Blind equalization of dispersive fast fading Ricean channels via the EMV algorithm

A blind maximum likelihood equalization method is proposed for frequency selective fast fading Ricean channels. This method employs the expectation-maximization Viterbi algorithm (EMVA) developed in for blind channel estimation and signal detection. Since the Viterbi algorithm (VA) is used to execute the E-phase of an expectation-maximization (EM) iteration, it requires that the observed sequence can be modelled as a finite-state hidden Markov process. We develop a hidden Markov model for frequency selective fast fading Ricean channels, so that the observed process can be viewed as the noisy output of a finite state machine (FSM), to which the VA is applicable. The EMVA is then employed to obtain a blind maximum likelihood estimate of the specular part of the channel and, for one special case, of a noise parameter measuring the total power of the additive and multiplicative channel noise components. Simulation results are presented which show that the EMVA achieves an accurate estimate of the channel specular part and has an error rate performance close to that of the maximum likelihood detector based on true parameters for the given FSM model.     

基于隐马尔科夫模型的CPM信号盲Turbo均衡算法

针对高阶连续相位调制信号(CPM)盲均衡中存在的均衡性能较差以及不容易收敛等问题,从隐马尔科夫模型(HMM)的角度出发,建立一种新的EM-SOVA信道盲均衡方法,并结合Turbo均衡思想,提出了一种适用于高阶CPM信号的盲Turbo均衡算法。该算法通过将SOVA内嵌到EM算法的迭代过程中,有效改善了信道均衡效果,同时使用Turbo均衡的软信息迭代处理来进一步提高低信噪比条件下系统性能。理论分析和仿真结果表明,所提算法具有良好的盲均衡性能以及收敛性。     

Blind sequence detection without channel estimation

This paper proposes a new blind sequence estimation method for single-input single-output (SISO) systems utilizing an optimal trellis search, which is performed by a channel-independent Viterbi algorithm (CIVA). In contrast to the traditional Viterbi algorithm that requires accurate channel estimation, CIVA does not require channel coefficients. Instead, the metrics are calculated from a bank of test vectors designed off-line. The proposed algorithm has outstanding performance under most of the channel conditions. Specifically, it does not suffer from ill-conditioned channels. In addition, it does not depend on channel correlation estimation and, therefore, has fast convergence. Simulations demonstrate its superior performance over even most training-based equalization algorithms     

On Approximate Maximum-Likelihood Methods for Blind Identification: How to Cope With the Curse of Dimensionality

We discuss approximate maximum-likelihood methods for blind identification and deconvolution. These algorithms are based on particle approximation versions of the expectation-maximization (EM) algorithm. We consider three different methods which differ in the way the posterior distribution of the symbols is computed. The first algorithm is a particle approximation method of the fixed-interval smoothing. The two-filter smoothing and the novel joined-two-filter smoothing involve an additional backward-information filter. Because the state space is finite, it is furthermore possible at each step to consider all the offsprings of any given particle. It is then required to construct a novel particle swarm by selecting, among all these offsprings, particle positions and computing appropriate weights. We propose here a novel unbiased selection scheme, which minimizes the expected loss with respect to general distance functions. We compare these smoothing algorithms and selection schemes in a Monte Carlo experiment. We show a significant performance increase compared to the expectation maximization Viterbi algorithm (EMVA), a fixed-lag smoothing algorithm and the Block constant modulus algorithm (CMA).     

The expectation-maximization algorithm for symbol unsynchronizedsequence detection

The expectation-maximization (EM) algorithm for maximizing likelihood functions, combined with the Viterbi algorithm, is applied to the problem of sequence detection when symbol timing information is not present. Although the EM algorithm is noncausal, results obtained using the algorithm on the problem of nonsynchronized sequence detection indicate that it converges most of the time in three iterations, making it both of theoretical and of practical interest. A practical algorithm based on the EM algorithm is introduced. It reduces the computational burden and improves performance by making use of timing estimates in previous observation windows     

基于EM算法的宽带信号DOA估计及盲分离

本文提出了一种基于EM算法的宽带信号DOA估计与盲分离方法.首先将宽带混合信号转换到频域,然后综合利用带宽内所有频点信息建立似然函数,在此基础上推导出宽带条件下的EM迭代式,从而实现宽带信号DOA及波形的联合估计.并且本文通过分析EM算法的收敛性,自适应的设定角度搜索空间,提高了算法的运算效率.与传统方法相比,本文方法运用的有效信息更多,因此,其在DOA估计精度及波形恢复性能方面都更有优势.仿真实验表明了该算法的有效性.     

