Blind MMSE Equalization of FIR/IIR Channels Using Oversampling and Multichannel Linear Prediction

A linear‐prediction‐based blind equalization algorithm for single‐input single‐output (SISO) finite impulse response/infinite impulse response (FIR/IIR) channels is proposed. The new algorithm is based on second‐order statistics, and it does not require channel order estimation. By oversampling the channel output, the SISO channel model is converted to a special single‐input multiple‐output (SIMO) model. Two forward linear predictors with consecutive prediction delays are applied to the subchannel outputs of the SIMO model. It is demonstrated that the partial parameters of the SIMO model can be estimated from the difference between the prediction errors when the length of the predictors is sufficiently large. The sufficient filter length for achieving the optimal prediction is also derived. Based on the estimated parameters, both batch and adaptive minimum‐mean‐square‐error equalizers are developed. The performance of the proposed equalizers is evaluated by computer simulations and compared with existing algorithms.     

Fast adaptive equalization/diversity combining for time-varyingdispersive channels

We examine adaptive equalization and diversity combining methods for fast Rayleigh-fading frequency selective channels. We assume a block adaptive receiver in which the receiver coefficients are obtained from feedforward channel estimation. For the feedforward channel estimation, we propose a novel reduced dimension channel estimation procedure, where the number of unknown parameters are reduced using a priori information of the transmit shaping filter's impulse response. Fewer unknown parameters require a shorter training sequence. We obtain least-squares, maximum-likelihood, and maximum a posteriori (MAP) estimators for the reduced dimension channel estimation problem. For symbol detection, we propose the use of a matched filtered diversity combining decision feedback equalizer (DFE) instead of a straightforward diversity combining DFE. The matched filter form has lower computational complexity and provides a well-conditioned matrix inversion. To cope with fast time-varying channels, we introduce a new DFE coefficient computation algorithm which is obtained by incorporating the channel variation during the decision delay into the minimum mean square error (MMSE) criterion. We refer to this as the non-Toeplitz DFE (NT-DFE). We also show the feasibility of a suboptimal receiver which has a lower complexity than a recursive least squares adaptation, with performance close to the optimal NT-DFE     

Block adaptive techniques for channel identification and datademodulation over band-limited channels

A new approach to the problem of data detection for communications over band-limited channels with unknown parameters is introduced. We propose a new way to implement the Viterbi algorithm (VA) for maximum-likelihood data sequence estimation (MLSE) in a known channel environment and utilize it to derive block adaptive techniques for joint channel and data estimation, when the channel-impulse response (CIR) is unknown. We show, via simulations, that we can achieve a probability of error very close to that of the known channel environment and nearly reach a mean-square error in the channel estimate as predicted by analytical bounds, operating on static channels, which exhibit deep nulls in their magnitude response and nonlinear phase. The proposed schemes accomplish channel acquisition after processing a few hundred symbols while operating without a training sequence, whereas linear blind equalizers, such as Sato's (1975) algorithm, fail to converge at all. The application of block processing to adaptive MLSE is also investigated for time-varying frequency-selective Rayleigh-fading channels, which are used for modeling mobile communication systems. In such environments it is shown that the proposed scheme exhibits improved performance compared to the conventional adaptive MLSE receiver using tentative delayed decisions     

Adaptive techniques for multiuser CDMA receivers

A number of CDMA receivers have been proposed that cover the whole spectrum of performance/complexity from the simple matched filter to the optimal Viterbi (1995) processor. Adaptive solutions, in particular, have the potential of providing the anticipated multiuser detection (MD) performance gains with a complexity that would be manageable for third generation systems. Our goal, in this article, is to provide an overview of previous work in MD with an emphasis on adaptive methods. We start with (suboptimal) linear receivers and discuss the data-aided MMSE receiver. Blind (nondata-aided) implementations are also reviewed together with techniques that can mitigate possible multipath effects and channel dispersion. In anticipation of those developments, appropriate discrete-time (chip rate) CDMA models are reviewed, which incorporate asynchronism and channel dispersion. For systems with large spreading factors, the convergence and tracking properties of conventional adaptive filters may be inadequate due to the large number of coefficients which must be estimated. In this context, reduced rank adaptive filtering is discussed. In this approach, the number of parameters is reduced by restricting the receiver tap vector to belong to a carefully chosen subspace. In this way the number of coefficients to be estimated is significantly reduced with minimal performance loss     

