Minimum Mean Square Error Research Articles

Unsupervised Fault Detection of Pharmaceutical Processes Using Long Short-Term Memory Autoencoders

Unsupervised multilayer long short-term memory autoencoder (LSTM-AE) models are proposed for monitoring nonlinear batch processes. The methodology is demonstrated for a simulation-based study of an industrial-scale penicillin process and for an industrial vaccine manufacturing process, using production data. The LSTM-AE model was trained with two different loss functions: minimizing mean square error (MSE) between the input and reconstructed data and maximizing the average fault detection rate (FDR¯) in the training data set. Two algorithms are also proposed for obtaining contribution plots for the diagnosis of faults. For the industrial case study, where the faults are not known a priori, the contribution plots are found to be a valuable tool for identifying possible sources of faults. Furthermore, a semisupervised procedure has been proposed to select the normal process region for training the model. Two metrics are also presented to evaluate the performance of the proposed methodology: one for the simulator case study in which fault knowledge is available and one for the industrial case study in which fault knowledge is not available a priori. The proposed unsupervised algorithms exhibit a clear improvement in accuracy over linear methods or nonlinear techniques that do not explicitly account for dynamic behavior.

Super-resolution Direction of Arrival Estimation Using a Minimum Mean-Square Error Framework

This paper develops a novel sparse direction-of-arrival (DOA) estimation technique that avoids the common requirement of hyperparameters, which are typically difficult to set suitably in practice. Using the presented minimum mean-square error (MMSE) estimation framework, we propose a computationally efficient super-resolution DOA estimator that is implemented using an alternate updating of the spatial power distribution of the signals and of the dictionary matrix using a ridge regression algorithm. The regularization parameter determining the sparsity of the solution is formed from the previous spatial power distribution estimates using a SPICE-based criteria. The method employs an adaptive gridding strategy to avoid the grid mismatch problem. The computational complexity is further reduced by the use of an integrated wideband dictionary, determing the active dictionary in an iterative manner. The method offers high resolution estimates of closely spaced sources even for very low sample support (single snapshot) without assuming prior knowledge of the number of sources. Our evaluations illustrate the preferable performance of the proposed estimator as compared to various state-of-the art estimators, also indicating that the method’s performance approaches the Cramér-Rao lower bound (CRB) for the examined problem as the signal-to-noise ratio (SNR) increases.

Design and Experiment of Capacitive Rice Online Moisture Detection Device.

To solve the problems of poor stability and low monitoring precision in the online detection of rice moisture in the drying tower, we designed an online detection device for rice moisture at the outlet of the drying tower. The structure of a tri-plate capacitor was adopted, and the electrostatic field of the tri-plate capacitor was simulated using COMSOL software. A central composite design of three factors and five levels was carried out with the thickness, spacing, and area of the plates as the influencing factors and the capacitance-specific sensitivity as the test index. This device was composed of a dynamic acquisition device and a detection system. The dynamic sampling device was found to achieve dynamic continuous sampling and static intermittent measurements of rice using a ten-shaped leaf plate structure. The hardware circuit of the inspection system with STM32F407ZGT6 as the main control chip was designed to realize stable communication between the master and slave computers. Additionally, an optimized BP neural network prediction model based on the genetic algorithm was established using the MATLAB software. Indoor static and dynamic verification tests were also carried out. The results showed that the optimal plate structure parameter combination includes a plate thickness of 1 mm, plate spacing of 100 mm, and relative area of 18,000.069 mm2 while satisfying the mechanical design and practical application needs of the device. The structure of the BP neural network was 2-90-1, the length of individual code in the genetic algorithm was 361, and the prediction model was trained 765 times to obtain a minimum MSE value of 1.9683 × 10-5, which was lower than that of the unoptimized BP neural network with an MSE of 7.1215 × 10-4. The mean relative error of the device was 1.44% under the static test and 2.103% under the dynamic test, which met the accuracy requirements for the design of the device.