A maximum likelihood approach to blind multiuser interferencecancellation

This paper addresses the problem of blind multiple access interference (MAI) and intersymbol interference (ISI) suppression in direct sequence code division multiple access (DS CDMA) systems. A novel approach to obtain the coefficients of a linear receiver using the maximum likelihood (ML) principle is proposed. The method is blind because it only exploits the statistical features of the transmitted symbols and Gaussian noise in the channel. We demonstrate that an adequate linear constraint on these coefficients ensures that the desired user is extracted and the resulting linearly constrained maximum likelihood linear (LCMLL) receiver can be efficiently implemented using the iterative space alternating generalized expectation-maximization (SAGE) algorithm. In order to take advantage of the diversity inherent to multipath channels, we also introduce a blind RAKE multiuser receiver that proceeds in two steps. First, soft estimates of the desired user transmitted symbols are obtained from each propagation path using a bank of appropriate LCMLL receivers. Afterwards, these estimates are adequately combined to enhance the signal-to-interference-and-noise ratio (SINR). Computer simulations show that the proposed blind algorithms for multiuser detection are near-far resistant and attain convergence using small blocks of data, thus outperforming existing linearly constrained minimum variance (LCMV) blind receivers     

基于粒子滤波和Viterbi序列检测的数字信号盲解调算法

针对非协作通信下数字信号解调的问题,提出一种基于粒子滤波和Viterbi序列检测的盲解调算法。粒子滤波使用一组具有相应权值的粒子来表示未知参数的后验分布,再利用Viterbi算法对信号符号作进一步估计,最终实现对数字信号的盲解调。经仿真实验验证,该方法可以有效完成对BPSK、QPSK、UQPSK、OQPSK、8 PSK等常用PSK数字信号类型的盲解调,且较传统方法实现起来更为方便。     

Hidden Gauss-Markov models for signal classification

Continuous-state hidden Markov models (CS-HMMs) are developed as a tool for signal classification. Analogs of the Baum (1972), Viterbi (1962), and Baum-Welch algorithms are formulated for this class of models. The CS-HMM algorithms are then specialized to hidden Gauss-Markov models (HGMMs) with linear Gaussian state-transition and output densities. A new Gaussian refactorization lemma is used to show that the Baum and Viterbi algorithms for HGMMs are implemented by two different formulations of the fixed-interval Kalman smoother. The measurement likelihoods obtained from the forward pass of the HGMM Baum algorithm and from the Kalman-filter innovation sequence are shown to be equal. A direct link between the Baum-Welch training algorithm and an existing expectation-maximization (EM) algorithm for Gaussian models is demonstrated. A new expression for the cross covariance between time-adjacent states in HGMMs is derived from the off-diagonal block of the conditional joint covariance matrix. A parameter invariance structure is noted for the HGMM likelihood function. CS-HMMs and HGMMs are extended to incorporate mixture densities for the a priori density of the initial state. Application of HGMMs to signal classification is demonstrated with a three-class test simulation     

Performance Analysis of Optimal Blind Fusion of Bits

This paper is devoted to a statistical performance analysis of blind estimation of bit error rates (BERs) of a bank of detectors, using empirical estimation algorithms that have appeared in the literature (by Dixit ). In particular, we prove that these blind estimators asymptotically (in the number of observed bits) achieve the accuracy obtained with perfect knowledge of the transmitted bits. We propose a maximum-likelihood solution which follows from the standard expectation-maximization (EM) algorithm, considered to be a reference algorithm. Finally, the optimal fusion rule is revisited and our theoretical results are compared to Monte Carlo simulations     

Error propagation in blind sequence estimation

We demonstrate how error propagation may occur with blind sequence estimation based on the Viterbi algorithm (BSE-VA). We further show that differential encoding can be used to alleviate this error propagation in blind sequence estimation. In addition, we compare the BSE-VA with a much simpler differential correlation approach (DCA) method for differentially encoded input symbols     

应用判决反馈的混合信号单通道盲分离算法

该文提出了一种基于判决反馈思想的DF-PSP单通道盲分离算法。该算法结合判决反馈的思想,利用Viterbi序列检测器最可能的幸存序列得到的预判决来合成信道冲激响应尾部造成的符号串扰,来弥补现有PSP单通道盲分离算法对信道冲激响应进行截断处理而带来的性能损失。仿真结果表明,对于两路混合QPSK信号,该算法较截断PSP单通道盲分离算法在复杂度相当的条件下有更好的性能,在误码率为 时,信噪比改善可达到2dB左右,且在同等过采样条件下,该算法能获得更好的性能提升。      

