Novel Techniques to Minimize the Error Propagation of Decision Feedback Equalizer in 8VSB DTV System

In this paper, novel and yet simple techniques are presented to minimize the error propagation caused by the large precursors and postcursors of the decision feedback equalizer (DFE) in 8VSB DTV system. A technique that selects a reference tap (symbol timing of DFE) from an estimated channel impulse response (CIR) is presented to minimize the effect of the large precursors. Another technique that selects the reference tap position, i.e., decision delay in a feedforward filter (FFF), from the estimated CIR and the amplitude of the selected reference tap is proposed to minimize the effect of large postcursors. The combined structure of a feedback filter (FBF) and Viterbi decoder for use in 8VSB DTV system is also proposed to replace the past unreliable decision symbols in FBF as well as to reduce the decision error probability. Simulation results show that our proposed DFE can prevent effectively the error propagation, in particular, by changing the reference tap and its position in FFF according to the channel condition. It is also shown that an echo removing capability of the proposed DFE, where 400 and 620taps are used for the FFF and FBF, respectively, is greater than that of conventional DFEs by about -20 mus in the single pre-echo of -10 dB channel and by about 10 mus in the single post-echo of -1 dB channel     

Adaptive feedforward/feedback architectures for multiuser detectionin high data rate wireless CDMA networks

We consider the design and performance of nonlinear minimum mean-square-error multiuser detectors for direct sequence code-division multiple-access (CDMA) networks. With multiple users transmitting asynchronously at high data rates over multipath fading channels, the detectors contend with both multiple-access interference (MAI) and intersymbol interference (ISI). The cyclostationarity of the MAI and ISI is exploited through a feedforward filter (FFF), which processes samples at the output of parallel chip-matched filters, and a feedback filter (FBF), which processes detected symbols. By altering the connectivity of the FFF and FBF, we define four architectures based on fully connected (FC) and nonconnected (NC) filters. Increased connectivity of the FFF gives each user access to more samples of the received signal, while increased connectivity of the FBF provides each user access to previous decisions of other users. We consider three methods for specifying the FFF sampling and propose a nonuniform FFF sampling scheme based on multipath ray tracking that can offer improved performance relative to uniform FFF sampling. For the FC architecture, we capitalize on the sharing of filter contents among users by deriving a multiuser recursive least squares (RLS) algorithm and direct matrix inversion approach, which determine the coefficients more efficiently than single-user algorithms. We estimate the uncoded bit-error rate (BER) of the feedforward/feedback detectors for CDMA systems with varying levels of power control and timing control for multipath channels with quasi-static Rayleigh fading. Simulations of packet-based QPSK transmission validate the theoretical BER analysis and demonstrate that the multiuser RLS adapted detectors train in several hundred symbols and avoid severe error propagation during data transmission mode     

Adaptive compensation techniques for communications systems with Tomlinson-Harashima precoding

To improve compensation to channel or interference changes, we propose adapting an auxiliary feedback filter (FBF) in the receiver of systems which use Tomlinson-Harashima (1971, 1972) precoding. We show how the auxiliary FBF can be adapted in conjunction with the receiver feedforward filter (FFF). Simulations demonstrate the performance advantage of our auxiliary FBF technique relative to FFF updating alone, and how the FFF combines interference suppression with despreading in wideband applications. Error propagation can be effectively avoided by using the auxiliary FBF values to decide when to update the precoder, while transient increases in mean-squared error are avoided by using the FBF values in the update equation.     

利用确定性信道盲估计改善DFE均衡器的收敛特性

针对一种全盲的判决反馈均衡器(DFE)进行研究,它对快速时变信道的均衡非常有效。利用基于二阶统计量(SOS)的子空间法来得到关于信道系数的确定性估计,然后利用这个估计值求出DFE抽头系数在MMSE意义上的最优解,以此进行DFE的初始化。相比传统的利用周期性训练序列初始化DFE的方法,文章提出的方法不仅节省了带宽资源,而且对于信道的突发性时变能够自适应地重新初始化,从而避免了DFE均衡器的病态收敛。     

Error-rate evaluation of linear equalization and decision feedbackequalization with error propagation