Joint-Transceiver Equalization Technique over a 1.4 km Multi-Mode Fiber Using Optical MIMO Technique in IM/DD Systems

In optical fiber communication, recent advances in multiple-input and multiple-output (MIMO) systems using space-division multiplexing have helped achieve higher spectral efficiency and data rates. Propagating higher-order modulation formats over MIMO systems further strengthens the capacity of the transmission link. In the optical-MIMO system, the dispersion impairments originating from a 1.4 km long multi-mode fiber (MMF) are mitigated using the proposed joint-transceiver equalization technique. A numerical convex optimization algorithm is used to compute and optimize the pre- and post-equalization (PPE) coefficients jointly restricted by cost and power budgets. The potential of the proposed joint-PPE technique is tested on an MMF link, which is severely degraded by dispersion compared to a single-mode fiber channel. From the experimental results, the average optical received power gain necessary to reach 10−4 bit-error rate is improved by nearly 2.5 dB using the joint-PPE compared to the post-equalization only based on the minimum mean-squared error principle. When the efficiency of the conventional zero-forcing (ZF) principle-based PPE and the joint-PPE is compared, the joint-PPE scheme outperforms the ZF-PPE by approximately 1.5 dB. The enhancement in the transmission quality is observed with experimentally measured eye diagrams using the joint-PPE scheme. Under the analyzed scenarios, computer simulation also confirms the hypothesis, which establishes the effectiveness of the proposed joint-transceiver equalization over the conventional ZF-PPE scheme. Moreover, the simulated performance benefits of the joint-PPE are evaluated using the singular value decomposition (SVD) technique. Improvement of ≈3.86 dB in the average optical received power gain required to reach 10−4 bit-error rate is witnessed with the PAM-4 format. Overall, the joint-transceiver equalization technique is proven to be beneficial in optical MIMO systems.

State of charge estimation for Li-ion batteries based on iterative Kalman filter with adaptive maximum correntropy criterion

Nonlinear filter methods are commonly employed for model-driven based battery state of charge (SOC) estimation because of their ability to suppress Gaussian noise. Due to the uncertainty of complicated operational conditions, the minimum mean square error (MMSE) criterion based Kalman filter (KF) methods may not guarantee sufficient SOC estimation accuracy in the presence of non-Gaussian noise. To enhance the anti-interference performance of the KFs based SOC estimation method, a novel methodology that combines the adaptive kernel width based maximum correntropy criterion (AMCC) with the Levenberg-Marguardt (L-M) principle based adaptive iterative extended KF (AIEKF) is proposed. Firstly, the MMSE criterion of the EKF is replaced by the MCC criterion and an adaptive kernel width strategy is designed to weaken the effect of anomalous data. Then, the AMCC-corrected covariance matrix and state are updated using an L-M optimized multi-step iterative filter during the measurement update phase. Finally, the combination of AMCC and AIEKF is devised to execute SOC estimation. Several sets of data from different temperatures and operational conditions are used to verify the validity of the proposed AMCC-AIEKF method. Compared with the adaptive EKF (AEKF) and the adaptive iterative EKF (AIEKF) method, the AMCC-AIEKF method has the advantage in terms of SOC estimation accuracy and robustness under different operational conditions with noiseless, Gaussian noise and non-Gaussian noise.

Joint Activity Detection and Channel Estimation for Intelligent-Reflecting-Surface-Assisted Wireless IoT Networks

Intelligent reflecting surfaces (IRSs) provide the ability to tune the wireless environments by introducing passive scattering elements between the base station (BS) or access points (APs) and users, and it is a promising technology for next generation wireless networks. In this paper, we consider joint activity detection and channel estimation in both centralized and distributed IRS assisted IoT networks. We determine the explicit distribution for the equivalent channel coefficients from the BS or APs to the users. It is shown that this distribution can be equivalently represented with a Gaussian scale mixture (GSM) model. With generalized approximate message passing (GAMP) algorithm, the received pilot signals at the BS or APs are decoupled into scalar Gaussian noise corrupted versions of the effective channel coefficients. Subsequently, minimum mean square error (MMSE) estimate of the effective channel coefficients and threshold detection rules are acquired. Finally, the optimal fusion rule is used to obtain the activity detection results of each user. As an additional low-complexity approach, we approximate the equivalent channel coefficients with a Gaussian approximation (GA) model. We derive the theoretical mean square error for the MMSE estimate of the effective channel coefficients using the GA model and the state evolution equations of the GAMP algorithm, under the assumption that the direct links from the BS to the users can be neglected due to unfavorable propagation conditions. Numerical results show that the Gaussian approximation for the distribution of the equivalent channel coefficients is accurate even for moderate number of elements at the IRS. And the theoretical mean square error for the MMSE estimate of the effective channel coefficients under the assumption that direct link is negligible is shown to overlap with the corresponding numerical simulations.

