Low Complexity Minimum Mean Square Error Channel Estimation for Adaptive Coding and Modulation Systems

Performance of the Adaptive Coding and Modulation(ACM) strongly depends on the retrieved Channel State Information(CSI),which can be obtained using the channel estimation techniques relying on pilot symbol transmission.Earlier analysis of methods of pilot-aided channel estimation for ACM systems were relatively little.In this paper,we investigate the performance of CSI prediction using the Minimum Mean Square Error(MMSE)channel estimator for an ACM system.To solve the two problems of MMSE:high computational operations and oversimplified assumption,we then propose the Low-Complexity schemes(LC-MMSE and Recursion LC-MMSE(R-LC-MMSE)).Computational complexity and Mean Square Error(MSE) are presented to evaluate the efficiency of the proposed algorithm.Both analysis and numerical results show that LC-MMSE performs close to the wellknown MMSE estimator with much lower complexity and R-LC-MMSE improves the application of MMSE estimation to specific circumstances.

Efficient Mean Estimation in Log-normal Linear Models with First-order Correlated Errors

In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error （MM） and the asymptotic bias （MB）, respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.

LMMSE-based SAGE channel estimation and data detection joint algorithm for MIMO-OFDM system

A new channel estimation and data detection joint algorithm is proposed for multi-input multi-output （MIMO） - orthogonal frequency division multiplexing （OFDM） system using linear minimum mean square error （LMMSE）- based space-alternating generalized expectation-maximization （SAGE） algorithm. In the proposed algorithm, every sub-frame of the MIMO-OFDM system is divided into some OFDM sub-blocks and the LMMSE-based SAGE algorithm in each sub-block is used. At the head of each sub-flame, we insert training symbols which are used in the initial estimation at the beginning. Channel estimation of the previous sub-block is applied to the initial estimation in the current sub-block by the maximum-likelihood （ML） detection to update channel estimatjon and data detection by iteration until converge. Then all the sub-blocks can be finished in turn. Simulation results show that the proposed algorithm can improve the bit error rate （BER） performance.

Image enhancement via MMSE estimation of Gaussian scale mixture with Maxwell density in AWGN

In optical techniques,noise signal is a classical problem in medical image processing.Recently,there has been considerable interest in using the wavelet transform with Bayesian estimation as a powerful tool for recovering image from noisy data.In wavelet domain,if Bayesian estimator is used for denoising problem,the solution requires a prior knowledge about the distribution of wavelet coeffcients.Indeed,wavelet coeffcients might be better modeled by super Gaussian density.The super Gaussian density can be generated by Gaussian scale mixture(GSM).So,we present new minimum mean square error(MMSE)estimator for spherically-contoured GSM with Maxwell distribution in additive white Gaussian noise(AWGN).We compare our proposed method to current state-of-the-art method applied on standard test image and we quantify achieved performance improvement.

THE INEFFICIENCY OF THE LEAST SQUARES ESTIMATOR AND ITS BOUND

It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.

Selection of the Linear Regression Model According to the Parameter Estimation

In this paper, based on the theory of parameter estimation, we give a selection method and, in a sense of a good character of the parameter estimation, we think that it is very reasonable. Moreover, we offer a calculation method of selection statistic and an applied example.

THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.

Adaptive Linear Filtering Design with Minimum Symbol Error Probability Criterion

Adaptive digital filtering has traditionally been developed based on the minimum mean square error （MMSE） criterion and has found ever-increasing applications in communications. This paper presents an alternative adaptive filtering design based on the minimum symbol error rate （MSER） criterion for communication applications. It is shown that the MSER filtering is smarter, as it exploits the non-Gaussian distribution of filter output effectively. Consequently, it provides significant performance gain in terms of smaller symbol error over the MMSE approach. Adopting Parzen window or kernel density estimation for a probability density function, a block-data gradient adaptive MSER algorithm is derived. A stochastic gradient adaptive MSER algorithm, referred to as the least symbol error rate, is further developed for sample-by-sample adaptive implementation of the MSER filtering. Two applications, involving single-user channel equalization and beamforming assisted receiver, are included to demonstrate the effectiveness and generality of the proposed adaptive MSER filtering approach.

Estimation of the Stress-Strength Reliability for Exponentiated Pareto Distribution Using Median and Ranked Set Sampling Methods

In reliability analysis,the stress-strength model is often used to describe the life of a component which has a random strength(X)and is subjected to a random stress(Y).In this paper,we considered the problem of estimating the reliability𝑅𝑅=P[Y<X]when the distributions of both stress and strength are independent and follow exponentiated Pareto distribution.The maximum likelihood estimator of the stress strength reliability is calculated under simple random sample,ranked set sampling and median ranked set sampling methods.Four different reliability estimators under median ranked set sampling are derived.Two estimators are obtained when both strength and stress have an odd or an even set size.The two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice versa.The performances of the suggested estimators are compared with their competitors under simple random sample via a simulation study.The simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random sample.In general,the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample methods.Keywords:Stress-Strength model,ranked set sampling,median ranked set sampling,maximum likelihood estimation,mean square error.corresponding estimates under ranked set sampling and simple random sample methods.

