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 transmissio...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.展开更多
The turbo equalization approach is studied for Orthogonal Frequency Division Multiplexing （OFDM） system with combined error control coding and linear precoding. While previous literatures employed linear precodcr of...The turbo equalization approach is studied for Orthogonal Frequency Division Multiplexing （OFDM） system with combined error control coding and linear precoding. While previous literatures employed linear precodcr of small size for complexity reasons, this paper proposes to use a linear precoder of size larger than or equal to the maximum length of the equivalent discrete-time channel in order to achieve full frequency diversity and reduce complexities of the error control coder/decoder. Also a low complexity Linear Minimum Mean Square Error （LMMSE） turbo equalizer is derived for the receiver. Through simulation and performance analysis, it is shown that the performance of the proposed scheme over frequency selective fading channel reaches the matched filter bound; compared with the same coded OFDM without linear precoding, the proposed scheme shows an Signal-to-Noise Ratio （SNR） improvement of at least 6dB at a bit error rate of 10 6 over a multipath channel with exponential power delay profile. Convergence behavior of the proposed scheme with turbo equalization using various type of linear precoder/transformer, various interleaver size and error control coder of various constraint length is also investigated.展开更多
In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias es...In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.展开更多
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 calcula...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.展开更多
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...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.展开更多
Sequential measurement processing is of benefit to both estimation accuracy and computational efficiency. When the noises are correlated across the measurement components, decorrelation based on covariance matrix fact...Sequential measurement processing is of benefit to both estimation accuracy and computational efficiency. When the noises are correlated across the measurement components, decorrelation based on covariance matrix factorization is required in the previous methods in order to perform sequential updates properly. A new sequential processing method, which carries out the sequential updates directly using the correlated measurement components, is proposed. And a typical sequential processing example is investigated, where the converted position measure- ments are used to estimate target states by standard Kalman filtering equations and the converted Doppler measurements are then incorporated into a minimum mean squared error （MMSE） estimator with the updated cross-covariance involved to account for the correlated errors. Numerical simulations demonstrate the superiority of the proposed new sequential processing in terms of better accuracy and consistency than the conventional sequential filter based on measurement decorrelation.展开更多
Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given qua...Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality （LMI） form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.展开更多
In this paper, compression LS estimate (k) of the regression coefficient B isconsidered when the design matrix present ill-condition in multivariate linear model.The MSE (mean square error)of the estimate(k)=Ve...In this paper, compression LS estimate (k) of the regression coefficient B isconsidered when the design matrix present ill-condition in multivariate linear model.The MSE (mean square error)of the estimate(k)=Vec( (k))is less than theMSE of LS estimate β￣* of the regression coefficient β= Vec(B) by choosing the pa-rameter k. Admissibility , numerical stability and relative efficiency of (k)are proved. The method of determining k value for practical use is also suggested展开更多
In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived ...In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.展开更多
There are four serious problems in the discriminant analysis. We developed an optimal linear discriminant function （optimal LDF） based on the minimum number of misclassification （minimum NM） using integer programm...There are four serious problems in the discriminant analysis. We developed an optimal linear discriminant function （optimal LDF） based on the minimum number of misclassification （minimum NM） using integer programming （IP）. We call this LDF as Revised IP-OLDF. Only this LDF can discriminate the cases on the discriminant hyperplane （Probleml）. This LDF and a hard-margin SVM （H-SVM） can discriminate the lineary separable data （LSD） exactly. Another LDFs may not discriminate the LSD theoretically （Problem2）. When Revised IP-OLDF discriminate the Swiss banknote data with six variables, we find MNM of two-variables model such as （X4, X6） is zero. Because MNMk decreases monotounusly （MNMk 〉= MNM（k＋1））, sixteen MNMs including （X4, X6） are zero. Until now, because there is no research of the LSD, we surveyed another three linear separable data sets such as： 18 exam scores data sets, the Japanese 44 cars data and six microarray datasets. When