Iterative algorithms and architectures in massive MIMO detection

Massive multiple-input multiple-output (MIMO) wireless systems play an important role in the 5G networks. The complexity of signal detection in massive MIMO is increasing rapidly due to the growth of the number of transmitting antennas. In this paper, we introduced different iterative algorithms to decrease the computational cost of the approximate minimum mean-square error (MMSE) algorithm, including the Neumann Series algorithm, Jacobi method, Gauss-Seidel method, Successive Over Relaxation method and the Conjugate Gradient method. In addition, the VLSI architecture implementations of algorithms mentioned above are also discussed in the article.

Pilot design and doubly-selective channel estimation for faster-than-Nyquist signaling

Being capable of enhancing the spectral efficiency (SE), faster-than-Nyquist (FTN) signaling is a promising approach for wireless communication systems. This paper investigates the doubly-selective (i.e., time- and frequency-selective) channel estimation and data detection of FTN signaling. We consider the intersymbol interference (ISI) resulting from both the FTN signaling and the frequency-selective channel and adopt an efficient frame structure with reduced overhead. We propose a novel channel estimation technique of FTN signaling based on the least sum of squared errors (LSSE) approach to estimate the complex channel coefficients at the pilot locations within the frame. In particular, we find the optimal pilot sequence that minimizes the mean square error (MSE) of the channel estimation. To address the time-selective nature of the channel, we use a low-complexity linear interpolation to track the complex channel coefficients at the data symbols locations within the frame. To detect the data symbols of FTN signaling, we adopt a turbo equalization technique based on a linear soft-input soft-output (SISO) minimum mean square error (MMSE) equalizer. Simulation results show that the MSE of the proposed FTN signaling channel estimation employing the designed optimal pilot sequence is lower than its counterpart designed for conventional Nyquist transmission. The bit error rate (BER) of the FTN signaling employing the proposed optimal pilot sequence shows improvement compared to the FTN signaling employing the conventional Nyquist pilot sequence. Additionally, for the same SE, the proposed FTN signaling channel estimation employing the designed optimal pilot sequence shows better performance when compared to competing techniques from the literature.

Adaptive LDPC coded high data rate based IR-UWB combined with VMIMO system for vehicular communication links

The automotive industry is developing significantly with the evolution of vehicular networks, intelligent transportation systems, and autonomous cars. These technologies are made achievable by recent advances in software, hardware, and communication systems, along with various applications and standardization efforts. On the other side, many impairments have existed due to these evolving, limiting the process of vehicular networks. So, this paper proposes an implementation of adaptive LDPC-coded, high data rate-based Impulse Radio-Ultra Wide Band (IR-UWB) combined with Virtual Multiple Input Multiple Output (VMIMO) systems for Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) wireless communications. Furthermore, they are merged with orthogonal pulse shaping using a modified Hermite pulse. Besides, the paper compares Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) detection techniques. To enhance and mitigate the existing impairments facing the vehicular networks. The proposed system’s performance is evaluated using both techniques, utilizing Bit Error Rate (BER), processing time, and resultant throughput analysis for both channel models. The simulation results include Non-Line of Sight (NLoS) and Line of Sight (LoS) scenarios for both channel models. Moreover, the simulation considers the effect of path loss and noise on the transmitted signal. In addition, the recent LDPC decoding algorithm termed “Modified Implementation Efficient Reliability Ratio Weighted Bit Flipping” (MIERRWBF) is evaluated through all latter channel models. At last, a novel adaptive LDPC decoder is proposed to further enhance the performance of all vehicular communication links under study. Consequently, the paper proposed an integrated adaptive LDPC-coded high data rate communication system to enhance vehicular communications using VMIMO mixed with modified Hermite orthogonal pulse shaping and deploying the MMSE recommended detection technique.

