MMSE Estimator Research Articles

Reliable Pilot Search Method for Enhancing BER Performance in Underwater Acoustic OFDM Systems with MMSE Estimator

Reliable Pilot Search Method for Enhancing BER Performance in Underwater Acoustic OFDM Systems with MMSE Estimator

Deep Learning-aided Channel Estimation Combined with Advanced Pilot Assignment Algorithm to Mitigate Pilot Contamination for Cell-Free Networks

Objectives: The performance of Cell-Free Massive Multiple Input Multiple Output (CFMM) is analyzed in this paper for its two bottlenecks i.e., Pilot Contamination (PC) and Channel Estimation Error (CEE). Methods: The CFMM network is strongly affected by PC which is one of the bottlenecks due to which quality of service and accuracy of channel estimation gets impacted. Therefore, we address this problem by presenting advanced pilot assignment algorithm to mitigate PC and deep learning aided channel estimation for reducing CEE for the CFMM systems to maximize spectral efficiency (SE). We derive achievable uplink and downlink SE expressions for the proposed system, and compare with Minimum Mean Square Error and Maximum Ratio combining techniques. As well, the performance is evaluated for different antenna configurations. The advanced pilot assignment algorithm is compared with greedy pilot assignment and random pilot assignment methods. The performance of cellular massive multiple input multiple output (MIMO) is derived for comparison. The performance of CFMM system is evaluated using MATLAB software. Findings: The UL and DL performance of the proposed system in terms of SE is 3.2 times higher than the conventional CFMM with MMSE and MR combining techniques. Average sum spectral efficiency of the proposed system increases with increase in number of access points (APs). Comparison with different antenna configurations reveals that, with 400 APs equipped with single antenna, only UE with good channel condition shows performance enhancement, but when each AP is equipped with 4 antennas, the UE with unfavourable channel condition also give better performance. Advanced pilot assignment scheme proves to be better than greedy and random pilot assignment techniques. For the same cellular set up, the proposed CFMM system achieves higher SE than the cellular massive MIMO. Novelty: Due to the advanced pilot assignment algorithm used in the proposed CFMM system, at a time, only one AP is selected and the selected AP with its full received power serves the desired UE, which suppresses interference resulting in improved SE performance. The serving AP is selected considering the distance between UE and AP, rather than using large scale fading coefficient which is the unique feature of pilot assignment algorithm. The proposed deep learning-aided channel estimation method, minimizes the mean square error (MSE) between the actual channel and the channel estimates obtained from the MMSE estimation resulting in reduction in channel estimation error. Thus, the use of the proposed advanced pilot assignment algorithm and deep learning-aided channel estimation method increase the SE performance of the CFMM system. Keywords: Cell­Free Massive Multiple Input Multiple Output, Pilot Contamination, Channel Estimation Error, Minimum Mean Square Error, Maximum Ratio

Optimized Sigmoid Functions for Speech Presence Probability and Gain Function in Speech Enhancement

Speech presence probability (SPP) and gain functions such as Wiener filter or MMSE estimators require an estimate of the a-priori signal-to-noise ratio (SNR). However, the estimation of the a-priori SNR is computationally involved and sensitive to noise variations. This paper proposes to approximate the SPP and the overall gain function of a speech enhancement system by using sigmoid functions to reduce the need of estimating the a-prior SNR. By applying an approximation via the sigmoid functions it is shown that only the a-posteriori estimate of SNR is needed, resulting in a low complexity system. The sigmoid function is designed with an optimization algorithm to optimize its parameters with respect to speech quality measures. The optimization algorithm is based on the idea that the solution obtained for a given problem should move towards the best solution and avoid the worst solution. The proposed algorithm requires minimal control parameters and does not require any algorithm specific parameters. Simulation results show that the proposed sigmoid functions achieve good results in terms of speech quality measures when compared with existing methods while providing significantly lower complexity for implementation.

