A Maximum-Likelihood Sequence Estimator with Decision-Feedback Equalization

A decision-feedback equalizer (DFE) is proposed as a prefilter which limits the complexity of a maximum-likelihood sequence estimator (MLSE) implemented by the Viterbi algorithm (VA) for channels having a long impulse response. By imbedding a DFE into the structure of the MLSE, the overall impulse response of the system is truncated to a short duration. With this practical receiver, a compromise may be made between performance and complexity by properly choosing the duration of a desired impulse response. A technique is also developed to estimate the performance of the receiver numerically, taking into account the effect of incorrect decision feedback on the VA. Analysis and computer simulation over a single-pole channel show that the proposed scheme can reduce the complexity of the MLSE while retaining much of its performance advantages.     

维特比均衡算法

基于符号级维特比译码算法,将信道等效为一时变卷积编码器,提出了一种将信道均衡和信道译码相结合的技术——维特比均衡。重点研究了采用维特比均衡技术的单载波系统,并对比给出了采用频域均衡技术和维特比均衡技术,系统误码性能随信噪比的变化曲线及系统的计算复杂度。仿真结果表明：信道的等效脉冲响应滤波器长度较长时,维特比均衡技术明显改善了系统的误码性能,然而系统的复杂度也随之增加。     

Near-Minimum Bit-Error Rate Equalizer Adaptation for PRML Systems

Receivers for partial response maximum-likelihood systems typically use a linear equalizer followed by a Viterbi detector. The equalizer tries to confine the channel intersymbol interference to a short span in order to limit the implementation complexity of the Viterbi detector. Equalization is usually made adaptive in order to compensate for channel variations. Conventional adaptation techniques, e.g., LMS, are, in general, suboptimal in terms of bit-error rate (BER). In this paper, we present a new equalizer adaptation algorithm that seeks to minimize the BER at the Viterbi detector output. The algorithm extracts information from the sequenced amplitude margin (SAM) histogram and incorporates a selection mechanism that focuses adaptation on particular data and noise realizations. The selection mechanism is based on the reliability of the add compare select (ACS) operations in the Viterbi detector. From a complexity standpoint, the algorithm is essentially as simple as the conventional LMS algorithm. Moreover, we present a further simplified version of the algorithm that does not require any hardware multiplications. Simulation results, for an idealized optical storage channel, confirm a substantial performance improvement relative to existing adaptation algorithms.     

Adaptive equalization for frequency-selective channels of unknown length

This paper studies adaptive equalization for time-dispersive communication channels whose impulse responses have unknown lengths. This problem is important, because an adaptive equalizer designed for an incorrect channel length is suboptimal; it often estimates an unnecessarily large number of parameters. Some solutions to this problem exist (e.g., attempting to estimate the "channel length" and then switching between different equalizers); however, these are suboptimal owing to the difficulty of correctly identifying the channel length and the risk associated with an incorrect estimation of this length. Indeed, to determine the channel length is effectively a model order selection problem, for which no optimal solution is known. We propose a novel systematic approach to the problem under study, which circumvents the estimation of the channel length. The key idea is to model the channel impulse response via a mixture Gaussian model, which has one component for each possible channel length. The parameters of the mixture model are estimated from a received pilot sequence. We derive the optimal receiver associated with this mixture model, along with some computationally efficient approximations of it. We also devise a receiver, consisting of a bank of soft-output Viterbi algorithms, which can deliver soft decisions. Via numerical simulations, we show that our new method can outperform conventional adaptive Viterbi equalizers that use a fixed or an estimated channel length.     

Doubly-selective fading channel equalization: A comparison of the Kalman filter approach with the basis expansion model-based equalizers

In this paper, we exploit the Kalman filter as a time-varying linear minimum mean-square error equalizer for doubly-selective fading channels. We use a basis expansion model (BEM) to approximate the doubly-selective channel impulse response. Several time-varying linear equalizers have been proposed in the literature where both the channel and the equalizer impulse responses are approximated by complex exponential (CE) BEMs. Our proposed Kalman filter formulation does not rely on a specific BEM for the underlying channel, therefore, it can be applied to any BEM, including the CE-BEM and the discrete prolate spheroidal (DPS) BEM. Moreover, the Kalman filter relies solely on the channel model and therefore, does not incur any approximation error inherent in the CE-BEM representation of the equalizer. Through computer simulations, we show that compared to two of the existing algorithms, the proposed Kalman filter formulation yields the same or an improved bit error rate at a much lower computational cost, where the latter is measured in terms of the number of flops needed for the equalizer design and implementation.     