16-state nonlinear equalizer for IS-54 digital cellular channels

A performance evaluation for a number of equalizers for frequency selective fading channels has been carried out. Linear and decision feedback equalizers have been considered. IS-54 digital cellular channels based on TDM concepts have delay spreads that result in at most one data symbol of overlap. Using a standard fading model, we find that a 16-state sequence estimator, following a receive filter matched to the transmitter filter, provides excellent performance for delay spreads from zero to one symbol interval. It is a low-complexity detector, and for this situation it is superior to both linear and decision feedback equalizers in this application. We assume perfect channel state information to establish ultimate performance. In practical applications, at most three complex samples of the overall channel impulse that includes the receiver filter must be estimated. The frequency selective channel is a two-path model with time variation following standard Doppler variations for IS-54 channels and co-channel interference is included. We present results for both root-raised-cosine filtered π/4-DQPSK and QPSK modulation formats. In the appendix, we provide an analysis to support our best result. It is shown that if the interbeam delay is one symbol interval on a slowly varying, two-beam channel, and maximum likelihood sequence estimation has a performance that attains Mazo's (1991) matched filter lower bound, even when the root-Nyquist receiver filter is only matched to its transmitter filter counterpart and not to the complete channel response     

Sequence estimation over the slow nonselective Rayleigh fadingchannel with diversity reception and its application to Viterbi decoding

The authors consider minimum error probability detection of a data sequence transmitted using linear-suppressed carrier modulations, specifically phase-shift keying (PSK), over the Gaussian channel with slow nonselective Rayleigh fading. Complete channel interleaving/deinterleaving and diversity reception are assumed. The problem is considered with application to Viterbi decoding in particular. It is first shown that the two presently available receivers, namely, the conventional maximum likelihood (ML) receiver and the simultaneous estimation receiver, do not perform adequately for this problem. A two-stage receiver is proposed in which the unknown channel fading gains are estimated in the first stage prior to data sequence estimation in the second stage. This receiver is shown to perform adequately, and leads to an efficient receiver/decoder for Viterbi decoding of convolutionally trellis-coded sequences. The issue of optimum estimation of channel fading gains is clarified. The bit error probability of the receiver/decoder is analyzed, and numerical performance results are presented     

Adaptive joint multiuser detection and channel estimation in multipath fading CDMA channels

The problem of joint multiuser detection and channel estimation in frequency-selective Rayleigh fading CDMA channels is considered. First the optimal multiuser detector for such channels is derived, which is seen to have a computational complexity exponential in the product of the number of users and the length of the transmitted data sequence. Two suboptimal detectors are then developed and analyzed, both of which employ decorrelating filters at the front-ends to eliminate the multiple-access interference and the multipath interference. The symbol-by-symbol detector uses a Kalman filter and decision feedback to track the fading channel for diversity combining. The per-survivor sequence detector is in the form of the Viterbi algorithm with the trellis updates being computed by a bank of Kalman filters in the per-survivor fashion. Both suboptimal detectors require the knowledge of all waveforms of all users in the channel and the channel fading model parameters. Adaptive versions of these suboptimal detectors that require only the knowledge of the waveform of the user of interest are then developed. The adaptive receivers employ recursive-least-squares (RLS) minimum-mean-square-error (MMSE) filters at the front-end to mitigate the interference, and use a bank of linear predictors to track the fading channels. It is shown that the front-end RLS-MMSE filters can be implemented using systolic arrays to exploit massively parallel signal processing computation, and to achieve energy efficiency. Finally, the performance of the suboptimal detectors and their adaptive versions are assessed by simulations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Clustering-Based Adaptive Channel Estimator for Optical Fiber Communication Systems

In this letter, a new clustering-based adaptive channel estimator is proposed for optical fiber communication systems with the maximum-likelihood sequence estimation (MLSE) receiver. The estimator is very effective in estimating the key channel parameters needed by the Viterbi processor without assuming that the channel memory length is known a priori to the receiver. Moreover, the application of the proposed channel estimator can induce a complexity-reduced MLSE receiver.     