Innovative Approach of Spectral Efficiency Optimization over Various Pilot Reuse Factors

The Massive MIMO with TDD is breakthrough technology for spectral efficiency gains. The CSI is essential for spectral efficiency gains and CSI can be obtained by channel estimation methods. The channel estimation methods employ known pilot s sequences to estimate the channel before actual data transmission. However, the channel coherence is time and frequency limited, which reflects the trade-off between the resources available for pilots and those available for data in coherent block for transmission. The pilot sequences reuse in other cells can reduce pilot overhead, called pilot reuse. However potential interference is introduced, by pilot reuse, in the channel estimation phase, called pilot contamination. The aim is to determine optimum pilot reuse factor for better SE using low computational complexity estimation method. The sum averaged SE has been obtained for pilot reuse factor 1, 2, 4, 8 and 16 using MMSE, EW-MMSE and LS channel estimation methods. The obtained results reveals that the difference between values of SEs for f=1 to f=2 to f=4 is very low and performance difference between estimators decreases as pilot reuse factor increases, which allows to use LS estimator to get performance almost equal to MMSE with less computational complexity. Also, the pilot reuse factor f=4 found optimum among all for given constraint.

Research on Language Evolution and Language Diversity Based on Chinese Speech Pitch Deviation Features

Abstract This paper constructs a Chinese speech evaluation system based on the characteristics of the vocal mechanism of Chinese speech and uses the detection framework of statistical speech recognition to realize the automatic detection function of pronunciation bias. Assuming that the amplitude spectra of speech and noise obey the generalized Gamma distribution and Gaussian distribution, respectively, the MMSE estimator of the logarithmic spectrum of the speech signal is derived. The speech presence probability under the generalized Gamma speech model is derived as a correction to the MMSE estimation based on language evolution and diversity features. The correct recognition rate of the proposed algorithm reaches 64%, which indicates that the proposed algorithm can effectively suppress the interference of convolutional noise on the speech signal features and improve the subjective perceptual quality of diverse languages.

Optimal Linear MMSE Estimation Under Correlation Uncertainty in Restricted Bayesian Framework

A restricted Bayes approach is proposed for linear estimation of a scalar random parameter based on a scalar observation under uncertainty regarding the correlation between the parameter and the observation. In particular, the optimal linear estimator that minimizes the average mean-squared error (MSE) is derived under a constraint on the worst-case MSE by considering possible values of the correlation coefficient and its probability distribution. A closed-form expression is derived for the optimal linear estimator in the proposed restricted Bayesian framework by considering a generic statistical characterization of the correlation coefficient. Performance of the proposed estimator is evaluated via numerical examples and its benefits are illustrated in various scenarios. The proposed framework is also extended to the case of vector-valued observation and the properties of the optimal linear estimator are characterized.

Doubly-Iterative Sparsified MMSE Turbo Equalization for OTFS Modulation

Currently, orthogonal time frequency space (OTFS) modulation has drawn much attention to reliable communications in high-mobility scenarios. This paper proposes a doubly-iterative sparsified minimum mean square error (DI-S-MMSE) turbo equalizer, which iteratively exchanges the extrinsic information between a soft-input-soft-input (SISO) MMSE estimator and a SISO decoder. Our proposed equalizer does not suffer from short loops and approaches the performance of the near-optimal symbol-wise maximum a posteriori (MAP) algorithm. To exploit the inherent sparsity of OTFS system, we resort to graph theory to investigate the sparsity pattern of the channel matrix, and propose two sparsification guidelines to reduce the complexity of calculating the matrix inverse at the MMSE estimator. Then, we apply two iterative algorithms to MMSE estimation, i.e., the Generalized Minimal Residual (GMRES) and Factorized Sparse Approximate Inverse (FSPAI) algorithms. The former is used at the initial turbo iteration, whose global convergence is proven in our equalizer, while the latter is used at the subsequent turbo iterations with the help of our proposed guidelines. Simulation results demonstrate that our equalizer can achieve a good bit-error-rate (BER) performance regardless of the fractional Doppler, and only has a linear order of complexity.