Doubly selective channel estimation and equalization based on ICI/ISI mitigation for OQAM-FBMC systems

Over a doubly selective channel, broadband transmission systems face challenges in channel estimation and equalization. High mobility causes inter-carrier interference (ICI), while multipath transmission induces inter-symbol interference (ISI). In this paper, we present a mitigation method of ICI/ISI for the offset quadrature amplitude-modulated filter bank multi-carrier (OQAM-FBMC) system. It features low inherent imaginary interference (IMI) sensitivity and high efficiency. Specifically, a pilot indices optimization algorithm and a sparse adaptive orthogonal subspace pursuit (SAOSP) algorithm are presented based on the 2-D channel modeling scheme. The guard pilots are first added to mitigate the effect of ICI. Then the index optimization and SAOSP algorithms are applied to achieve a high-accuracy estimation of sparse channel coefficients. In addition, a threshold judgment suboptimal minimum mean square error (MMSE) equalization method is presented based on the variability of the interference power. The method uses normalized interference power thresholds to estimate the ISI dimension and reduce the equalization data, thus mitigating the effect of ISI and achieving efficient equalization. To verify the above methods, single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) models are built. Simulation results indicate a 3-5 dB improvement in channel estimation accuracy. The suboptimal MMSE equalization results are close to the optimal MMSE with about four orders of magnitude reduction in complexity.

Forecasting Electricity Demand in Turkey Using Optimization and Machine Learning Algorithms

Medium Neural Networks (MNN), Whale Optimization Algorithm (WAO), and Support Vector Machine (SVM) methods are frequently used in the literature for estimating electricity demand. The objective of this study was to make an estimation of the electricity demand for Turkey’s mainland with the use of mixed methods of MNN, WAO, and SVM. Imports, exports, gross domestic product (GDP), and population data are used based on input data from 1980 to 2019 for mainland Turkey, and the electricity demands up to 2040 are forecasted as an output value. The performance of methods was analyzed using statistical error metrics Root Mean Square Error (RMSE), Mean Absolute Error (MAE), R-squared, and Mean Square Error (MSE). The correlation matrix was utilized to demonstrate the relationship between the actual data and calculated values and the relationship between dependent and independent variables. The p-value and confidence interval analysis of statistical methods was performed to determine which method was more effective. It was observed that the minimum RMSE, MSE, and MAE statistical errors are 5.325 × 10−14, 28.35 × 10−28, and 2.5 × 10−14, respectively. The MNN methods showed the strongest correlation between electricity demand forecasting and real data among all the applications tested.

Evaluation of massive multiple-input multiple-output communication performance under a proposed improved minimum mean squared error precoding

<span lang="EN-US">The fundamental of a downlink massive multiple-input multiple-output (MIMO) energy- issue efficiency strategy is known as minimum mean squared error (MMSE) implementation degrades the performance of a downlink massive MIMO energy-efficiency scheme, so some improvements are adding for this precoding scheme to improve its workthat is called our proposal solution as a proposed improved MMSE precoder (PIMP). The energy efficiency (EE) study has also taken into mind drastically lowering radiated power while maintaining high throughput and minimizing interference issues. We further find the tradeoff between spectral efficiency (SE) and EE although they coincide at the beginning but later their interests become conflicting and divergent then leading EE to decrease so gradually while SE continues increasing logarithmically. The results achieved that for a single-cellular massive MU-MIMO downlink model, our PIMP scheme is the appropriate scenario to achieve higher precoding performance system. Furthermore, both maximum ratio transmission (MRT) and PIMP are suitable for performance improvement in massive MIMO results of EE and SE. So, the main contribution comes with this work that highest EE and SE are belong to use a PIMP which performs better appreciably than MRT at bigger ratio of number of antennas to the number of the users. </span>

Relation between penalized least squares regression and Bayesian estimation in AWGN based on novel penalty function of Pareto density

