Likelihood sensitivity and the Cramér-Rao bound (Corresp.)

The Cramér-Rao bound on the error variance of an unbiased estimator of all unknown parameter is given an intuitively pleasing interpretation in terms of the sensitivity of the likelihood function to changes in parameter value.     

A modified Cramér-Rao bound and its applications (Corresp.)

A new way of treating extraneous or nuisance parameters in applying the Cramér-Rao bound is presented. The modified method duces substantially fighter bounds in two important applications. In particular, new bounds are obtained for the variance of estimates of arrival times for the Rayleigh channel.     

A unification of Cramér-Rao type bounds (Corresp.)

This correspondence examines multiparameter generalizations of the Cramér-Rao (C-R) bound and related bounds from a new viewpoint. We derive a general class of bounds and show that Rao's generalization is the tightest (bes0 of the class. A bound reported by Zacks is another member of the class. This derivation of the C-R bound emphasizes its optimum nature. The relationship of the general class to Barankin bounds is also discussed.     

Maximum-Likelihood Estimation, the CramÉr–Rao Bound, and the Method of Scoring With Parameter Constraints

Maximum-likelihood (ML) estimation is a popular approach to solving many signal processing problems. Many of these problems cannot be solved analytically and so numerical techniques such as the method of scoring are applied. However, in many scenarios, it is desirable to modify the ML problem with the inclusion of additional side information. Often this side information is in the form of parametric constraints, which the ML estimate (MLE) must now satisfy. We unify the asymptotic constrained ML (CML) theory with the constrained Cramer-Rao bound (CCRB) theory by showing the CML estimate (CMLE) is asymptotically efficient with respect to the CCRB. We also generalize the classical method of scoring using the CCRB to include the constraints, satisfying the constraints after each iterate. Convergence properties and examples verify the usefulness of the constrained scoring approach. As a particular example, an alternative and more general CMLE is developed for the complex parameter linear model with linear constraints. A novel proof of the efficiency of this estimator is provided using the CCRB.     

A CramÉr-Rao Bound Characterization of the EM-Algorithm Mean Speed of Convergence

This paper deals with the mean speed of convergence of the expectation-maximization (EM) algorithm. We show that the asymptotic behavior (in terms of the number of observations) of the EM algorithm can be characterized as a function of the Cramer-Rao bounds (CRBs) associated to the so-called incomplete and complete data sets defined within the EM-algorithm framework. We particularize our result to the case of a complete data set defined as the concatenation of the observation vector and a vector of nuisance parameters, independent of the parameter of interest. In this particular case, we show that the CRB associated to the complete data set is nothing but the well-known modified CRB. Finally, we show by simulation that the proposed expression enables to properly characterize the EM-algorithm mean speed of convergence from the CRB behavior when the size of the observation set is large enough.     

MPSK信号的最大似然SNR估计方法

该文利用最大似然准则分别推导了对于MPSK信号的数据辅助SNR估计方法、判决指向SNR估计方法和一种新的盲信噪比估计方法。文章对这些算法的性能进行了分析和计算机仿真,并与其它一些SNR估计算法进行了比较。分析和仿真的结果显示数据辅助的SNR方法性能优越,很好地符合了信噪比估计性能下限(CRLB)。判决指向算法性能依赖于判决的准确程度,在高信噪比时性能较好;而在低信噪比条件时,特别是小于OdB以后其估计有较大偏差。新的盲SNR估计算法对于BPSK信号具有估计范围广、精度高和复杂度小的特点,但是当M增加时性能会明显下降。     

Maximum-Likelihood Phase and Channel Estimation for Coherent Optical OFDM

We present a channel model for a coherent optical orthogonal frequency-division-multiplexed (CO-OFDM) system including linear fiber dispersion effects and noises from optical amplifiers and intercarrier interference induced by laser phase noise. Based upon this model, we derive maximum-likelihood (ML) phase estimation and channel estimation for the CO-OFDM system. Both computer simulation and transmission experiment of the CO-OFDM system show that the ML decision-feedback following pilot-assisted phase estimation gives the optimal performance.     

空时网格码的联合迭代最大似然估计和译码

该文提出了一种适合空时网格码的联合迭代最大似然估计和译码的方法,利用较少的导频,能够获得比传统非迭代最大似然译码更好的系统性能,仿真结果显示经过4次迭代,其性能与接收机已知理想信道信息下的最大似然译码比较只有不到1dB的损失,最后根据仿真结果给出一个导频数目和迭代次数的合理选择。     

Joint Maximum-Likelihood Estimation of Frequency Offset and Channel in MIMO Systems

This paper addresses the problem of frequency offsets and channel gains estimation for a Multiinput multi-output （MIMO） system in fiat-fading channels. The general case where the frequency offsets are possibly different for each transmit antenna is considered, The Maximum-likelihood （ML） estimation of the carrier frequency offset for each transmit antenna in a MIMO system is investigated in this paper. The exact solution to this estimation problem turns out to be too complex as it involves a search over a multi-dimensional domain. However, by making use of the Particle swarm optimization （PSO） method, we efficiently solve the above complex problem. So based on the PSO theory, a novel joint estimation algorithm of frequency offsets and channel gains is proposed. Simulation results show that the proposed algorithm has better performance as compared with the correlation-based estimation algorithm and asymptotically achieves the Cramer-Rao lower bound （CRLB）, which provides a new idea to solve the problem of joint frequency offsets and channel gains estimation for MIMO systems.     