Widely-Linear MMSE Estimation of Complex-Valued Graph Signals

In this paper, we consider the problem of recovering random graph signals with complex values. For general Bayesian estimation of complex-valued vectors, it is known that the widely-linear minimum mean-squared-error (WLMMSE) estimator can achieve a lower mean-squared-error (MSE) than that of the linear minimum MSE (LMMSE) estimator for the estimation of improper complex-valued signals. Inspired by the WLMMSE estimator, in this paper we develop the graph signal processing (GSP)-WLMMSE estimator, which minimizes the MSE among estimators that are represented as a two-channel output of a graph filter, i.e. widely-linear GSP estimators. We discuss the properties of the proposed GSP-WLMMSE estimator. In particular, we show that the MSE of the GSP-WLMMSE estimator is always equal to or lower than the MSE of the GSP-LMMSE estimator. The GSP-WLMMSE estimator is based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">diagonal</i> covariance matrices in the graph frequency domain, and thus has reduced complexity compared with the WLMMSE estimator. This property is especially important when using the sample-mean versions of these estimators that are based on a training dataset. We state conditions under which the low-complexity GSP-WLMMSE estimator coincides with the WLMMSE estimator. In simulations, we investigate a synthetic linear estimation problem and the nonlinear problem of state estimation in power systems. For these problems, it is shown that the GSP-WLMMSE estimator outperforms the GSP-LMMSE estimator and achieves similar performance to that of the WLMMSE estimator. Moreover, the sample-mean version of the GSP-WLMMSE estimator outperforms the sample-mean WLMMSE estimator for a limited training dataset and is more robust to topology changes.

Racial differences in positive findings on embedded performance validity tests

Introduction Embedded performance validity tests (PVTs) may show increased positive findings in racially diverse examinees. This study examined positive findings in an older adult sample of African American (AA) and European American (EA) individuals recruited as part of a study on aging and cognition. Method The project involved secondary analysis of deidentified National Alzheimer’s Coordinating Center data (N = 22,688). Exclusion criteria included diagnosis of dementia (n = 5,550), mild cognitive impairment (MCI; n = 5,160), impaired but not MCI (n = 1,126), other race (n = 864), and abnormal Mini Mental State Examination (MMSE < 25; n = 135). The initial sample included 9,853 participants (16.4% AA). Propensity score matching matched AA and EA participants on age, education, sex, and MMSE score. The final sample included 3,024 individuals with 50% of participants identifying as AA. Premorbid ability estimates were calculated based on demographics. Failure rates on five raw score and six age-adjusted scaled score PVTs were examined by race. Results Age, education, sex, MMSE, and premorbid ability estimate were not significantly different by race. Thirteen percent of AA and 3.8% of EA participants failed two or more raw score PVTs (p < .0001). On age-adjusted PVTs, 20.6% of AA and 5.9% of EA participants failed two or more (p < .0001). Conclusions PVT failure rates were significantly higher among AA participants. Findings indicate a need for cautious interpretation of embedded PVTs with underrepresented groups. Adjustments to embedded PVT cutoffs may need to be considered to improve diagnostic accuracy.

Privacy-preserving state estimation with unreliable channels

A co-design problem of privacy-preserving encoding and filtering is concerned in this paper. A remote legal user estimates states of a dynamic system by the received innovation messages. However, the communication channel is neither reliable nor secure. The messages may be missing during the transmission and have a risk of being intercepted by an eavesdropper. Therefore, in this work, an encoding scheme together with an MMSE estimation algorithm are designed for preserving information privacy and meanwhile guaranteeing estimation performance. We introduce a novel encoding approach using a weighted innovation with a public key to achieve privacy security as well as low computational expense. A filtering algorithm is designed under such an encoding mechanism. And the performance of the filter and the encoding method is analyzed. The feasibility of the encoding approach and the filtering algorithm is illustrated through numerical examples of an unstable system and a stable ballistic roll rate estimation system.

Deep Learning for Joint Pilot Design and Channel Estimation in MIMO-OFDM Systems.

In MIMO-OFDM systems, pilot design and estimation algorithm jointly determine the reliability and effectiveness of pilot-based channel estimation methods. In order to improve the channel estimation accuracy with less pilot overhead, a deep learning scheme for joint pilot design and channel estimation is proposed. This new hybrid network structure is named CAGAN, which is composed of a concrete autoencoder (concrete AE) and a conditional generative adversarial network (cGAN). We first use concrete AE to find and select the most informative position in the time-frequency grid to achieve pilot optimization design and then input the optimized pilots to cGAN to complete channel estimation. Simulation experiments show that the CAGAN scheme outperforms the traditional LS and MMSE estimation methods with fewer pilots, and has good robustness to environmental noise.