Multiuser receivers for CDMA systems in Rayleigh fading channels

Multiuser demodulation in relatively fast fading channels is analyzed. The optimal maximum likelihood sequence detection (MLSD) receiver is derived and a general suboptimal receiver to approximate the MLSD is proposed. The performance of the parallel interference cancellation (PIC) and decorrelating receivers is compared. The PIC receiver is demonstrated to achieve better performance in known channels than the decorrelating receiver, but it is observed to be more sensitive to the channel coefficient estimation errors than the decorrelator. At high channel loads the PIC receiver suffers from bit error rate (BER) saturation, whereas the decorrelating receiver does not. The performance of data-aided (DA) and decision-directed (DD) multiuser channel estimation is also compared. DA channel estimation is shown to be more robust than DD channel estimation, which may suffer from BER saturation caused by hangups at high signal-to-noise ratios (SNRs). The impact of channel estimation filter impulse response on the BER is studied by comparing optimal and suboptimal channel estimation filters. The implementation complexity of the decorrelating and PIC receivers is compared in terms of required floating point operations and clock cycles in a practical communication scenario. It is observed that the PIC receiver is only moderately more complex to implement than the conventional matched filter bank receiver, whereas the decorrelating receiver is significantly more complex     

Nonrecursive decoding algorithm for PR4 channel

The Viterbi algorithm (VA) is a recursive optimal solution to the state sequence estimation problem. The recursive nature of this algorithm puts limitations on high-speed implementations of Viterbi decoders. The authors propose a nonrecursive suboptimal decoding algorithm for the PR4 channel. The new decoder has negligible performance loss     

Nonrecursive decoding algorithm for PR4 channel

The Viterbi algorithm (VA) is a recursive optimal solution to the state sequence estimation problem. The recursive nature of this algorithm puts limitations on high-speed implementations of Viterbi decoders. The authors propose a nonrecursive suboptimal decoding algorithm for the PR4 channel. The new decoder has negligible performance loss     

Robust MSE equalizer design for MIMO communication systems in the presence of model uncertainties

This paper considers a robust mean-square-error (MSE) equalizer design problem for multiple-input multiple-output (MIMO) communication systems with imperfect channel and noise information at the receiver. When the channel state information (CSI) and the noise covariance are known exactly at the receiver, a minimum-mean-square-error (MMSE) equalizer can be employed to estimate the transmitted signal. However, in actual systems, it is necessary to take into account channel and noise estimation errors. We consider here a worst-case equalizer design problem where the goal is to find the equalizer minimizing the equalization MSE for the least favorable channel model within a neighborhood of the estimated model. The neighborhood is formed by placing a bound on the Kullback-Leibler (KL) divergence between the actual and estimated channel models. Lagrangian optimization is used to convert this min-max problem into a convex min-min problem over a convex domain, which is solved by interchanging the minimization order. The robust MSE equalizer and associated least favorable channel model can then be obtained by solving numerically a scalar convex minimization problem. Simulation results are presented to demonstrate the MSE and bit error rate (BER) performance of robust equalizers when applied to the least favorable channel model.     

一种低复杂度聚类估计MLSE均衡器

给出了一种新的聚类估计最大似然序列均衡器(CBSE),避开了传统MLSE均衡需要估计信道脉冲响应(CIR)和卷积运算,由接收信号估计聚类中心,同时利用聚类中心之间的对称性,仅需估计其中部分中心,其余中心可通过简单运算获取,从而在缩短训练序列的同时减少了运算量.仿真表明,新方法在取得与RLS均衡器相近收敛性能的同时,计算量比LMS均衡器小.     

Parallel structures for joint channel estimation and data detectionover fading channels

Joint data and channel estimation for mobile communication receivers can be realized by employing a Viterbi detector along with channel estimators which estimate the channel impulse response. The behavior of the channel estimator has a strong impact on the overall error rate performance of the receiver. Kalman filtering is an optimum channel estimation technique which can lead to significant improvement in the receiver bit error rate (BER) performance. However, a Kalman filter is a complex algorithm and is sensitive to roundoff errors. Square-root implementation methods are required for robustness against numerical errors. Real-time computation of the Kalman estimator in a mobile communication receiver calls for parallel and pipelined structures to take advantage of the inherent parallelism in the algorithm. In this paper different implementation methods are considered for measurement update and time update equations of the Kalman filter. The unit-lower-triangular-diagonal (LD) correction algorithm is used for the time update equations, and systolic array structures are proposed for its implementation. For the overall implementation of joint data and channel estimation, parallel structures are proposed to perform both the Viterbi algorithm and channel estimation. Simulation results show the numerical stability of different implementation techniques and the number of bits required in the digital computations with different estimators     

