This paper consider the penalized least squares estimators with convex penalties or regularization norms.We provide sparsity oracle inequalities for the prediction error for a general convex penalty and for the partic...This paper consider the penalized least squares estimators with convex penalties or regularization norms.We provide sparsity oracle inequalities for the prediction error for a general convex penalty and for the particular cases of Lasso and Group Lasso estimators in a regression setting.The main contribution is that our oracle inequalities are established for the more general case where the observations noise is issued from probability measures that satisfy a weak spectral gap(or Poincaré)inequality instead of Gaussian distributions.We illustrate our results on a heavy tailed example and a sub Gaussian one;we especially give the explicit bounds of the oracle inequalities for these two special examples.展开更多
It＇s well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It＇s of the form｜f（x） - s（x）｜≤（Cd）c/d｜｜f｜｜h where C, c are constants, h is the Gaussian ...It＇s well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It＇s of the form｜f（x） - s（x）｜≤（Cd）c/d｜｜f｜｜h where C, c are constants, h is the Gaussian function, s is the interpolating function, and d is called fill distance which, roughly speaking, measures the spacing of the points at which interpolation occurs. This error bound gets small very fast as d → 0. The constants C and c are very sensitive. A slight change of them will result in a huge change of the error bound. The number c can be calculated as shown in [9]. However, C cannot be calculated, or even approximated. This is a famous question in the theory of radial basis functions. The purpose of this paper is to answer this question.展开更多
This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels sub...This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels subject to an additive non-Gaussian noise. The obtained expressions take into account static and mobile wireless receivers. In addition, a closed-form expression for the outage probability in mobile networks is obtained. Please note that all derived expressions in this paper a valid for integer and non-integer values of the fading parameters. Analytical results are presented to study the impact of noise shaping parameter, severity of fading, and mobility on the average SER. Monte-Carlo simulations results are also provided to validate the accuracy of the analytical results.展开更多
A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularit...A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularity error. The finely-designed GA (FDGA)characterized dynamical bisexual recombination and Gaussian mutation. The mathematical model of thenonlinear problem is given. The implementation details in FDGA are described such as the crossoveror recombination mechanism which utilized a bisexual reproduction scheme and the elitist reservationmethod; and the adaptive mutation which used the Gaussian probability distribution to determine thevalues of the offspring produced by mutation mechanism. The examples are provided to verify thedesigned FDGA. The computation results indicate that the FDGA works very well in the field of formerror evaluation such as circularity evaluation.展开更多
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 ad...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.展开更多
The Bjorck and Pereyra algorithms used for solving Vandermonde systemof equation are modified for the case where the points are symmetricly situated aroundzero. The working operation is saved about half. A forward err...The Bjorck and Pereyra algorithms used for solving Vandermonde systemof equation are modified for the case where the points are symmetricly situated aroundzero. The working operation is saved about half. A forward error analysis is presentedfor the modified algorithms, and it's shown that if the points are situated in some order,the error bound are as good as Higham's result in 1987.展开更多
Based on the target scatterer density, the range-spread target detection of high-resolution radar is addressed in additive non-Gaussian clutter, which is modeled as a spherically invariant random vector. Firstly, for ...Based on the target scatterer density, the range-spread target detection of high-resolution radar is addressed in additive non-Gaussian clutter, which is modeled as a spherically invariant random vector. Firstly, for sparse scatterer density, the detection of target scatterer in each range cell is derived, and then an M/K detector is proposed to detect the whole range-spread target. Se- condly, an integrating detector is devised to detect a range-spread target with dense scatterer density. Finally, to make the best of the advantages of M/K detector and integrating detector, a robust detector based on scatterer density （DBSD） is designed, which can reduce the probable collapsing loss or quantization error ef- fectively. Moreover, the density decision factor of DBSD is also determined. The formula of the false alarm probability is derived for DBSD. It is proved that the DBSD ensures a constant false alarm rate property. Furthermore, the computational results indi- cate that the DBSD is robust to different clutter one-lag correlations and target scatterer densities. It is also shown that the DBSD out- performs the existing scatterer-density-dependent detector.展开更多
The pilotless frame synchronization approach and implementations of LDPC code are the crucial issue of LDPC decoder. The Maximum-A-Posteriori probability( MAP) decoder has a perfect frame synchronization error rate( F...The pilotless frame synchronization approach and implementations of LDPC code are the crucial issue of LDPC decoder. The Maximum-A-Posteriori probability( MAP) decoder has a perfect frame synchronization error rate( FSER) performance. In this paper,a theoretical derivation of the FSER performance of pilotless frame synchronization for LDPC code is presented. The FSER performance by theoretical analysis coincides well with that by simulation in additive white Gaussian channel and Rician fading channel. So it is estimated the FSER performance of an LDPC code by theoretical analysis can be used instead of the simulations which are much more time-consuming.展开更多
基金This work has been(partially)supported by the Project EFI ANR-17-CE40-0030 of the French National Research Agency.
文摘This paper consider the penalized least squares estimators with convex penalties or regularization norms.We provide sparsity oracle inequalities for the prediction error for a general convex penalty and for the particular cases of Lasso and Group Lasso estimators in a regression setting.The main contribution is that our oracle inequalities are established for the more general case where the observations noise is issued from probability measures that satisfy a weak spectral gap(or Poincaré)inequality instead of Gaussian distributions.We illustrate our results on a heavy tailed example and a sub Gaussian one;we especially give the explicit bounds of the oracle inequalities for these two special examples.
