基于正交小波的判决反馈均衡算法

本文提出了一种基于正交小波的线性均衡算法，用一组规范正交小波及其对应的系数来表示均衡器，在此基础上，提出基于正交小波的判决反馈均衡算法，文中给出了自适应算法，并对算法性能做了分析，采用这种结构的均衡算法，比传统的基于ＬＭＳ算法的线性均衡器和判决反馈均衡器收敛速度快，误码性能相同，而计算量增加不多，计算机模拟也证实了上述结论。     

Adaptive combined DFE/MLSE techniques for ISI channels

By embedding a decision-feedback equalizer (DFE) into the structure of a maximum-likelihood sequence estimator (MLSE), an adaptive combined DFE/MLSE scheme is proposed. In this combined DFE/MLSE, the embedded DFE has three functions: (i) prefiltering the received signals and truncating the equivalent channel response into the desired one, (ii) compensating for channel distortions, and (iii) providing the MLSE detector with predicted values of input signals. Since the embedded MLSE detector operates on the predicted signals the detected symbols at the output of the DFE/MLSE do not suffer any delay and can be directly fed back into the embedded DFE so that the error propagation, which usually takes place in a conventional DFE, can be greatly reduced. Analytical and simulation results indicate that the performance is significantly improved by the DFE/MLSE compared to the conventional DFE while its computation complexity is much less than that of the conventional MLSE receiver. The combined DFE/MLSE can use different adaptive structures (block-updating, sliding window updating or symbol-by-symbol updating) to meet different performance objectives. Moreover, the proposed DFE/MLSE provides a trade-off between performance and complexity with a parameter m representing the MLSE detection depth as well as the number of predicting steps of the embedded DFE. For some particular values of m, this scheme is capable of emulating the conventional DFE, MLSE-VA, adaptive LE-MLSE equalizer, adaptive DDFSE, and adaptive BDFE without detection delay     

A mixed-signal decision-feedback equalizer that uses a look-aheadarchitecture

A mixed-signal decision-feedback equalizer (DFE) that uses a look-ahead architecture is described. The parallelism in the look-ahead DFE (LA DFE) achieves an increase in the data rate over a conventional DFE with a small increase in area. Fully differential analog circuits perform the convolution operation in the LA DFE, and the coefficient adaption is carried out by digital circuits. The LA DFE occupies 23 mm ² in a 2-μm CMOS process and operates at 50 Mb/s while dissipating 260 mW     

运用误差反馈的判决反馈均衡器的性能分析

判决反馈均衡器（Decision Feedback Equalizer，DFE）能补偿具有严重符号间干扰（Inter Symbol Interference，ISI）的信道，且不存在线性均衡器增强噪声的影响。而在其基础上改进的运用误差反馈的DFE，可利用误差反馈滤波器来减少传统DFE中存在的误差信号的相关性，同时其硬件实现的复杂度没有明显提高。理论分析和仿真表明，这种方法比传统的DFE更有效，特别是针对信道有严重符号间干扰的情况。     

Adaptive Lattice Decision-Feedback Equalizers--Their Performance and Application to Time-Variant Multipath Channels

This paper presents two types of adaptive lattice decisionfeedback equalizers (DFE), the least squares (LS) lattice DFE and the gradient lattice DFE. Their performance has been investigated on both time-invariant and time-variant channels through computer simulations and compared to other kinds of equalizers. An analysis of the self-noise and tracking characteristics of the LS DFE and the DFE employing the Widrow-Hoff least mean square adaptive algorithm (LMS DFE) are also given. The analysis and simulation results show that the LS lattice DFE has the faster initial convergence rate, while the gradient lattice DFE is computationally more efficient. The main advantages of the lattice DFE's are their numerical stability, their computational efficiency, the flexibility to change their length, and their excellent capabilities for tracking rapidly time-variant channels.     

Tentative chip decision-feedback equalizer for multicode wideband CDMA

We investigate a chip-level minimum mean-square-error (MMSE) decision-feedback equalizer (DFE) for the downlink receiver of multicode wideband code-division multiple-access systems over frequency-selective channels. First, the MMSE per symbol achievable by an optimal DFE is derived, assuming that all interchip interference (ICI) of the desired user can be eliminated. The MMSE of DFE is always less than or at most equal to that of linear equalizers (LE). When all the active codes belong to the desired user, the ideal DFE is able to eliminate multicode interference (MCI) and approach the performance of the single-code case at high signal-to-noise ratio (SNR) range. Second, we apply the hypothesis-feedback equalizer or tentative-chip (TC)-DFE in the multicode scenario. TC-DFE outperforms the chip-level LE, and the DFE that only feeds back the symbols already decided. The performance gain increases with SNR, but decreases with the number of active codes owned by the other users. When all the active codes are assigned to the desired user, TC-DFE asymptotically eliminates MCI and achieves single-user (or code) performance at high SNR, similarly, to the ideal DFE. The asymptotic performance of the DFE is confirmed through bit error rate simulation over various channels.     

