The expectation-maximization Viterbi algorithm for blind adaptive channel equalization

A blind maximum-likelihood equalization algorithm is described and its convergence behavior is analyzed. Since the algorithm employs the Viterbi algorithm (VA) to execute the expectation step of the expectation-maximization (EM) iteration, we call it the expectation-maximization Viterbi algorithm (EMVA). An EMVA-based blind channel-acquisition technique which achieves a high global convergence probability is developed. The performance of the method is evaluated via numerical simulations under static and fading channel conditions.     

A continuously adaptive MLSE receiver for mobile communications:algorithm and performance

The paper presents a Euclidean distance maximum likelihood sequence estimation (MLSE) receiver, based on the Viterbi algorithm (VA), suitable for fading and noisy communications channels, as that specified by the Group Special Mobiles (GSM). In a mobile cellular system, the fast varying channel characteristics, due to the fading and Doppler effects, require adaptive methods to update the channel coefficients to the MLSE receiver. The proposed technique continuously estimates the channel characteristics directly within the metric calculation of the VA. At each step of the VA, the sequence associated to the path with the best metric value (minimum-survivor method) among the survivor paths is used to update the channel estimate (employing conventional adaptive algorithms) throughout the entire informative sequence. However, the detection of the transmitted data sequence is performed by the VA only at the end of each burst. The proposed technique allows simpler receiver implementation and the simulation results show a good performance of this adaptive MLSE receiver in typical GSM environments     

Maximum likelihood blind channel estimation in the presence ofDoppler shifts

Transmitter/receiver motion in mobile radio channels may cause frequency shifts in each received path due to Doppler effects. Most blind equalization methods, however, assume time-invariant channels and may not be applicable to fading channels with severe Doppler spread. We address the problem of simultaneously estimating the Doppler shift and channel parameters in a blind setup. Both deterministic and stochastic maximum likelihood methods are developed and iterative solutions proposed. The stochastic maximum likelihood solution is based on the modified version of the Baum-Welch (1970) algorithm, which originated in the study of hidden Markov models. The proposed methods are well suited for short data records appearing in TDMA systems. Identifiability and performance analysis issues are discussed, and Cramer-Rao bounds are derived. In addition, some illustrative simulations are presented     

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     

Blind equalization of quadrature partial response‐trellis coded modulated signals in Rician fading

In this paper, a blind maximum‐likelihood channel estimation algorithm is developed for quadrature partial response‐trellis coded modulated (QPR‐TCM) signals propagating through a Rician fading environment. A hidden Markov model (HMM) formulation of the problem is introduced and the Baum–Welch parameter estimation algorithm is modified to provide a computationally efficient solution to the resulting optimization problem. Performance analysis of the proposed method is carried out through the evaluation of bit‐error probability upper bound for Rician fading channels. Also, some illustrative simulations are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Blind equalization of IIR channels using hidden Markov models andextended least squares

In this paper, we present a blind equalization algorithm for noisy IIR channels when the channel input is a finite state Markov chain. The algorithm yields estimates of the IIR channel coefficients, channel noise variance, transition probabilities, and state of the Markov chain. Unlike the optimal maximum likelihood estimator which is computationally infeasible since the computing cost increases exponentially with data length, our algorithm is computationally inexpensive. Our algorithm is based on combining a recursive hidden Markov model (HMM) estimator with a relaxed SPR (strictly positive real) extended least squares (ELS) scheme. In simulation studies we show that the algorithm yields satisfactory estimates even in low SNR. We also compare the performance of our scheme with a truncated FIR scheme and the constant modulus algorithm (CMA) which is currently a popular algorithm in blind equalization     

Joint Semi-Blind Channel Estimation and Data Sequence Detection of OFDM Systems

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A new adaptive equalizer with channel estimator for mobile radiocommunication