文摘It＇s well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It＇s of the form｜f（x） - s（x）｜≤（Cd）c/d｜｜f｜｜h where C, c are constants, h is the Gaussian function, s is the interpolating function, and d is called fill distance which, roughly speaking, measures the spacing of the points at which interpolation occurs. This error bound gets small very fast as d → 0. The constants C and c are very sensitive. A slight change of them will result in a huge change of the error bound. The number c can be calculated as shown in [9]. However, C cannot be calculated, or even approximated. This is a famous question in the theory of radial basis functions. The purpose of this paper is to answer this question.
基金the support of SNCS Research Center and the Deanship of Scientific Research at the University of Tabukfinancial and inkind support for the project no. S-1438-0161
文摘This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels subject to an additive non-Gaussian noise. The obtained expressions take into account static and mobile wireless receivers. In addition, a closed-form expression for the outage probability in mobile networks is obtained. Please note that all derived expressions in this paper a valid for integer and non-integer values of the fading parameters. Analytical results are presented to study the impact of noise shaping parameter, severity of fading, and mobility on the average SER. Monte-Carlo simulations results are also provided to validate the accuracy of the analytical results.
基金The project is supported by National Natural Science Foundation of China(No.59975025).
文摘A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularity error. The finely-designed GA (FDGA)characterized dynamical bisexual recombination and Gaussian mutation. The mathematical model of thenonlinear problem is given. The implementation details in FDGA are described such as the crossoveror recombination mechanism which utilized a bisexual reproduction scheme and the elitist reservationmethod; and the adaptive mutation which used the Gaussian probability distribution to determine thevalues of the offspring produced by mutation mechanism. The examples are provided to verify thedesigned FDGA. The computation results indicate that the FDGA works very well in the field of formerror evaluation such as circularity evaluation.
文摘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.
基金Supported by National Natural Science Foundation of China,under Grant Number 60175008.and Natural Science Foundation of Fujian Province under Grant A0110004.
文摘The Bjorck and Pereyra algorithms used for solving Vandermonde systemof equation are modified for the case where the points are symmetricly situated aroundzero. The working operation is saved about half. A forward error analysis is presentedfor the modified algorithms, and it's shown that if the points are situated in some order,the error bound are as good as Higham's result in 1987.
基金supported by the National Natural Science Foundation of China (61102166)the Scientific Research Foundation of Naval Aeronautical and Astronautical University for Young Scholars (HY2012)
文摘Based on the target scatterer density, the range-spread target detection of high-resolution radar is addressed in additive non-Gaussian clutter, which is modeled as a spherically invariant random vector. Firstly, for sparse scatterer density, the detection of target scatterer in each range cell is derived, and then an M/K detector is proposed to detect the whole range-spread target. Se- condly, an integrating detector is devised to detect a range-spread target with dense scatterer density. Finally, to make the best of the advantages of M/K detector and integrating detector, a robust detector based on scatterer density （DBSD） is designed, which can reduce the probable collapsing loss or quantization error ef- fectively. Moreover, the density decision factor of DBSD is also determined. The formula of the false alarm probability is derived for DBSD. It is proved that the DBSD ensures a constant false alarm rate property. Furthermore, the computational results indi- cate that the DBSD is robust to different clutter one-lag correlations and target scatterer densities. It is also shown that the DBSD out- performs the existing scatterer-density-dependent detector.
基金Supported by the National Natural Science Foundation of China(No.61271230,61472190)the Open Research Fund of National Mobile Communications Research Laboratory,Southeast University(No.2013D02)the Open Research Fund of National Key Laboratory of Electromagnetic Environment,China Research Institute of Radiowave Propagation(No.201500013)
文摘The pilotless frame synchronization approach and implementations of LDPC code are the crucial issue of LDPC decoder. The Maximum-A-Posteriori probability( MAP) decoder has a perfect frame synchronization error rate( FSER) performance. In this paper,a theoretical derivation of the FSER performance of pilotless frame synchronization for LDPC code is presented. The FSER performance by theoretical analysis coincides well with that by simulation in additive white Gaussian channel and Rician fading channel. So it is estimated the FSER performance of an LDPC code by theoretical analysis can be used instead of the simulations which are much more time-consuming.
文摘【目的】超宽带测距误差分布表明,在存在显著重尾的情况下,高斯混合模型比简单的高斯概率包络更接近经验分布。通过传统的超界分布(Overbounding Distribution)模型获得的保护水平过于保守,会降低系统可用性。【方法】为提高系统可用性,提出了基于高斯混合模型(GMM)的超界框架来处理基于TOA(Time of Arrival)定位的超宽带测距误差样本。首先,结合EM算法获得测距误差的双组分GMM概率密度函数,并修正边界参数,使左右边界均满足双边超界条件,以构建双组分GMM形式的距离域双边超界模型。随后,基于GMM双边超界模型推导出计算位置域保护级(PL)的方法,对距离域的概率密度函数进行卷积以获得位置概率密度函数,求逆运算出PL。【结果】最后,开展实验验证应用GMM双边超界模型收紧PL的效果,采集3~93 m范围内的样本数据用于误差模型的构建,真实测试的性能评估表明,基于GMM双边超界模型比传统高斯双边超界模型计算所得的PL减小了20%以上。【结论】GMM双边超界模型能够以较小的计算成本收紧PL,增强系统可用性。