We propose applying an approximate Fourier series to evaluate efficiently the bit-error-rate (BER) performance of finite-length linear equalization (LE) and decision feedback equalization (DFE). By extending the Fourier series, we enable BER calculations for quadrature phase-shift keying (QPSK) transmission on complex channels with in-phase and crosstalk intersymbol interference (ISI). The BER calculation is based on determining the residual ISI samples and background Gaussian noise variance at the equalizer output for static channels or for realizations of quasi-static fading channels. A simple bound on the series error magnitude in terms of the Fourier series parameters ensures the required accuracy and precision. Improved state transition probability estimates are derived and verified by simulation for an approximate Markov model of the DFE error propagation for the case in which residual ISI exists even when the previous decisions stored in the feedback filter (FBF) are correct. We demonstrate the ease and widespread applicability of our approach by producing results which elucidate a variety of equalization tradeoffs. Our analysis includes symbol-spaced and fractionally spaced minimum mean-square error (MMSE)-LE, zero-forcing (ZF)-LE, and MMSE-DFE (with and without error propagation) on static ISI channels and multipath channels with quasi-static Rayleigh fading; a comparison between suboptimum and optimum receiver filtering in conjunction with equalization; and an assessment of the accuracy of some widely used equalization BER approximations and bounds     

Pole-zero decision feedback equalization with a rapidly convergingadaptive IIR algorithm

A decision feedback equalizer (DFE) containing a feedback filter with both poles and zeros is proposed for high-speed digital communications over the subscriber loop. The feedback filter is composed of a relatively short FIR filter that cancels the initial part of the channel impulse response, which may contain rapid variations due to bridge taps, and a pole-zero, or IIR, filter that cancels the smoothly decaying tail of the impulse response. Modifications of an adaptive IIR algorithm, based on the Steiglitz-McBride (1965) identification scheme, are proposed to adapt the feedback filter. A measured subscriber loop impulse response is used to compare the performance of the adaptive pole-zero DFE, assuming a two-pole feedback filter, with a conventional DFE having the same number of coefficients. Results show that the pole-zero DFE offers a significant improvement in mean squared error relative to the conventional DFE. The speed convergence of the adaptive pole-zero DFE is comparable to that of the conventional DFE using the standard least mean square (LMS) adaptive algorithm     

Realizable linear and decision feedback equalizers: properties and connections

Recently, there has been renewed interest in the use of infinite impulse response (IIR) linear equalizers (LEs) for digital communication channels as a means for both improving performance and blindly initializing decision feedback structures (DFEs). Theoretical justification for such an approach is usually given assuming unconstrained filters, which are not causal and therefore not implementable in practice. We present an analysis of realizable (i.e., causal, stable, and of finite degree) minimum mean square error (MMSE) equalizers for single-input multiple-output channels, both in the LE and DFE cases, focusing on their structures and filter orders, as well as the connections between them. The DFE resulting from rearranging the MMSE LE within a decision feedback loop is given special attention. It is shown that although this DFE does not in general coincide with the MMSE DFE, it still enjoys certain optimality conditions. The main tools employed are the Wiener theory of minimum variance estimation and Kalman filtering theory, which show interesting properties of the MMSE equalizers not revealed by previous polynomial approaches.     

Digital Subscriber Line Terminals for Use with Correlated Line Codes

This paper is a mathematical analysis of digital subscriber lines that use adaptive decision feedback equalization (DFE). Adaptive transversal feedforward filters (FFF) and feedback filters (FBF) with baud rate sampling are assumed. In order that all block codes are considered in the model, correlation between the values of the transmitted symbol values is included. Additionally, added noise is not assumed to be white, to permit the eyaluation of the effects of near end crosstalk and residual echo noise. It is shown that the correlation between the transmitted symbols causes the FBF to adapt differently than they usually do (i.e., cancel intersymbol interference within the range of the FBF) in two ways: the FBF uses the correlation between transmitted symbols to reduce the intersymbol interference outside of its range, and a bias vector is added to the FBF tap weights that adjusts future slicing levels to account for the variable likelihood of future transmitted symbol values. It is found that the received signal-to-noise ratio is approximately a linear function of loop insertion loss when the loss is high and noise is low.     

Spatial and temporal equalization for broadband wireless indoornetworks at millimeter waves

The combined use of adaptive antennas and decision feedback equalization (DFE) is analyzed in a realistic propagation scenario at millimeter waves, taking the direction of arrivals (DOA's) of the received paths into account. The joint antennas and DFE scheme, with one forward filter for each antenna and a single feedback filter (FBF), can be viewed as a spatial and temporal DFE (ST-DFE). The performance of this solution is compared with the cascade of adaptive antenna used for beamforming and DFE. It is found that ST-DFE achieves better performance since it combines the beamforming capability of the antenna array with the equalization properties of the DFE, with great advantages especially when rays arrive from similar angles. The mean square error (MSE) is analytically derived for infinitely long filters in a quasi-static environment with multiple rays having different DOAs, and compared (for the two-path model) with simulation results assuming filters with a small number of taps. Finally, service availability through coverage evaluation is developed and compared with that of a coded-orthogonal frequency division multiplexing (C-OFDM) system     