Towards Event-Based State Estimation for Neuromorphic Event Cameras

In this work, a dynamic information extraction problem for neuromorphic event cameras is investigated from a state estimation perspective. The ego-motion pose estimation task of an event camera is formulated as a state estimation problem for a finite-state hidden Markov model subject to a special event-triggering mechanism. We model the threshold mismatch and the bandwidth limit of the event camera output generalization process as a stochastic event-triggering condition equipped with a state-dependent packet dropout process. For this problem, the recursive expression of the system state conditioned on the event-triggered measurement information is constructed under a suitably designed reference probability measure, based on which the event-based MMSE estimate for the considered estimation problem is further obtained. The effectiveness of proposed results is illustrated by numerical analysis and comparative evaluation of an ego-motion pose estimation example.

Spatial channel correlation for local scattering with linear MMSE‐based estimator and detector in multi‐cell large scale MU‐MIMO networks

AbstractScalable Multi‐antenna systems are designed to gain improvement in energy and spectral efficiency under different propagation conditions by equipping the BSs with hundreds or even more antennas. A better understanding of such systems leads to overcome the essential challenges, which is important for the beneficial deployment in future networks. In wireless communication systems, channel models describe the main characteristics of the propagation environment and are essential for systems performance evaluation. This article considers a multi‐cell large scale multiuser MIMO (LS‐MU‐MIMO) system with a physical correlated channel model and linear‐based MMSE estimator and detector. A physical local scattering geometric‐based stochastic channel model for dense urban and suburban scenarios is presented in this article to illustrate the impact of propagation environment on signal transmission in a general framework of antenna spatial correlation. Also, a pilot signaling‐based channel estimation in the uplink scenario, the effect of pilot contamination (PC), and spatial correlation on the channel estimation are studied. The effect of PC and channel estimation on the performance of LS‐MU‐MIMO system is investigated by applying MMSE‐based channel estimator and detector over uniform linear arrays (ULA) of BS antennas in different scattering environments. Moreover, different pilot reuse patterns are considered, and their impact on the average sum SE has been investigated. The simulation results show that LS‐MU‐MIMO system can provide higher performance for dense urban scenarios where the user terminals (UTs) have limited mobility and higher coherence time than suburban scenarios. Furthermore, while higher spatial correlation will result in improvement in the channel estimation quality, it contributes imperfectly to the channel hardening effect.

Multi-Layer Bilinear Generalized Approximate Message Passing

In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as matrix-factorization problem arising in relay communication among others. Assuming statistically independent matrix entries with known priors, the new algorithm called ML-BiGAMP could approximate the general sum-product loopy belief propagation (LBP) in the high-dimensional limit enjoying a substantial reduction in computational complexity. We demonstrate that, in large system limit, the asymptotic MSE performance of ML-BiGAMP could be fully characterized via a set of simple one-dimensional equations termed state evolution (SE). We establish that the asymptotic MSE predicted by ML-BiGAMP' SE matches perfectly the exact MMSE predicted by the replica method, which is well-known to be Bayes-optimal but infeasible in practice. This consistency indicates that the ML-BiGAMP may still retain the same Bayes-optimal performance as the MMSE estimator in high-dimensional applications, although ML-BiGAMP's computational burden is far lower. As an illustrative example of the general ML-BiGAMP, we provide a detector design that could estimate the channel fading and the data symbols jointly with high precision for the two-hop amplify-and-forward relay communication systems.

Performance Analysis of Compressive Sensing based LS and MMSE Channel Estimation Algorithm

In this paper, the optimality of Compressive Sensing based Least Square (LS-CS) and Compressive Sensing based Minimum Mean Square (MMSE-CS) channel estimation algorithms in Multi Input Multi Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) system is investigated for a sparse communication channel. The performance of LS, MMSE, LS-CS and MMSE-CS channel estimation algorithms in terms of sparsity of the channel, compressive sensing and mathematical complexity is investigated and analyzed so that optimum ranges can be recommended.

Deep Learning for MMSE Estimation of a Gaussian Source in the Presence of Bursty Impulsive Noise

We develop a deep learning (DL) based Gaussian source estimation technique when the source is impaired by bursty impulsive noise. This noise is correlated in time, and hence estimating the source with a low-complexity algorithm is a challenging task. To address this challenge, we train a long short term memory (LSTM) based deep neural network (DNN) model offline with different bursty noisy observations and deploy the trained model in real-time. The trained model detects the noise state online and thus applies a linear minimum mean square error (LMMSE) method to estimate the source signal. To demonstrate the effectiveness of the proposed scheme, we compare its performance with baseline schemes. Simulation results reveal the effectiveness of the proposed estimation technique in terms of mean square error and computational complexity.