we discriminate the exam scores with MNM=0, we find the generalized inverse matrix technique causes the serious Problem3 and confirmed this fact by the cars data. At last, we claim the discriminant analysis is not the inferential statistics because there is no standard errors （SEs） of error rates and discriminant coefficients （Problem4）. Therefore, we poroposed the ＂100-fold cross validation for the small sample＂ method （the method）. By this break-through, we can choose the best model having minimum mean of error rate （M2） in the validation sample and obtaine two 95% confidence intervals （CIs） of error rate and discriminant coefficients. When we discriminate the exam scores by this new method, we obtaine the surprising results seven LDFs except for Fisher＇s LDF are almost the same as the trivial LDFs. In this research, we discriminate the Japanese 44 cars data because we can discuss four problems. There are six independent variables to discriminate 29 regular cars and 15 small cars. This data is linear separable by the emission rate （X1） and the number of seats （X3）. We examine the validity of the new model selection procedure of the discriminant analysis. We proposed the model with minimum mean of error rates （M2） in the validation samples is the best model. We had examined this procedure by the exam scores, and we obtain good results. Moreover, the 95% CI of eight LDFs offers us real perception of the discriminant theory. However, the exam scores are different from the ordinal data. Therefore, we apply our theory and procedure to the Japanese 44 cars data and confirmed the same conclution.展开更多
针对正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)系统中最小均方误差(Minimum Mean Squared Error,MMSE)信道估计算法误码率(BER)高的问题,提出一种平均最小均方误差(Averaged-Minimum Mean Squared Error,A-MMSE)...针对正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)系统中最小均方误差(Minimum Mean Squared Error,MMSE)信道估计算法误码率(BER)高的问题,提出一种平均最小均方误差(Averaged-Minimum Mean Squared Error,A-MMSE)信道估计算法。该算法首先基于802.11n标准而构造了一种新的导频结构,收发两端分别进行降采样和过采样处理,利用已知训练序列和导频获得信道频域响应。仿真结果表明,所提出的A-MMSE信道估计算法与传统的MMSE算法相比,在BER为10^(-3)时,信噪比改善了约8dB。因而所提出的信道估计算法能明显改善系统的BER性能。展开更多
基金supported by the 2011 China Aerospace Science and Technology Foundationthe Certain Ministry Foundation under Grant No.20212HK03010
文摘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.
基金Supported by the National High Technology ResearchDevelopment Program of China (863 Program)(No.2001AA 123014)
文摘The turbo equalization approach is studied for Orthogonal Frequency Division Multiplexing （OFDM） system with combined error control coding and linear precoding. While previous literatures employed linear precodcr of small size for complexity reasons, this paper proposes to use a linear precoder of size larger than or equal to the maximum length of the equivalent discrete-time channel in order to achieve full frequency diversity and reduce complexities of the error control coder/decoder. Also a low complexity Linear Minimum Mean Square Error （LMMSE） turbo equalizer is derived for the receiver. Through simulation and performance analysis, it is shown that the performance of the proposed scheme over frequency selective fading channel reaches the matched filter bound; compared with the same coded OFDM without linear precoding, the proposed scheme shows an Signal-to-Noise Ratio （SNR） improvement of at least 6dB at a bit error rate of 10 6 over a multipath channel with exponential power delay profile. Convergence behavior of the proposed scheme with turbo equalization using various type of linear precoder/transformer, various interleaver size and error control coder of various constraint length is also investigated.
文摘In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.
基金Supported by the Natural Science Foundation of Anhui Education Committee
文摘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.
基金the Knowledge Innovation Program of the Chinese Academy of Sciences(KJCX3-SYW-S02)the Youth Foundation of USTC
文摘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.
基金Supported by National Natural Science Foundation of China （61135001, 61075029, 61074179, 61074155） and the Postdoctoral Science Foundation of China （20110491692）
基金supported by the National Natural Science Foundation of China(6120131161132005)the Aerospace Science Foundation of China(20142077010)
文摘Sequential measurement processing is of benefit to both estimation accuracy and computational efficiency. When the noises are correlated across the measurement components, decorrelation based on covariance matrix factorization is required in the previous methods in order to perform sequential updates properly. A new sequential processing method, which carries out the sequential updates directly using the correlated measurement components, is proposed. And a typical sequential processing example is investigated, where the converted position measure- ments are used to estimate target states by standard Kalman filtering equations and the converted Doppler measurements are then incorporated into a minimum mean squared error （MMSE） estimator with the updated cross-covariance involved to account for the correlated errors. Numerical simulations demonstrate the superiority of the proposed new sequential processing in terms of better accuracy and consistency than the conventional sequential filter based on measurement decorrelation.