The penalized least squares regression (PLSR) is usually used for solving linear inverse problems in signal processing, such as the denoising (noise reduction) and deconvolution problems. The performance of this method is based on the penalty function (regularization). Therefore, we propose the novel regularization based on the Pareto distribution. Here, famous regularizations, such as the logarithm and ratio regularizations, are included in the mathematical form of this proposed regularization. Moreover, mathematical models of the Bayesian estimator, such as the maximum a posteriori (MAP) and minimum mean square error (MMSE) estimations, in additive white Gaussian noise (AWGN) are similar to the PLSR. Therefore, we propose denoising methods via PLSRs using the proposed regularization which are equivalent to the MAP and MMSE estimations. In numerical results, proposed methods give good denoising results.

Trade-Off Between Positioning and Communication for Millimeter Wave Systems With Ziv-Zakai Bound

In this paper, we investigate the trade-off between positioning and communication for an integrated positioning and communication (IPAC) millimeter wave system. First, in terms of the positioning in the IPAC system, the Cramér-Rao bound (CRB) is commonly used as a performance metric. Unfortunately, the CRB is only tight in a certain region for the high signal-to-noise ratio (SNR). To compensate for this deficiency, we derive the Ziv-Zakai bound (ZZB) for the IPAC system by exploiting the a priori delay information extracted from both the time delay parameter and the channel amplitude attenuation. Further, we derive the expected CRB (ECRB) and the weighted CRB (WCRB) of the system for comparisons. Second, we analyze the trade-off between positioning and communication for this IPAC system based on the derived ZZB. Specifically, we aim to optimize the power allocation to maximize the achievable data rate subject to the ZZB and total transmit power constraints. Numerical results show that the ZZB provides a tighter and more reasonable bound for the minimum mean square error (MMSE) estimator over the wide range of SNRs compared to the ECRB and WCRB. Moreover, the trade-off between positioning and communication is revealed via changing critical parameters by simulations.

Efficient Massive Machine Type Communication (mMTC) via AMP

We propose efficient and low-complexity multiuser detection (MUD) algorithms for Gaussian multiple access channel (G-MAC) for short-packet transmission in massive machine type communications. To do so, we first formulate the G-MAC MUD problem as a sparse signal recovery problem and obtain the exact and approximate joint prior distribution of the sparse vector to be recovered. Then, we employ the Bayesian approximate message passing (AMP) algorithms with the optimal separable and nonseparable minimum mean squared error (MMSE) denoisers for soft decoding of the sparse vector. The effectiveness of the proposed MUD algorithms for a large number of devices is supported by simulation results. For packets of 8 information bits, while the state-of-the-art AMP with soft-threshold denoising achieves 8/100 of the upper bound at Eb/N0 = 4 dB, the proposed algorithms reach 4/7 and 1/2 of the upper bound.

Low-Resolution MMSE Equalization for Massive MU-MIMO Systems

Finite-alphabet equalization that represents a spatial equalization matrix with low-resolution coefficients is a promising technique to reduce the power consumption, processing delay, and circuit area of baseband processing in the context of all-digital massive multiuser multiple-input multiple-output uplink systems. However, to minimize the performance loss caused by a coarse-resolution spatial equalization matrix, its coefficients must be carefully designed in the minimum mean-square error sense to achieve the desired bit error rate (BER) performance, which unfortunately constitutes an NP-hard optimization problem. To tackle this problem, we first reformulate the finite-alphabet equalization design problem as an unconstrained optimization on a smooth Riemannian manifold. Then we propose an algorithm based on Riemannian manifold optimization (RMO) to solve the reformulated problem. Based on simulation results, the proposed 2-bit RMO-assisted equalizer outperforms its state-of-the-art counterparts while maintaining the same asymptotic complexity. In addition, the proposed 2-bit RMOassisted equalizer exhibits a loss of only 1.47 dB at a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> compared to an unquantized linear minimum mean squared error equalizer.