Uplink Performance of Cell-Free Massive MIMO Over Spatially Correlated Rician Fading Channels

We consider a practical cell-free massive multiple-input-multiple-output (MIMO) system with multi-antenna access points (APs) and spatially correlated Rician fading channels. The significant phase-shift of the line-of-sight component induced by the user equipment movement is modeled randomly. Furthermore, we investigate the uplink spectral efficiency (SE) with maximum ratio (MR)/local minimum mean squared error (L-MMSE) combining and optimal large-scale fading decoding based on the phase-aware MMSE, phase-aware element-wise MMSE and linear MMSE (LMMSE) estimators. Then new closed-form SE expressions with MR combining are derived. Numerical results validate our derived expressions and show that the SE benefits from the spatial correlation. It is important to observe that the performance gap between L-MMSE and MR combining increases with the number of antennas per AP and the SE of the LMMSE estimator is lower than that of other estimators due to the lack of phase-shifts knowledge.

Randomized Approximate Channel Estimator in Massive-MIMO Communication

Massive MIMO is considered as one key enabling technology in 5G communications. Although the high-quality channel state information (CSI) estimation is essential to improve the energy/spectrum efficiency of massive MIMO systems, the optimal MMSE estimator unfortunately creates one major challenge, due to its formidable computation complexity. In this letter, we propose a rank-restrained low-complexity MMSE channel estimator for massive MIMO communications, leveraging a novel concept of randomized low-rank approximation. To accomplish this, we first design a two-stage pilot training scheme. Rather than directly estimating the large channel matrix as usual, we then acquire two low-dimensional subsets of it, which respectively gives the row and column sampling version of unknown channel matrix. Finally, we reconstruct the complete channel matrix via such two estimated low-dimensional sketches, by exploiting the low-rank structure of channel. As demonstrated, our scheme significantly reduces the time complexity as well as the energy consumption in CSI acquisition, which yet attains the near-optimal estimation accuracy. It thus provides great promises to the practical deployment of massive MIMO communications.

Speech enhancement using modified wiener filter based MMSE and speech presence probability estimation

In the present-day communications speech signals get contaminated due to various sorts of noises that degrade the speech quality and adversely impacts speech recognition performance. To overcome these issues, a novel approach for speech enhancement using Modified Wiener filtering is developed and power spectrum computation is applied for degraded signal to obtain the noise characteristics from a noisy spectrum. In next phase, MMSE technique is applied where Gaussian distribution of each signal i.e. original and noisy signal is analyzed. The Gaussian distribution provides spectrum estimation and spectral coefficient parameters which can be used for probabilistic model formulation. Moreover, a-priori-SNR computation is also incorporated for coefficient updation and noise presence estimation which operates similar to the conventional VAD. However, conventional VAD scheme is based on the hard threshold which is not capable to derive satisfactory performance and a soft-decision based threshold is developed for improving the performance of speech enhancement. An extensive simulation study is carried out using MATLAB simulation tool on NOIZEUS speech database and a comparative study is presented where proposed approach is proved better in comparison with existing technique.

Accurate colorimetric images using LEDs

It is well known that more than three or four spectral measurements are required for accurate measurement of color under arbitrary illumination. Previous work has shown 6 to 10 measurements can yield accurate results on average, but with significant numbers of errors above the threshold of obvious visual detection. We demonstrate an imaging system (LED box) consisting of a monochrome camera, multiple LED illumination in a diffuse reflecting chamber that produces excellent color capture in perceptual quality measured in ΔE00. We evaluate this system with respect to practical applications with emphasis on textile quality assessment. Our system of 12 LEDs produces average and maximum training ΔE00 errors around 0.7 and 2.4, respectively; and average and maximum testing ΔE00 errors around 1.5 and 5.0, respectively. This performance exceeds that of reported colorimetric camera systems, except highly specialized configurations. We find that the stability of the system to LED variability under operating conditions is good. We show that pseudoinverse estimate produces better results than the MMSE estimate under actual operating conditions.