High-Performance VLSI Architecture of Decision Feedback Equalizer for Gigabit Systems

This brief addresses the design of a decision feedback equalizer (DFE) for gigabit throughput rate. It is well known that the feedback loop in a DFE limits an upper bound of the achievable speed. For a$L$-tap feedbackward filter (FBF) and$M$-pulse amplitude modulation, Parhi (1991) and Kasturia and Winters (1991) reformulated the FBF as a$(M) ^L$-to-1 multiplexer. Due to the reformulation, the overhead of extra adders and extra multiplexers are as large as$(M) ^L$. The required hardware overhead should be more severe when the DFE is implemented in parallel. In this brief, we propose two new approaches to implement the DFE when gigabit throughput rate is desired. The first approach is partial pre-computation scheme, which can trade-off between hardware complexity and computational speed. The second approach is two-stage pre-computation scheme, which can be applied to higher speed applications. In the later case, we can reduce the hardware overhead to about$2(M) ^(-L/2)$times of , , and the iteration bound is$(log _2 W+2)/(L/2+1)+(log _2 M)$multiplexer-delays, where$W$is the wordlength of weight coefficient of a FBF. We demonstrate the proposed architectures by apply it to the 10 Gbase-LX4 optical communication systems.     

Fast initialization of equalizers for VSB-based DTV transceivers in multipath channel

This paper proposes a fast initialization technique for equalization of 8-VSB-based digital television (DTV) signal in severe multipath channels. We consider the use of a modified decision feedback equalizer (MDFE) , for fast initialization. The feedback filter (FBF) of the MDFE can be initialized simply by estimating the channel impulse response and only the feedforward filter (FFF) of the MDFE need training for initialization. To overcome the shortage of the training sequence in the VSB DTV signal, we propose a new initialization method by generating a virtual training signal to initialize the FFF of the MDFE. Simulation results show that the proposed scheme can fast initialize the equalizer using less than 5000 symbols, while providing the receiver performance comparable to that of conventional schemes.     

An adaptive RAM-DFE for storage channels

A modification of the decision feedback equalizer (DFE), RAM-DFE, is presented and analyzed for use in channels with trailing nonlinear intersymbol interference, especially binary saturation-recording channels. In the RAM-DFE, a look-up table, which can be easily implemented with random access memory, (RAM), replaces the transversal filter feedback section of the DFE. The feedforward section of the equalizer remains linear. A general nonlinear Markov (or finite-state machine) model is used to model the nonlinear intersymbol interference (ISI) channel. With this Markov model, a method is introduced for computing the minimum-mean-squared-error settings of the feedforward filter coefficients and the feedback filter and look-up table contents for the linear DFE and the RAM-DFE, respectively. RAM-DFE with these settings can be significantly better than the linear DFE for channels with trailing nonlinear ISI. Globally convergent gradient-type algorithms for updating the feedforward section coefficients and the contents of the feedback table are introduced and analyzed. Results based on data taken from disk storage units are discussed     

Adaptive DFE Multiuser Receiver for CDMA Systems using Two-Step LMS-Type Algorithm: An Equalization Approach

This paper presents an adaptive decision feedback equalizer (DFE) based multiuser receiver for code division multiple access (CDMA) systems over smoothly time-varying multipath fading channels using the two-step LMS-type algorithm. The frequency-selective fading channel is modeled as a tapped-delay-line filter with smoothly time-varying Rayleigh-distributed tap coefficients. The receiver uses an adaptive minimum mean square error (MMSE) multiuser channel estimator based on the reduced Kalman least mean square (RK-LMS) algorithm to predict these tap coefficients (Kohli and Mehra, Wireless Personal Communication 46:507–521, 2008). We propose the design of adaptive MMSE feedforward and feedback filters by using the estimated channel response. Unlike the previously available Kalman filtering algorithm based approach (Chen and Chen, IEEE Transactions on Signal Processing 49:1523–1532, 2001), the incorporation of RK-LMS algorithm reduces the computational complexity of multiuser receiver. The computer simulation results are presented to show the substantial improvement in its bit error rate performance over the conventional LMS algorithm based receiver. It can be inferred that the proposed multiuser receiver proves to be robust against the nonstationarity introduced due to channel variations, and it is also beneficial for the multiuser interference cancellation and data detection in CDMA systems.     