Cyclostationary crosstalk suppression by decision feedbackequalization on digital subscriber loops

Interference from digital signals in multipair cables has been shown to be cyclostationary under some conditions. This work evaluates the performance of a decision feedback equalizer (DFE) in the presence of cyclostationary interference (CI), intersymbol interference (ISI), and additive white noise (AWN). A comparison between a DFE with CI and one with stationary interference (SI) shows the ability of the DFE to substantially suppress CI. Fractionally spaced and symbol-rate DFE equalizers are also compared and the former is found to yield better performance, especially in the presence of CI. The use of a symbol-rate DFE using an adaptive timing technique that finds the receiver's best sampling phase is proposed for when the fractionally spaced DFE cannot be used because of its complexity. The results also demonstrate the potential benefits of synchronizing central office transmitter clocks, if a fractionally spaced DFE is used at the receiver     

Introducing erasures in decision-feedback equalization to reduceerror propagation

A simple modification of the decision feedback equalizer (DFE) slicer is proposed to reduce the effect of error propagation. A comparison of the performance of the modified DFE and conventional DFE is made for specific channels. On these channels, the modified DFE performs only marginally better than the conventional DFE in terms of average error probability, but may offer some advantages in terms of error probability conditioned on specific input sequences and in terms of the distribution of error burst lengths. Some examples are given, concerning binary PAM and multilevel quadrature amplitude modulation (M-QAM) systems     

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     

Decision Feedback Equalization for Multipath Induced Interference in Digital Microwave LOS Links

The performance of a 49-QPRS, 90 Mbit/s digital radio receiver equipped with a decision feedback equalizer (DFE) to counter multipath fading is investigated via computer simulation. The simulation includes the transmitted data, multipath fade model, receiver model, and DFE. The results indicate that a DFE equipped with five forward and five feedback taps can adequately compensate a 40 dB minimum-phase fade anywhere in the receiver passband. The study is extended to other receiver configurations including the use of space diversity and/or slope equalizers and the use of a transversal equalizer (TE) with the same delay-span in place of the DFE. The results indicate that the DFE equipped receiver outperforms the TE receiver and that still better performance may be achieved using a combination of space diversity and DFE.     

On the Decision-Feedback Equalizer in Optically Amplified Direct-Detection Systems

This paper investigates the combined feed-forward and decision-feedback equalizer (DFE) in a lightwave system with optical amplifiers and a direct-detection receiver. Based on a nonlinear channel model, the paper provides a modification of the classical minimum mean square error theory of the DFE. Furthermore, an analytical method that is capable of accurate bit error rate (BER) evaluation is used to optimize the DFE for minimum BER. The paper evaluates the DFE performance for both optical ON-OFF keying and duobinary modulation formats in the presence of chromatic dispersion as well as the DFE performance for the mitigation of higher order polarization mode dispersion in first-order compensated systems. The paper shows that the DFE can compensate for the BER degradation due to narrow-band receiver-side optical filtering and can significantly improve the spectral efficiency of dense wavelength-division multiplexed systems.     

Adaptive turbo reduced-rank equalization for MIMO channels

An adaptive iterative (turbo) decision-feedback equalizer (DFE) for channels with intersymbol interference (ISI) is presented. The filters are computed directly from the soft decisions and received data to minimize a least-squares (LS) cost function. Numerical results show that this method gives a substantial improvement in performance relative to a turbo DFE computed from an exact channel estimate, assuming perfect feedback. Adaptive reduced-rank estimation methods are also presented, based on the multistage Wiener filter (MSWF). The adaptive reduced-rank turbo DFE for single-input/single-output channels is extended to multiple-input/multiple-output (MIMO) channels with ISI and multiple receive antennas. Numerical results show that for MIMO channels with limited training, the reduced-rank turbo DFE can perform significantly better than the full-rank turbo DFE.     

Optimized decision-feedback equalization for convolutional coding with reduced delay

Error propagation is a significant problem with the decision-feedback equalizer (DFE) at low-to-moderate signal-to-noise ratios. In particular, when a DFE is concatenated with a convolutional code, the burst errors associated with error propagation can severely degrade performance, since the convolutional code is optimized for the additive white Gaussian noise channel. In this paper, we explore the compensation of error propagation in the DFE so as to break up error bursts and improve performance with convolutional codes, without incurring larger overall decoding delay. We propose certain stationary error models and derive a modified DFE (MDFE) based on these models which can compensate for the error propagation. The MDFE differs from the conventional DFE only in its tap values. The incorporation of the bias into the model and the removal of the bias during the design process is discussed. Simulations explore the performance of the MDFE for both uncoded and convolutionally coded systems. With coding, the MDFE can significantly improve on the conventional DFE in terms of bit-error rate, and the MDFE without interleaving can improve on the conventional DFE with interleaving in terms of decision delay.     