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     

Linear Minimum Mean-Square Error Estimators Applied to Channel Equalization

This concise paper investigates various aspects of the application of unbiased linear minimum mean-square error (ULMMSE) estimators to the equalization of channels used for digital data transmission. One application is to the equalization of the channel to a response free from intersymbol interference. Previous results regarding this application are clarified and extended. The other application is to the equalization of the channel to a finite short memory response. This stems from an interest in reducing the complexity of the Viterbi algorithm. Various new results on the optimum ULMMSE equalizer and its performance are presented. In both applications, the optimum ULMMSE equalizer is a stable, realizable, finite dimensional recursive filter.     

A space-time-filtered Viterbi receiver for CCI/ISI reduction in TDMA systems

In this paper, we present a hybrid space-time-filtered Viterbi receiver using multiple antennas for co-channel interference (CCI) reduction and intersymbol interference (ISI) equalization in a slow Rayleigh fading channel. In this approach, a space-time filter is first applied at the antenna outputs to maximize the signal-to-interference-plus-noise ratio (SINR), and the scalar output is then sent to a Viterbi equalizer. We propose a closed-form solution to jointly determine the weight vector for the space-time filter and the channel vector for the Viterbi equalizer. We also examine the need for a whitening filter prior to the Viterbi equalizer and show that it only marginally improves the performance. Simulation results are provided to validate our approach and to compare the performance of our receiver with that of different existing receivers.     

Blind channel estimation via combining autocorrelation and blind phase estimation

Symbol spaced blind channel estimation methods are presented which can essentially use the results of any existing blind equalization method to provide a blind channel estimate of the channel. Blind equalizer's task is reduced to only phase equalization (or identification) as the channel autocorrelation is used to obtain the amplitude response of the channel. Hence, when coupled with simple algorithms such as the constant modulus algorithm (CMA) these methods at baud rate processing provide alternatives to blind channel estimation algorithms that use explicit higher order statistics (HOS) or second-order statistics (subspace) based fractionally-spaced/multichannel algorithms. The proposed methods use finite impulse response (FIR) filter linear receiver equalizer or matched filter receiver based infinite impulse response+FIR linear cascade equalizer configurations to obtain blind channel estimates. It is shown that the utilization of channel autocorrelation information together with blind phase identification of the CMA is very effective to obtain blind channel estimation. The idea of combining estimated channel autocorrelation with blind phase estimation can further be extended to improve the HOS based blind channel estimators in a way that the quality of estimates are improved.     

A new channel estimator for fast start-up equalization

A novel noniterative algorithm is proposed for estimating the sampled impulse response of unknown channels. With the proper choice of the training sequence, implementation of the proposed channel estimator requires only additions and subtractions, i.e. no multiplications of the estimator is so simple that it can be easily implemented using an ordinary microprocessor with minimal storage. The channel estimate can serve to reduce the effects of intersymbol interference either by the maximum likelihood sequence estimator using the Viterbi algorithm or by channel equalization with a direct solution to obtain the optimum equalizer taps. A new procedure for the latter case is proposed using the Levinson-Trench algorithm for fast start-up of adaptive equalizers in noisy environments. The performance of the proposed algorithm is evaluated through simulation, and it is compared to some previous techniques. Computational efficiency is also taken into account. The results of the simulation show the superiority of the proposed scheme     

Demodulation with a Multichannel Estimation Method Using a Reduced Rank Constraint

This paper deals with the Maximum Likelihood Estimation of the multichannel impulse response in a mobile communication system whose base stations are equipped with antennas arrays. The following problem is solved: using the training sequence, find the maximum likelihood multichannel impulse response from one mobile to the base station under a reduced rank constraint in the presence of gaussian noise and jammers with unknown covariance matrix. This method finds applications in demodulation (the reduced rank channel estimate can be used in a Viterbi Algorithm), and experimental results using real signals demonstrate its high performance compared with the standard Minimum Mean Square Error (MMSE) multichannel estimate.     

Time-varying FIR equalization for doubly selective channels

We propose a time-varying (TV) finite impulse response (FIR) equalizer for doubly selective (time- and frequency-selective) channels. We use a basis expansion model (BEM) to approximate the doubly selective channel and to design the TV FIR equalizer. This allows us to turn a complicated equalization problem into an equivalent simpler equalization problem, containing only the BEM coefficients of both the doubly selective channel and the TV FIR equalizer. The minimum mean-square error (MMSE) as well as the zero-forcing (ZF) solutions are considered. Comparisons with the block linear equalizer (BLE) are made. The TV FIR equalization we propose here unifies and extends many previously proposed serial equalization approaches. In contrast to the BLE, the proposed TV FIR equalizer allows a flexible tradeoff between complexity and performance. Moreover, through computer simulations, we show that the performance of the proposed MMSE TV FIR equalizer comes close to the performance of the ZF and MMSE BLE, at a point where the design as well as the implementation complexity are much lower.     