Mobile channel estimation for MU-MIMO systems using KL expansion based extrapolation

In multi-user multiple input multiple output （MU-MIMO） systems, the outdated channel state information at the transmit- ter caused by channel time variation has been shown to greatly reduce the achievable ergodic sum capacity. A simple yet effec- tive solution to this problem is presented by designing a channel extrapolator relying on Karhunen-Loeve （KL） expansion of time- varying channels. In this scheme, channel estimation is done at the base station （BS） rather than at the user terminal （UT）, which thereby dispenses the channel parameters feedback from the UT to the BS. Moreover, the inherent channel correlation and the parsimonious parameterization properties of the KL expan- sion are respectively exploited to reduce the channel mismatch error and the computational complexity. Simulations show that the presented scheme outperforms conventional schemes in terms of both channel estimation mean square error （MSE） and ergodic capacity.

Convolutional Neural Network Auto Encoder Channel Estimation Algorithm in MIMO-OFDM System

Higher transmission rate is one of the technological features of promi-nently used wireless communication namely Multiple Input Multiple Output-Orthogonal Frequency Division Multiplexing(MIMO–OFDM).One among an effective solution for channel estimation in wireless communication system,spe-cifically in different environments is Deep Learning(DL)method.This research greatly utilizes channel estimator on the basis of Convolutional Neural Network Auto Encoder(CNNAE)classifier for MIMO-OFDM systems.A CNNAE classi-fier is one among Deep Learning(DL)algorithm,in which video signal is fed as input by allotting significant learnable weights and biases in various aspects/objects for video signal and capable of differentiating from one another.Improved performances are achieved by using CNNAE based channel estimation,in which extension is done for channel selection as well as achieve enhanced performances numerically,when compared with conventional estimators in quite a lot of scenar-ios.Considering reduction in number of parameters involved and re-usability of weights,CNNAE based channel estimation is quite suitable and properlyfits to the video signal.CNNAE classifier weights updation are done with minimized Sig-nal to Noise Ratio(SNR),Bit Error Rate(BER)and Mean Square Error(MSE).

On the Estimation of a Univariate Gaussian Distribution: A Comparative Approach

Estimation of the unknown mean, μ and variance, σ2 of a univariate Gaussian distribution given a single study variable x is considered. We propose an approach that does not require initialization of the sufficient unknown distribution parameters. The approach is motivated by linearizing the Gaussian distribution through differential techniques, and estimating, μ and σ2 as regression coefficients using the ordinary least squares method. Two simulated datasets on hereditary traits and morphometric analysis of housefly strains are used to evaluate the proposed method (PM), the maximum likelihood estimation (MLE), and the method of moments (MM). The methods are evaluated by re-estimating the required Gaussian parameters on both large and small samples. The root mean squared error (RMSE), mean error (ME), and the standard deviation (SD) are used to assess the accuracy of the PM and MLE;confidence intervals (CIs) are also constructed for the ME estimate. The PM compares well with both the MLE and MM approaches as they all produce estimates whose errors have good asymptotic properties, also small CIs are observed for the ME using the PM and MLE. The PM can be used symbiotically with the MLE to provide initial approximations at the expectation maximization step.

ADJUSTMENT OF LEVELING NETWORK BY INFORMATION SPREAD ESTIMATION

In practical parameter estimation,we have always chosen either Least Squares Estimation(LSE) or Robust Estimation.Since the distribution of observations is unknown,to select a correct estimation method is very difficult.It is well known that if observations include gross errors,the result of LSE will be badly containinated.On the other hand,if observations do not include any gross errors,the result of robust estimation is not as good as that of LSE.To solve this problem,Wang (1999) developed an estimation method called Information Spread Estimation (ISE) based on the information spread principle.The ISE is a very good method for estimating one parameter which is very robust.However, most of instances in surveying data processing are multi_parameters’ estimation,owing to the inherent restrictions of ISE,it can not be applied to the surveying data processing directly.To apply the good method to the field of surveying data processing widely,the author has done the research deeply.This paper applies ISE successfully to the adjustment of leveling network by using the specialties of leveling.