A blind sequence detection and its application to digital mobilecommunication

A method of sequence detection without the knowledge of the channel response is proposed. The Viterbi algorithm is extended to a blind form by introducing a new branch-metric, defined as the minimum of the short time-average of the squared error (yˆk-yk)², where yk and yˆk are the received signal and its replica, respectively. All possible candidate sequences contained in the short time squared error are defined as trellis states, for which the short time squared error is minimized in respect to a variable of the unknown channel response. The proposed implicit blind sequence detection need not keep each variable after the branch metric is calculated. The consistency of the algorithm is justified by proving that a unique sequence is detected in noise free case. The proof is accomplished under condition that the period of the time-average is longer than the channel response. If the additive white Gaussian noise is assumed, the short time squared errors are minimized beyond the desired minimum by the standard Viterbi algorithm using an apriori known channel response. We call this phenomenon over-minimization. The over-minimization is a major reason of the unavoidable error rate degradation in the blind receiver. An objective of this paper is to establish blind sequence detection for digital mobile communication. Provided the channel response can be regarded as time-invariant during the period of the short time-average of the squared error, the blind sequence detection keeps the same performance as in time-invariant case. In order to improve the error rate performance, an algorithm based on the fractional sampling scheme is introduced. Several error rate performances and behaviors of error events are investigated by computer simulation     

多通道SAR-GMTI通道盲均衡算法

基于回波数据相关矩阵特征分解的通道盲均衡算法可有效校正多通道SAR系统中由各种非理想因素引起的通道幅度相位误差,但该算法主要的缺点是收敛速度慢。该文首先分析了基于回波数据相关矩阵特征分解的通道盲均衡算法的基本工作原理;在此基础上,针对算法收敛性差的缺点,结合降维处理技术,提出一种快速收敛的通道盲均衡算法。仿真及实测数据实验结果表明:与常规的基于回波数据相关矩阵特征分解的通道盲均衡算法相比,该文所提算法收敛所需的样本数目显著减少,即可在小训练样本条件下实现对通道幅度相位误差的均衡。     

Blind maximum likelihood sequence estimation of digital sequencesin presence of intersymbol interference

A blind maximum likelihood (ML) sequence estimator for unknown linear dispersive channels is described. The estimator assumes a channel model with quantised parameters. A channel trellis and a data trellis are defined to search for the ML channel and data estimates using the Viterbi algorithm (VA). This approach provides a good performance/complexity tradeoff     

Adaptive maximum-likelihood sequence estimation by means ofcombined equalization and decoding in fading environments

This paper proposes an adaptive maximum-likelihood sequence estimation (MLSE) by means of combined equalization and decoding, i.e., adaptive combined MLSE, which employs separate channel estimation for respective states in the Viterbi algorithm. First, an approximate metric including channel estimation is derived analytically for this proposed adaptive combined MLSE. Secondly, procedures to accomplish blind equalization are investigated for the proposed MLSE. Finally, its excellent BER performance on fast time-varying fading channels is confirmed by computer simulation, when the proposed MLSE operates as a blind equalizer     

A New Sequential Detection Based on Hopfield Neural Network in Frequency Selective Fading Channels

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Convergence of the maximum a posteriori path estimator in hiddenMarkov models

In a hidden Markov model (HMM) the underlying finite-state Markov chain cannot be observed directly but only by an additional process. We are interested in estimating the unknown path of the Markov chain. The most widely used estimator is the maximum a posteriori path estimator (MAP path estimator). It can be calculated effectively by the Viterbi (1967) algorithm as is, e.g., frequently done in the field of coding theory, correction of intersymbol interference, and speech recognition. We investigate (component-wise) convergence of the MAP path estimator. Convergence is shown under the condition of unbounded likelihood ratios. This condition is satisfied in the important case of HMMs with additive white Gaussian noise. We also prove convergence, if the Markov chain has two states. The so-called Viterbi paths are an important tool for obtaining these results     

Comparative convergence analysis of EM and SAGE algorithms in DOAestimation

In this work, the convergence rates of direction of arrival (DOA) estimates using the expectation-maximization (EM) and space alternating generalized EM (SAGE) algorithms are investigated. The EM algorithm is a well-known iterative method for locating modes of a likelihood function and is characterized by simple implementation and stability. Unfortunately, the slow convergence associated with EM makes it less attractive for practical applications. The SAGE algorithm proposed by Fessler and Hero (1994), based on the same idea of data augmentation, has the potential to speed up convergence and preserves the advantage of simple implementation. We study both algorithms within the framework of array processing. Theoretical analysis shows that SAGE has faster convergence speed than EM under certain conditions on observed and augmented information matrices. The analytical results are supported by numerical simulations carried out over a wide range of signal-to-noise ratios (SNRs) and various source locations