Imrpoving QPSK Transmission in Band-Limited Channels with Interchannel Interference Through Equalization

This paper describes the use of equalization in conjunction with channel filtering to improve QPSK transmission subject to both intersymbol interference (ISI) and interchannel interference (ICI). Performance bounds are computed using the nonclassical Gaussquadrature rule (GQR) method. The signal-to-noise ratio (SNR) gain due to linear equalization over nonequalization is thereby obtained and presented. The performance of a linear equalizer thus obtained is compared with the Viterbi algorithm sequence estimator (VASE). In the absence of bounds for the VASE receiver under the channel conditions considered, simulation results are used to make the comparison. With a possible difference in the accuracies of the performance thus obtained it is shown that the VASE provides improved performance over the linear equalizer under the channel conditions considered.     

A suboptimum linear receiver based on a parametric channel model

A suboptimum, linear, minimum mean-squared error (MMSE) data communication receiver that is based on a parametric model for a linear, time-invariant, or slowly time-varying channel is shown to perform well at reasonable input signal-to-noise ratios (SNRs) and for short training periods. The receiver makes use of a fractionally spaced equalizer (FSE) design whose time span is a single symbol period. It is assumed that a parametric model, with parameter estimates that are obtainable from a training sequence prior to data acquisition, is adequate for representing the impulse response of the equivalent baseband channel     

The Viterbi algorithm for sparse channels

This paper presents a reduced complexity Viterbi algorithm for use as sequence estimator for linear intersymbol interference channels with coarsely located coefficients. In particular, the complexity does not depend on the channel impulse response length but only on the number of nonzero coefficients. No approximations are used in the algorithm. We consider a multipath environment producing time spreads     

DSL系统时域均衡训练中一种新的时延优化算法

在数字用户线(DSL)系统中,每个符号在进行传输时要加入循环前缀(CP)以消除符号间干扰。理论上,CP的长度等于信道冲激响应的记忆长度,较长的CP大大降低了DSL系统的数据传输效率。为了避免使用较长CP,通常在接收端采用时域均衡缩短信道冲激响应长度。但是,信道冲激响应最优缩短算法的复杂度很高,为此,提出了一种实用的时延优化算法,该算法将信道的冲激响应与矩形序列进行卷积,用得到的序列进行时延估计,使得算法的复杂度大幅下降,满足了系统的实时性要求,并且缩短信噪比的损失很小。     

Complex noncoherent receivers for GMSK signals

Noncoherent demodulators are very attractive for high performance radio LAN (HIPERLAN) systems because of their low implementation costs and their inherent robustness against frequency and carrier phase offsets. However, when the channel is time dispersive, the nonlinear intersymbol interference (ISI) introduced by these demodulators precludes the use of conventional linear equalization strategies. We present an alternative noncoherent receiver structure followed by a nonlinear equalizer, which includes a RAM and a Viterbi detector, capable of equalizing nonlinear multipath fading channels. In addition, we also present a new algorithm specifically for noncoherent demodulators, which allows estimation of all useful signal values at the input of the equalizer to be stored in the RAM. By means of computer simulations, we report the performance and computational complexity tradeoffs of the receiver/equalizer structure, including antenna diversity. We show that demodulators which consist of a complex receiver and a Viterbi detector are much more robust against multipath fading channels than traditional real noncoherent demodulators. The results suggest that in a typical HIPERLAN scenario, where the channel delay spread is less than 50 ns and a reliable line of sight component exists, it is feasible to combat multipath effects using noncoherent demodulation     

Improving bit-error-rate performance of the free-space optical communications system with channel estimation based on radiative transfer theory

In order to improve the performance of terrestrial free-space optical communication systems in adverse visibility conditions, we present a method for estimation of the atmospheric channel impulse response function which governs the optical intensity propagation. This method reduces run-time computational demands and system complexity in comparison to our previously proposed dual-wavelength channel estimation technique. We consider propagation of optical wavelengths in fog, where the droplet diameters are close to the wavelength and thus scattering and absorption effects are significant. A method for rapid calculation of a channel response function based on estimating the effective optical depth of the channel and curve-fitting is described. The channel response estimate can then be used to design a receiver-side equalizer (minimum meansquared error linear equalizer) to correct the signal distortion due to propagation through the dispersive channel. The channel estimates are based on parametric curve-fitting functions which have been developed using the modified-vector radiative transfer theory to model the channel response. The optimal fit parameters are found using particle-swarm optimization to minimize the simulated bit-error rate of the received signal.