基于SDW-MMSE的广义特征值稳健波束形成方法

最大输出信噪比(Signal-to-noise ratio,SNR)准则下,广义特征值(Generalized eigenvalue,GEV)波束形成存在复系数难以控制的问题,在复杂的声学环境中容易导致输出信号严重失真。针对复系数估计问题,本文提出一种基于最小均方误差(Minimum mean square error,MMSE)的复系数估计方法,并通过引入语音失真权重因子(Speech distortion weight,SDW),调节降噪效果和语音失真之间的权重关系,进而提出了基于SDW-MMSE的广义特征值稳健波束形成方法。通过最大似然法估计目标信号和噪音信号的功率谱,进而求解主广义特征向量。进一步基于SDW-MMSE估计复系数,将复系数与主广义特征向量相结合,从而得到基于SDW-MMSE的广义特征值稳健波束形成滤波向量。仿真实验结果表明,本文提出的波束形成方法可有效消除相干噪声和非相干噪声,具有输出信噪比高、语音失真少等稳健性能。

Optimal sensor placement for structural response estimation

A methodology, termed estimation error minimization(EEM) method, was proposed to determine the optimal number and locations of sensors so as to better estimate the vibration response of the entire structure. Utilizing the limited sensor measurements, the entire structure response can be estimated based on the system equivalent reduction-expansion process(SEREP) method. In order to compare the capability of capturing the structural vibration response with other optimal sensor placement(OSP) methods, the effective independence(EI) method, modal kinetic energy(MKE) method and modal assurance criterion(MAC) method, were also investigated. A statistical criterion, root mean square error(RMSE), was employed to assess the magnitude of the estimation error between the real response and the estimated response. For investigating the effectiveness and accuracy of the above OSP methods, a 31-bar truss structure is introduced as a simulation example. The analysis results show that both the maximum and mean of the RMSE value obtained from the EEM method are smaller than those from other OSP methods, which indicates that the optimal sensor configuration obtained from the EEM method can provide a more accurate estimation of the entire structure response compared with the EI, MKE and MAC methods.

Generalized Class of Mean Estimators with Known Measures for Outliers Treatment

In estimation theory,the researchers have put their efforts to develop some estimators of population mean which may give more precise results when adopting ordinary least squares(OLS)method or robust regression techniques for estimating regression coefficients.But when the correlation is negative and the outliers are presented,the results can be distorted and the OLS-type estimators may give misleading estimates or highly biased estimates.Hence,this paper mainly focuses on such issues through the use of non-conventional measures of dispersion and a robust estimation method.Precisely,we have proposed generalized estimators by using the ancillary information of non-conventional measures of dispersion(Gini’s mean difference,Downton’s method and probabilityweighted moment)using ordinary least squares and then finally adopting the Huber M-estimation technique on the suggested estimators.The proposed estimators are investigated in the presence of outliers in both situations of negative and positive correlation between study and auxiliary variables.Theoretical comparisons and real data application are provided to show the strength of the proposed generalized estimators.It is found that the proposed generalized Huber-M-type estimators are more efficient than the suggested generalized estimators under the OLS estimation method considered in this study.The new proposed estimators will be useful in the future for data analysis and making decisions.

Estimation of Hazard Function for Censoring Random Variable by Using Wavelet Decomposition and Evaluation of MISE, AMSE with Simulation

Wavelet analysis is one of the mostly new methods of pure and applied mathematics science. In this paper, we use the wavelet method to estimate the hazard function for censoring random variable. We consider the convergence ratio of given estimator. Also we present the simulation in order to test purpose estimator by calculating the mean integrated squared error (MISE) and average mean squared error (AMSE).

Estimation of Population Ratio in Post-Stratified Sampling Using Variable Transformation

Extending the work carried out by [1], this paper proposes six combined-type estimators of population ratio of two variables in post-stratified sampling scheme, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations,(on–1), both for achieved sample configurations (conditional argument) and over repeated samples of fixed size n (unconditional argument). Efficiency conditions were obtained. Under these conditions the proposed combined-type estimators would perform better than the associated customary combined-type estimator. Furthermore, optimum estimators among the proposed combined-type estimators were obtained both under the conditional and unconditional arguments. An empirical work confirmed the theoretical results.

An Effective Method of SNR Estimation for LDPC-CPM

The technique of SNR estimation is one of the key technologies in adaptive frequency hopping system. The methods of channel quality estimation for non-linear continuous phase modulation (CPM) signals have some limitations. Therefore, the algorithm of channel quality estimation for CPM signals is worthy of further study. Some similar phase characteristics between sampling CPM and MPSK motivate us to propose a channel estimation algorithm with applications to nonlinear CPM using linear modulation signal processing. A comprehensive analysis of LDPC-CPM schemes using proposed algorithm is presented, and simulation results indicate that the proposed method can not only estimate channel quality well but also make the normalized MSE (NMSE) of SNR estimate close to/less than 0.1 dB at SNR of 4 dB using short block codes. It shows that the algorithm in this paper is effective enough to estimate the signal to noise ratio (SNR). Meanwhile, the algorithm in this paper reduces the complexity of computation compared with other traditional algorithms.

Estimation of Population Variance Using the Coefficient of Kurtosis and Median of an Auxiliary Variable under Simple Random Sampling

In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order of Taylor’s series expansion. The efficiency conditions derived theoretically under which the proposed estimator performs better than existing estimators. Empirical studies have been done using real populations to demonstrate the performance of the developed estimator in comparison with the existing estimators. The proposed estimator as illustrated by the empirical studies performs better than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared Error and the highest Percentage Relative Efficiency. The developed estimator therefore is suitable to be applied to situations in which the variable of interest has a positive correlation with the auxiliary variable.