Performance Analysis of Maximum-Likelihood Multiuser Detection in Space–Time-Coded CDMA With Imperfect Channel Estimation

In this paper, the performance of maximum-likelihood multiuser detection in space-time-coded code-division multiple-access (CDMA) systems with imperfect channel estimation is analyzed. A K-user synchronous CDMA system that employs orthogonal space-time block codes with M transmit antennas and N receive antennas is considered. A least-squares estimate of the channel matrix is obtained by sending a sequence of pilot bits from each user. The channel matrix is perturbed by an error matrix that depends on the thermal noise and the correlation between the signature waveforms of different users. Because of the linearity of the channel estimation technique, the characteristic function of the decision variable is used to obtain an exact expression for the pairwise error probability, and by using it, an upper bound on the bit error rate (BER) is obtained. The analytical BER bounds are compared with the BER obtained through simulations. The BER bounds are shown to be increasingly tight for large SNR values. It is shown that the degradation in BER performance due to imperfect channel estimation can be compensated by using a larger number of transmit/receive antennas     

Unbiased Maximum-Likelihood Estimation of a Weibull Percentile when the Shape Parameter is Known

The maximum-likelihood (ML) estimator for a percentile of a Weibull distribution with a known shape parameter is considered. Multiplicative correction factors are listed for rendering the ML estimator mean or median unbiased in the cases where the samples are type II censored with or without replacement. The correction factors depend upon the number of failures and the shape parameter but are independent of the sample size and the percentile being estimated.     

Joint Maximum-Likelihood CFO and Channel Estimation for OFDMA Uplink Using Importance Sampling

In this paper, the optimal carrier frequency offset (CFO) and channel estimator for an orthogonal frequency-division multiple-access (OFDMA) uplink based on a joint maximum-likelihood (ML) criterion is derived. Direct implementation of the resultant estimation scheme is challenging due to the need for a multidimensional exhaustive search in multi-CFO estimation. To solve this problem, an optimization theorem is exploited, and a computationally efficient method using an importance sampling technique is proposed. Without the need to provide an initial estimate, the proposed estimator guarantees the generation of the global optimal solution. Simulation results clearly verify the effectiveness of the proposed estimation scheme.      

Maximum-Likelihood Digital Data Sequence Estimation Over the Gaussian Channel with Unknown Carrier Phase

We consider the problem of simultaneous ML estimation of data and carrier phase from a linear suppressed-carrier modulated signal received in the presence of additive white Gaussian noise. The ML detector of the data sequence is derived, and its error probability performance is analyzed. The result shows that the performance loss due to the unknown carrier phase can be reduced by increasing the sequence length. A suboptimum decision-aided subsequence-by-subsequence detector whose complexity does not increase exponentially with sequence length is proposed, and its performance is analyzed.     

Comments on “Semi-Blind Channel Estimation and Equalization for MIMO Space–Time Coded OFDM”

A semiblind channel estimation scheme of the multiple-input–multiple-output space–time coded orthogonal frequency-division multiplexing system was proposed in the aforementioned paper for either real or complex with symmetric signals. We point out that this scheme cannot work correctly for complex signal scenario.      

基于可见光通信的室内定位算法及相应参数估计克拉美罗界

基于可见光通信的新型室内定位方法具有传统无线定位方法难以替代的优势,且室内光源布局对定位性能的好坏有着直接影响。在满足室内光照条件要求的前提下,针对典型可见光通信室内定位模拟环境,推导了待测点的克拉美罗界(CRB)和定位性能最佳的光源布局,并使用高斯-牛顿算法进行了仿真分析,证明了文中推导的正确性。     

MIMO雷达GMTI性能及DOA估计的克拉美·罗界分析

研究了MIMO雷达GMTI 性能及其DOA估计的克拉美·罗界(CRB)。首先建立机载平台下MIMO雷达信号模型,通过对系统参数设置,可使MIMO雷达工作在3种不同模式中。接着分析了MIMO雷达GMTI性能,并推导出了在MIMO雷达空时信号模型下,利用空时联合域信息时DOA估计的CRB。仿真结果表明,无论是GMTI性能还是DOA估计性能,MIMO雷达均优于相控阵雷达,尤其是发射稀疏阵MIMO雷达性能最佳。同时,利用空时联合域信息能有效改善MIMO雷达DOA估计的CRB,在目标多普勒频率相差较大时效果更加明显。