Indexed-channel estimation under frequency and time-selective fading channels in high-mobility systems

&lt;p&gt;&lt;span lang="EN-US"&gt;Index modulation (IM) techniques have been employed in different communication systems to improve bandwidth efficiency by carrying additional information bits. In high-mobility communication systems and under both time-selective and frequency-selective fading channels with Doppler spread, channel variations can be tracked by employing pilot-aided channel estimation with minimum mean-squared error estimation. However, inserting pilot symbols among information symbols reduces the system's spectral efficiency in pilot-aided channel estimation schemes. We propose pilot-aided channel estimation with zero-pilot symbols and an energy detection scheme to tackle this issue. Part of the information bit-stream is conveyed by the indices of zero-pilot symbols leading to an increase in the system's spectral efficiency. We used an energy detector at the receiver to detect the transmitted zero-pilot symbols. This paper examines the impacts of diversity order on the zero-pilot symbol detection error probability and the mean-squared of error estimation. The impacts of pilot symbols number and the zero-pilot symbol number on the mean-squared error of the minimum mean-squared error (MMSE) estimator and the system error performance are also investigated in this paper.&lt;/span&gt;&lt;/p&gt;

Real-Time Monitoring Ornstein–Uhlenbeck Process: Improving Fidelity Under Freshness Guarantees

This work studies improving the data fidelity for real-time monitoring of an Ornstein-Uhlenbeck process in a sensor-monitor status update system under stringent information freshness provision. Violation probability of age of information (VPA), i.e., the long-term proportion the age of information exceeds a given threshold is adopted to strictly assess freshness. Based on the automatic repeat-request transmission protocol, the VPA at the monitor is derived in closed-form. To evaluate the fidelity, the time-average mean squared error (MSE) between the real-time process value and the estimation at the monitor is also obtained, where the coupling between the time-average MSE and the VPA is characterized in detail. By analyzing the monotonicity of the time-average MSE and the VPA, the optimal quantization precision that achieves the minimal time-average MSE under a given VPA constraint is proposed, where an algorithm for quickly addressing the optimum is also given. Numerical results validate the effectiveness of the proposed optimal quantization design.

81 Gb/s Dual-Polarization Discrete Eigenvalue Transmission Based on Nonlinear Fourier Transform

We investigated dual-polarization (DP) discrete eigenvalue transmissions and propose to shift the solitons in one polarization by half a symbol period with respect to the soliton train in the other polarization. Simulation results are conducted to illustrate its advantages over conventional schemes. Experiments of a net 81 Gb/s dual-polarization discrete eigenvalue transmissions over 650 km are also demonstrated with the help of DP multi-symbol linear minimum mean-squared error (DP-MS-LMMSE) filters for eigenvalues and b-coefficients.

Subspace-Based Pilot Decontamination in User-Centric Scalable Cell-Free Wireless Networks

We consider a cell-free wireless system operated in Time Division Duplex (TDD) mode with user-centric clusters of remote radio units (RUs). Since the uplink pilot dimensions per channel coherence slot is limited, co-pilot users might incur mutual pilot contamination. In the current literature, it is assumed that the long-term statistical knowledge of all user channels is available. This enables Minimum Mean-Square Error channel estimation or simplified dominant subspace projection, which achieves significant pilot decontamination under certain assumptions on the channel covariance matrices. However, estimating the channel covariance matrix or even just its dominant subspace at all RUs forming a user cluster is not an easy task. In fact, if not properly designed, a piloting scheme for such long-term statistics estimation will also be subject to the contamination problem. In this paper, we propose a new channel subspace estimation scheme explicitly designed for cell-free wireless networks. Our scheme is based on 1) a sounding reference signal (SRS) using latin squares wideband frequency hopping, and 2) a subspace estimation method based on robust Principal Component Analysis (R-PCA). The SRS hopping scheme ensures that for any user and any RU participating in its cluster, only a few pilot measurements will contain strong co-pilot interference. These few heavily contaminated measurements are (implicitly) eliminated by R-PCA, which is designed to regularize the estimation and discount the “outlier” measurements. Our simulation results show that the proposed scheme achieves almost perfect subspace knowledge, which in turns yields system performance very close to that with ideal channel state information, thus essentially solving the problem of pilot contamination in cell-free user-centric TDD wireless networks.