided OFDM systems suffer from performance degradation, especially in low signal-to-noise ratio (SNR) regions, due to noise amplification in the estimation process, intercarrier interference, a lack of primary channel data, and poor performance with few pilots, although they exhibit lower complexity and require implicit knowledge of the channel statistics. A new method for estimating channels using DL with peephole long short-term memory (peephole LSTM) is proposed. The proposed peephole LSTM-based channel state estimator is deployed online after offline training with generated datasets to track channel parameters, which enables robust recovery of transmitted data. A comparison is made between the proposed estimator and conventional LSTM and GRU-based channel state estimators using three different DL optimization techniques. Due to the outstanding learning and generalization properties of the DL-based peephole LSTM model, the suggested estimator significantly outperforms the conventional least square (LS) and minimum mean square error (MMSE) estimators, especially with a few pilots. The suggested estimator can be used without prior information on channel statistics. For this reason, it seems promising that the proposed estimator can be used to estimate the channel states of an OFDM communication system.

Collaborative Management of Resource Allocation and Precoding for Dual-Mode Networks

A sub-6GHz (μWave) and millimeter wave (mmWave) dual-mode network can deliver high data rates while maintaining dependable coverage. This paper proposes a novel resource allocation and precoding algorithm based on collaborative sensing in the dual-mode network. We formulated the collaborative optimization problem of resource allocation and precoding, which maximizes the sum of data rates while meeting minimum acceptable rate requirements and ensuring proportional fairness. Considering the spatial similarity between mmWave channel and μWave channel, the prior information of mmWave channel predicted by μWave band is generated to process sensing weight (i.e., subchannel allocation weight of Markov algorithm), which realizes fast dual-mode network resource allocation. Furthermore, a low complexity two-stage precoding scheme for dual-mode networks is proposed based on μWave spatial information. Low-complexity analog precoding is realized in the first stage based on μWave spatial information. In the second stage, inspired by the correlation between minimum mean square error (MMSE) and mutual information, this paper proposes an alternating optimization algorithm to find a local weighted sum-rate (WSR) optimum with low complexity. Compared with other heuristic algorithms, simulation results demonstrate the apparent advantages of the proposed collaborative sensing optimization algorithm. Most importantly, it can be seen that we can achieve a performance that approaches an upper bound.