基金supported by the National Natural Science Foundation of China (60974001)Jiangsu "Six Personnel Peak" Talent-Funded Projects
文摘Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality （LMI） form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.
文摘In this paper, compression LS estimate (k) of the regression coefficient B isconsidered when the design matrix present ill-condition in multivariate linear model.The MSE (mean square error)of the estimate(k)=Vec( (k))is less than theMSE of LS estimate β￣* of the regression coefficient β= Vec(B) by choosing the pa-rameter k. Admissibility , numerical stability and relative efficiency of (k)are proved. The method of determining k value for practical use is also suggested
文摘In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.
文摘There are four serious problems in the discriminant analysis. We developed an optimal linear discriminant function （optimal LDF） based on the minimum number of misclassification （minimum NM） using integer programming （IP）. We call this LDF as Revised IP-OLDF. Only this LDF can discriminate the cases on the discriminant hyperplane （Probleml）. This LDF and a hard-margin SVM （H-SVM） can discriminate the lineary separable data （LSD） exactly. Another LDFs may not discriminate the LSD theoretically （Problem2）. When Revised IP-OLDF discriminate the Swiss banknote data with six variables, we find MNM of two-variables model such as （X4, X6） is zero. Because MNMk decreases monotounusly （MNMk 〉= MNM（k＋1））, sixteen MNMs including （X4, X6） are zero. Until now, because there is no research of the LSD, we surveyed another three linear separable data sets such as： 18 exam scores data sets, the Japanese 44 cars data and six microarray datasets. When we discriminate the exam scores with MNM=0, we find the generalized inverse matrix technique causes the serious Problem3 and confirmed this fact by the cars data. At last, we claim the discriminant analysis is not the inferential statistics because there is no standard errors （SEs） of error rates and discriminant coefficients （Problem4）. Therefore, we poroposed the ＂100-fold cross validation for the small sample＂ method （the method）. By this break-through, we can choose the best model having minimum mean of error rate （M2） in the validation sample and obtaine two 95% confidence intervals （CIs） of error rate and discriminant coefficients. When we discriminate the exam scores by this new method, we obtaine the surprising results seven LDFs except for Fisher＇s LDF are almost the same as the trivial LDFs. In this research, we discriminate the Japanese 44 cars data because we can discuss four problems. There are six independent variables to discriminate 29 regular cars and 15 small cars. This data is linear separable by the emission rate （X1） and the number of seats （X3）. We examine the validity of the new model selection procedure of the discriminant analysis. We proposed the model with minimum mean of error rates （M2） in the validation samples is the best model. We had examined this procedure by the exam scores, and we obtain good results. Moreover, the 95% CI of eight LDFs offers us real perception of the discriminant theory. However, the exam scores are different from the ordinal data. Therefore, we apply our theory and procedure to the Japanese 44 cars data and confirmed the same conclution.
文摘针对正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)系统中最小均方误差(Minimum Mean Squared Error,MMSE)信道估计算法误码率(BER)高的问题,提出一种平均最小均方误差(Averaged-Minimum Mean Squared Error,A-MMSE)信道估计算法。该算法首先基于802.11n标准而构造了一种新的导频结构,收发两端分别进行降采样和过采样处理,利用已知训练序列和导频获得信道频域响应。仿真结果表明,所提出的A-MMSE信道估计算法与传统的MMSE算法相比,在BER为10^(-3)时,信噪比改善了约8dB。因而所提出的信道估计算法能明显改善系统的BER性能。
文摘针对无线传感网络中传统DV-Hop(Distance Vector Hop)定位算法节点分布不均匀导致定位误差较大的问题,提出了非均匀网络中半径可调的ARDV-Hop(Adjustable Radius DV-Hop in Non-uniform Networks)定位算法。该算法通过半径可调的方式对节点间的跳数进行细化,用细化后呈小数级的跳数代替传统的整数级跳数,并建立了数据能量消耗模型,优化了网络传输性能。ARDV-Hop算法还针对节点分布不均匀的区域提出跳距优化算法:在节点密度大的区域,采用余弦定理优化跳距;密度小的区域,采用最小均方误差(Least Mean Square,LMS)来修正跳距。仿真实验表明,在同等网络环境下,与传统DV-Hop算法、GDV-Hop算法和WOA-DV-Hop算法相比,ARDV-Hop算法能更有效地降低定位误差.