For unknown mobile radio channels with severe intersymbol interference (ISI), a maximum likelihood sequence estimator, such as a decision feedback equalizer (DFE) having both feedforward and feedback filters, needs to handle both precursors and postcursors. Consequently, such an equalizer is too complex to be practical. This paper presents a new reduced-state, soft decision feedback Viterbi equalizer (RSSDFVE) with a channel estimator and predictor. The RSSDFVE uses maximum likelihood sequence estimation (MLSE) to handle the precursors and truncates the overall postcursors with the soft decision of the MLSE to reduce the implementation complexity. A multiray fading channel model with a Doppler frequency shift is used in the simulation. For fast convergence, a channel estimator with fast start-up is proposed. The channel estimator obtains the sampled channel impulse response (CIR) from the training sequence and updates the RSSDFVE during the bursts in order to track changes of the fading channel. Simulation results show the RSSDFVE has nearly the same performance as the MLSE for time-invariant multipath fading channels and better performance than the DFE for time-variant multipath fading channels with less implementation complexity than the MLSE. The fast start-up (FS) channel estimator gives faster convergence than a Kalman channel estimator. The proposed RSSDFVE retains the MLSE structure to obtain good performance and only uses soft decisions to subtract the postcursor interference. It provides the best tradeoff between complexity and performance of any Viterbi equalizers     

莱斯多径衰落信道下OFDM系统的容量方差分析

方差是系统容量的一个重要参数,可以用来估计通信系统的中断容量。该文研究了正交频分复用（OFDM）系统在莱斯衰落信道下的容量方差。首先该文建立了多径莱斯信道的模型并且定义了多径莱斯信道的莱斯因子,基于此信道模型推出了一个OFDM系统容量方差新的数学表达式,此表达式以OFDM系统的子载波数、信噪比、信道的多径时延等为参数。基于此表达式,计算机仿真和数值计算研究了信噪比、多径数目、莱斯因子对OFDM系统容量方差的影响。结果表明:计算机仿真和数值计算基本吻合,验证了所推导数学表达式的正确性;系统容量方差与信噪比成正比,与莱斯因子和信道的多径数目成反比。另外,该文以积分的形式给出了任意两个相关莱斯随机变量的联合概率密度函数。      

Extended MLSE receiver for the frequency-flat, fast-fading channel

This paper develops a maximum likelihood sequence estimation (MLSE) receiver for the frequency-flat, fast-fading channel corrupted by additive Gaussian noise when linear modulations (M-ASK, M-PSK, and M-QAM) are employed. This paper extends Ungerboeck's derivation of the extended MLSE receiver for the purely frequency-selective channel to the time-selective channel. Although the new receiver's structure and metric assume ideal channel state information (CSI) at the receiver, the receiver structure can be used wherever high-quality CSI is available. The receiver is maximum likelihood for a variety of channels, including Ricean, Rayleigh, lognormal, and additive white Gaussian noise (AWGN) channels. Bounds on the receiver's bit error rate (BER) are deduced for ideal and pilot tone CSI for fast Rayleigh fading. A crude lower bound is developed on the BER of predictor-based receivers for the same channel. This paper offers insight into matched filtering and receiver processing for the fast-fading channel and shows how pilot symbols and tones should be exploited     

MAP decoding in channels with memory

The expectation-maximization (EM) algorithm is popular in estimating the parameters of various statistical models. We consider applications of the EM algorithm to the maximum a posteriori (MAP) sequence decoding assuming that sources and channels are described by hidden Markov models (HMMs). The HMMs can accurately approximate a large variety of communication channels with memory and, in particular, wireless fading channels with noise. The direct maximization of the a posteriori probability (APP) is too complex. The EM algorithm allows us to obtain the MAP sequence estimation iteratively. Since each step of the EM algorithm increases the APP, the algorithm can improve the performance of any decoding procedure     

Soft decision-directed MAP estimate of fast Rayleigh flat fading channels

An iterative receiver with soft-decision feedback is derived by using the expectation-maximization algorithm for maximum a posteriori estimate of fast Rayleigh flat fading channels. Simulation results indicate that in a fast fading environment, the derived receiver can perform better than an iterative receiver with hard-decision feedback.     

Joint estimation of symbol timing and carrier frequency offset of OFDM signals over fast time-varying multipath channels

In this paper, we present a novel joint algorithm to estimate the symbol timing and carrier frequency offsets of wireless orthogonal frequency division multiplexing (OFDM) signals. To jointly estimate synchronization parameters using the maximum likelihood (ML) criterion, researchers have derived conventional models only from additive white Gaussian noise (AWGN) or single-path fading channels. We develop a general ML estimation algorithm that can accurately calculate symbol timing and carrier frequency offsets over a fast time-varying multipath channel. To reduce overall estimation complexity, the proposed scheme consists of two estimation stages: coarse and fine synchronizations. A low complexity coarse synchronization based on the least-squares (LS) method can rapidly estimate the rough symbol timing and carrier frequency offsets over a fast time-varying multipath channel. The subsequent ML fine synchronization can then obtain accurate final results based on the previous coarse synchronization. Simulations demonstrate that the coarse-to-fine method provides a good tradeoff between estimation accuracy and computational complexity.     