The Choice of the Desired Impulse Response in Combined Linear-Viterbi Algorithm Equalizers

Equalizer structures using the Viterbi Algorithm achieve at least order of magnitude performance improvement over linear equalizers on some intersymbol interference channels. Using a linear equalizer to shape the original channel impulse response to some shorter desired impulse response (DIR) is a technique which reduces the complexity of the Viterbi Algorithm equalizer. This paper looks at three techniques for choosing a DIR. These are choosing the DIR by truncation, minimum mean square error and matching the power spectrum to that of the original channel. Using effective signal to noise ratio as the figure of merit for comparison, results are given for one particular channel.     

A reduced-state Viterbi receiver with prefiltering for the mobile radio channel

This paper presents a possible receiver structure for high bit rate transmission on the mobile radio channel. The receiver is based on a reduced-state Viterbi algorithm combined with decision feedback, known as Decision Feedback Sequence Estimation. A tdma concept using a training sequence for channel estimation and continuous phase modulation is assumed. For channel estimation a least squares method is studied, and an adaptive prefilter is used to improve the receiver performance on minimum phase channels. Estimates on the computational complexity of the receiver and simulation results showing the performance on a typical urban (tu) channel are presented. The results show that the prefilter improves the performance of the receiver significantly when a small number of states is used in the Viterbi algorithm. However, the computational complexity for 2 Mbit/s continuous transmission is very high.     

Set-membership adaptive equalization and an updator-sharedimplementation for multiple channel communications systems

This paper considers the problems of channel estimation and adaptive equalization in the novel framework of set-membership parameter estimation. Channel estimation using a class of set-membership identification algorithms known as optimal bounding ellipsoid (OBE) algorithms and their extension to tracking time-varying channels are described. Simulation results show that the OBE channel estimators outperform the least-mean-square (LMS) algorithm and perform comparably with the RLS and the Kalman filter. The concept of set-membership equalization is introduced along with the notion of a feasible equalizer. Necessary and sufficient conditions are derived for the existence of feasible equalizers in the case of linear equalization for a linear FIR additive noise channel. An adaptive OBE algorithm is shown to provide a set of estimated feasible equalizers. The selective update feature of the OBE algorithms is exploited to devise an updator-shared scheme in a multiple channel environment, referred to as updator-shared parallel adaptive equalization (USHAPE). U-SHAPE is shown to reduce the hardware complexity significantly. Procedures to compute the minimum number of updating processors required for a specified quality of service are presented     

一种用于无线信道的逐幸存处理均衡器

提出了一种适用于无线时变信道的逐幸存处理均衡器。通过训练序列得到信道参数的初始估计值,此后在Viterbi算法进行网格搜索的过程中,使得每一条幸存路径维持各自的信道参数,并在确定幸存分支后利用历史幸存序列对信道参数值进行更新,实现了信道参数的无时延估计。仿真结果表明,在无线时变信道环境下,逐幸存处理均衡器的性能明显优于其他传统均衡器。     

Using denoising at the receiver front-end for frequency-selective channels

This article proposes the use of denoising techniques at the receiver front-end in order to combat the effects of additive noise in digital transmission over frequency-selective channels. The proposed technique does not require knowledge of the channel impulse response, and is, therefore, potentially suitable for application in several receiver structures, including those with blind equalizers and adaptive receivers for mobile communications.     

Performance of Volterra and MLSD receivers for nonlinearband-limited satellite systems

This paper evaluates the performance of Volterra equalizers and maximum-likelihood sequence detection (MLSD) receivers for compensation of signal distortion in nonlinear band-limited satellite systems. In addition, the performance of a receiver with a fractionally-spaced equalizer followed by a Volterra equalizer is studied (FSE-Volterra equalizer). For the equalizers, adaptation of the equalizer weights is considered including a multiple-step LMS algorithm which improves the convergence characteristics. Two MLSD receiver structures are considered: the optimum receiver consisting of a matched-filter bank followed by a Viterbi (1967) detector and a suboptimum receiver consisting of a single receiver filter followed by a Viterbi detector. The performance of the MLSD receivers is then compared to that of the equalizers