Realizable MIMO decision feedback equalizers: structure and design

We present and discuss the structure and design of optimum multivariable decision feedback equalizers (DFEs). The equalizers are derived under the constraint of realizability, that is, causal and stable filters and finite decision delay. The design is based on a known dispersive discrete-time multivariable channel model with infinite impulse response. The additive noise is described by a multivariate ARMA model. Equations for obtaining minimum mean square error (MMSE) and zero-forcing DFEs are derived under the assumption of correct past decisions. The design of a realizable MMSE DFE requires the solution of a linear system of equations in the model parameters. No spectral factorization is required. We derive novel necessary and sufficient conditions for the existence of zero-forcing DFEs and point out the significance of these conditions for the design of multiuser detectors. An optimal MMSE DFE will contain IIR filters in general. Simulations indicate that the performance improvement obtained with an IIR DFE is reduced more than for a (suboptimal) FIR DFE when error propagation is taken into account since the use of IIR feedback filters tends to worsen the error propagation     

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     

一种基于二次规划计算DFE系数的新方法

判决反馈均衡器(DFE)是一种常见的均衡器类型,在实际中得到了广泛应用。对于采用最小均方误差(MMSE)准则设计的DFE,其系数计算一般利用正交原理推导获得。该文推导了一种新颖的基于二次规划方法计算MMSE准则下DFE系数的方法。仿真表明,该文所提方法与传统方法计算得到的结果是一致的,并且由于运用矩阵运算,在一定程度上简化了计算。     

Decision feedback equaliser design using support vector machines

The conventional decision feedback equaliser (DFE) that employs a linear combination of channel observations and past decisions is considered. The design of this class of DFE is to construct a hyperplane that separates the different signal classes. It is well known that the popular minimum mean square error (MMSE) design is generally not the optimal minimum bit error rate (MBER) solution. A strategy is proposed for designing the DFE based on support vector machines (SVMs). The SVM design achieves asymptotically the MBER solution and is superior in performance to the usual MMSE solution. Unlike the exact MBER solution, this SVM solution can be computed very efficiently     

Minimum mean-squared error decision-feedback equalization fordigital subscriber line transmission with possibly correlated line codes

The author presents a theory on MMSE (minimum mean-squared error) decision-feedback equalization which augments previously published results by allowing both a correlated symbol sequence and a fractionally spaced DFE (decision-feedback equalizer) forward filter. This theory facilitates calculating the potential DSL (digital subscriber line) transmission performance in cases of correlated line codes, especially for situations where one or both of the DFE filters are infinite in length. The situation of an infinite-length DFE is of interest because it provides information on the limit of MMSE equalization and can thus serve as a benchmark against which the performance of a finite-length DFE may be compared. The author also presents a few numerical examples of the performance of MMSE decision-feedback equalization in DSL transmission at ISDN (integrated services digital network) basic access rates with several well-known line codes     

Combined trellis coding and DFE through Tomlinson precoding

The authors propose and evaluate a receiver architecture which combines the power of a decision feedback equalizer (DFE) with trellis coding, while allowing for minimal decoding delay in such a way that the total gain of the system is additive. The system is based on a structure that transposes the feedback filter of the DFE into the transmitter and, for high-order constellations, provides negligible increase in transmitter power. The first known hardware realization of a high bit rate digital subscriber line (HDSL) system that achieves the coding gain provided by a trellis code in addition to the equalization gain provided by the DFE is presented. A system whose complexity of implementation is comparable to that of a typical DFE and an independent Viterbi decoder is proposed     

Performance of a hybrid decision feedback equalizer structure forCAP-based DSL systems

We study the performance of a class of derision feedback equalizer (DFE) structures for high-speed digital transmission systems. We first present mathematical formulation of minimum mean-square error (MMSE) and the optimum tap coefficients for various finite-length phase-splitting equalizers over the loop in the presence of colored noise, such as near-end crosstalk (NEXT) and far-end crosstalk (FEXT). The performance of the equalizers is also analyzed in the presence of narrowband interference and the channel reflections introduced by bridged taps. The hybrid-type DFE (H-DFE) is presented as a practical equalizer structure for these applications. The results of analysis show that the H-DFE has advantages in the performance and/or in the implementation complexity as compared with the existing DFE structures. An additional advantage of the H-DFE is in the transmission systems that employ the precoding technique. The precoding for the H-DFE allows the system to track small changes in the channel