Bit error rate analysis of reduced-state Viterbi differentialdetection of M-ary DPSK signals

A tight upper bound or bit error rate (BER) is derived for approximate maximum likelihood differential detection (DD) implemented by the reduced state Viterbi algorithm (VA) known as RSVDD. The BER performance of RSVDD is compared with Viterbi DD (VDD) for M-ary DPSK in additive white Gaussian noise (AWGN) channels     

Spectrum estimation of short-time stationary signals in additivenoise and channel distortion

In this work, spectrum estimation of a short-time stationary signal that is degraded by both channel distortion and additive noise is addressed. A maximum likelihood estimation (MLE) algorithm is developed to jointly identify the degradation system and estimate short-time signal spectra. The source signal is assumed to be generated by a hidden Markov model (HMM) with state-dependent short-time spectral distributions described by mixtures of Gaussian densities. The distortion channel is linear time-invariant, and the noise is Gaussian. The algorithm is derived by using the principle of expectation-maximization (EM), where the unknown parameters of channel and noise are estimated iteratively, and the short-time signal power spectra are obtained from the posterior sufficient statistics of the source signal. Other spectral representation parameters, such as autoregressive model parameters or cepstral parameters, are obtained by minimum mean-squared error (MMSE) estimation from the power spectral estimates. The estimation algorithm was evaluated on simulated signals at the signal-to-noise ratios (SNRs) of 20 dB down to 0 dB, where it produced convergent estimation and significantly reduced spectral distortion     

An EM Algorithm for Ion-Channel Current Estimation

Parameter estimation of a continuous-time Markov chain observed through a discrete-time memoryless channel is studied. An expectation-maximization (EM) algorithm for maximum likelihood estimation of the parameter of this hidden Markov process is developed and applied to a simple example of modeling ion-channel currents in living cell membranes. The approach follows that of Asmussen, Nerman and Olsson, and Ryden, for EM estimation of an underlying continuous-time Markov chain.     

Detection techniques for fading multipath channels with unresolvedcomponents

In this paper we consider noncoherent detection structures for multipath Ricean/Rayleigh fading channels. The multipath components are assumed to be unresolved, with known delays. These delays could have been estimated, for example, by using super-resolution techniques or sounding the channel with a wide-band pulse. We show that the Rayleigh channel optimum receiver (R OPT) consists of an “orthogonalization” (or decorrelation) stage and then it implements an optimum decision rule for a resolved multipath channel. Since the optimum decision rule over Ricean channels is in general too complex for implementation, we propose several suboptimum structures such as the quadratic decorrelation receiver (QDR) and the quadratic receiver (QR). The QDR scheme exploits the decorrelation performed on the input samples. The nonlinear term due to the Ricean specular term is replaced by a quadratic form that is more suitable for implementation. Single-pulse performance of these schemes are studied for commonly used binary modulation formats such as FSK and DPSK. This paper shows that it is possible to have diversity-like gains over Ricean/Rayleigh multipath fading channels with unresolved components even if the channel is not fully tracked. Furthermore, this paper demonstrates the importance of using generalizations of RAKE receivers designed to handle the unresolvability condition. For two-path mixed-mode Ricean/Rayleigh channels, it is shown that improved performance can be obtained by using receivers that know the strength of the Ricean specular term     

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     

Markov characterization of channels with soft decision outputs

It is shown that a methodology based on hidden Markov models is applicable to the modeling of slowly varying Rayleigh fading channels with additive Gaussian noise and soft decision outputs. The fading is considered to be frequency nonselective, and ideal demodulation is considered throughout. To prove the validity of robustness of the modeling technique, various results that show good agreement between the simulated channels and the models found are presented. Two soft decision statistical distributions, namely, the soft burst and soft burst interval distributions, are defined and compared. To illustrate the accuracy of the models obtained, the simulation and model outputs are compared for a convolutional encoder with Viterbi decoding and various degrees of interleaving