Near‐Optimum Blind Decision Feedback Equalization for ATSC Digital Television Receivers

This paper presents a near‐optimum blind decision feedback equalizer (DFE) for the receivers of Advanced Television Systems Committee (ATSC) digital television. By adopting a modified trellis decoder (MTD) with a trace‐ back depth of 1 for the decision device in the DFE, we obtain a hardware‐efficient, blind DFE approaching the performance of an optimum DFE which has no error propagation. In the MTD, the absolute distance is used rather than the squared Euclidean distance for the computation of the branch metrics. This results in a reduction of the computational complexity over the original trellis decoding scheme. Compared to the conventional slicer, the MTD shows an outstanding performance improvement in decision error probability and is comparable to the original trellis decoder using the Euclidean distance. Reducing error propagation by use of the MTD in the DFE leads to the improvement of convergence performance in terms of convergence speed and residual error. Simulation results show that the proposed blind DFE performs much better than the blind DFE with the slicer, and the difference is prominent at the trellis decoder following the blind DFE.     

Parallel adaptive decision feedback equalizers

Several algorithms for parallel implementation of adaptive decision feedback equalizers (DFEs) are proposed. The first is a double-row DFE algorithm that outperforms previous approaches. Under the no-error-propagation assumption, the algorithm will perform exactly like a serially adapting DFE. The multiplication complexity of the double-row DFE algorithm is of the same order as that of the parallel DFE algorithm and the extended least-mean-square (LMS) method. The previous algorithms and the double-row DFE algorithm may become impractical to implement due to their large computational complexity, so three additional parallel implementations of the DFE, which lead to considerable hardware savings and avoid the coding loss of the former approaches, are presented. The different algorithms are compared on the basis of convergence analysis and simulation results     

Adaptive Bayesian decision feedback equalizer for dispersive mobileradio channels

The paper investigates adaptive equalization of time-dispersive mobile radio fading channels and develops a robust high performance Bayesian decision feedback equalizer (DFE). The characteristics and implementation aspects of this Bayesian DFE are analyzed, and its performance is compared with those of the conventional symbol or fractional spaced DFE and the maximum likelihood sequence estimator (MLSE). In terms of computational complexity, the adaptive Bayesian DFE is slightly more complex than the conventional DFE but is much simpler than the adaptive MLSE. In terms of error rate in symbol detection, the adaptive Bayesian DFE outperforms the conventional DFE dramatically. Moreover, for severely fading multipath channels, the adaptive MLSE exhibits significant degradation from the theoretical optimal performance and becomes inferior to the adaptive Bayesian DFE     

Efficient decision feedback equalization for sparse wireless channels

A new efficient decision feedback equalizer (DFE) appropriate for channels with long and sparse impulse response (IR) is proposed. Such channels are encountered in many high-speed wireless communications applications. It is shown that, in cases of sparse channels, the feedforward and feedback (FB) filters of the DFE have a particular structure, which can be exploited to derive efficient implementations of the DFE, provided that the time delays of the channel IR multipath components are known. This latter task is accomplished by a novel technique, which estimates the time delays based on the form of the channel input-output cross-correlation sequence in the frequency domain. A distinct feature of the resulting DFE is that the involved FB filter consists of a reduced number of active taps. As a result, it exhibits considerable computational savings, faster convergence, and improved tracking capabilities as compared with the conventional DFE. Note that faster convergence implies that a shorter training sequence is required. Moreover, the new algorithm has a simple form and its steady-state performance is almost identical to that of the conventional DFE.     

Performance analysis of error propagation effects in the DFE for ATSC DTV receivers

The paper analyzes the error propagation phenomenon in the decision feedback equalizer (DFE) for the receivers of Advanced Television Systems Committee (ATSC) digital television (DTV) and presents the performance upper-limits of the DFE by comparing various error propagation cases and the no-error propagation case. As one approach to the performance limit, we consider a blind DFE, adopting a trellis decoder with a trace-back depth of 1 as a decision device. Through simulation, we show how much the DFE performance in ATSC DTV receivers is affected by error propagation. We found that while blind equalization is preferable to decision-directed (DD) equalization at signal-to-noise ratio (SNR) values less than 18 dB, DD equalization is superior to blind equalization at SNR values greater than 18 dB. In addition, symbol error rate curves quantitatively show that the performance difference in the DFE caused by error propagation becomes clearer at the trellis decoder following the DFE. The analysis results presented are very informative for developing equalization algorithms for ATSC DTV receivers.     

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。     

Serially connected bi-directional DFE suitable for 8-VSB modulation

A serially connected bi-directional decision feedback equalizer (SB-DFE) is proposed to improve the performance of channel equalization by exploiting implicit multipath diversity. The SB-DFE improves equalization performance by cascading normal and time-reversed DFEs. Conventional bi-directional DFEs obtain improved performance by combining the two DFEs in parallel. They, however, need accurate channel estimation and the performance is not guaranteed for multi-level modulation because they utilize each DFEs hard decided output symbols. On the other hand, the SB-DFE utilizes the soft output of the normal DFE at the first DFE as the input to the following time-reversed DFE without channel estimation. The performance of the SB-DFE is compared with that of the normal DFE and the bi-directional arbitrated DFE (BAD) in the 8-level vestigial sideband (8-VSB) modulation system with Brazilian digital high-definition television (HDTV) test channels. The SB-DFE has 1 /spl sim/ 1.8 dB signal-to-noise ratio (SNR) gains over the others.