A decision-feedback equalizer with pattern-dependent feedback formagnetic recording channels

A new nonlinear equalizer for high-density magnetic recording channels is presented. It has a structure of the decision-feedback equalizer (DFE) with a nonlinear model at the feedback section and a dynamic threshold detector. The feedback nonlinear model is a sequence of look-up tables (LUTs) indexed by time, and each table is addressed by a transition pattern formed by one future and ν past transitions. We call this new nonlinear equalizer the pattern-dependent DFE (PDFE). The feedback nonlinear model cancels the trailing nonlinear intersymbol interference (ISI), and then the data decision is made by considering the precursor nonlinear ISI caused by one future symbol. We propose a tap optimization criterion SNR_d for the PDFE which in effect tries to maximize the output signal to noise ratio, and derive a closed-form solution for the tap values. We compare the detection performance of PDFE with that of the DFE and the RAM-DFE on experimental channels. The RAM-DFE is a DFE with one large LUT at its feedback section. The results show that the PDFE yields a significant performance improvement over the DFE and the RAM-DFE. Also the PDFE derived in this paper achieves a superior performance compared with the PDFE derived by the minimum mean-square-error criterion     

On the equivalence of the simultaneous and separate MMSEoptimizations of a DFE FFF and FBF

There is great interest in the use of decision feedback equalization (DFE) to mitigate the effects of intersymbol interference (ISI) on wireless multipath fading channels. The coefficients of a DFE feedforward filter (FFF) and feedback filter (FBF) are usually adjusted based on the minimum mean square error (MMSE) criterion. The equalizer coefficients can be calculated by recursive adaptation or by direct computation based on a channel estimate. The equivalence of the simultaneous and separate MMSE optimization of the FFF and FBF of a finite-length DFE is established     

A CMOS adaptive continuous-time forward equalizer, LPF, and RAM-DFEfor magnetic recording

A continuous-time forward equalizer with one adaptive zero and a seventh-order linear-phase low-pass filter are described. The forward equalizer cancels precursor intersymbol interference (ISI). A mixed-signal four-tap RAM decision-feedback equalizer (DFE) is also included on the prototype to cancel the postcursor ISI. Both precursor and postcursor ISI are canceled in the analog domain. The adaption is done digitally. The low-pass filter and forward equalizer together occupy 6.7 mm² in a 1 μm CMOS process. They dissipate 280 mW from a 5 V supply when operating at 80 Mb/s. Including the RAM-DFE, the entire chip occupies 11.2 mm² and dissipates 630 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 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.     

A new adaptive functional-link neural-network-based DFE forovercoming co-channel interference

A new approach for the decision feedback equalizer (DFE) based on the functional-link neural network is described. The structure is applied to the problem of adaptive equalization in the presence of intersymbol interference (ISI), additive white Gaussian noise, and co-channel interference (CCI). It is shown through simulation results for a severe amplitude distorted co-channel system that the decision feedback functional-link equalizer (DFFLE) provides significantly superior bit-error rate (BER) performance characteristics compared to the conventional DFE, the linear transversal equalizer (LTE), the nonlinear radial basis function (RBF) neural-network-based structures and the feed-forward functional-link equalizer (FFLE)-based structures. The DFFLE is also shown to have a significantly simpler computational requirement relative to the RBF and the FFLE     

Decision feedback equalization

As real world communication channels are stressed with higher data rates, intersymbol interference (ISI) becomes a dominant limiting factor. One way to combat this effect that has recently received considerable attention is the use of a decision feedback equalizer (DFE) in the receiver. The action of the DFE is to feed back a weighted sum of past decision to cancel the ISI they cause in the present signaling interval. This paper summarizes the work in this area beginning with the linear equalizer. Three performance criteria have been used to derive optimum systems; 1) minimize the noise variance under a "zero forcing" (ZF) constraint i.e., insist that all intersymbol interference is cancelled, 2) minimize the mean-square error (MMSE) between the true sample and the observed signal just prior to the decision threshold, and 3) minimize the probability of error (Min Pe). The transmitter can be fixed and the receiver optimized or one can obtain the joint optimum transmitter and receiver. The number of past decisions used in the feedback equalization can be finite or infinite. The infinite case is easier to handle analytically. In addition to reviewing the work done in the area, we show that the linear equalizer is in fact a portion of the DFE receiver and that the processing done by the DFE is exactly equivalent to the general problem of linear prediction. Other similarities in the various system structures are also shown. The effect of error propagation due to incorrect decisions is discussed, and the coaxial cable channel is used as an example to demonstrate the improvement available using DFE.     

A quadratic sigmoid neural equalizer for nonlinear digital magneticrecording channels

A new neural equalizer is proposed in order to compensate for intersymbol interference and to mitigate nonlinear distortions in digital magnetic recording systems. The proposed equalizer uses the quadratic sigmoid function as the activation function. The performance of the proposed equalizer is compared to those of a decision-feedback equalizer (DFE) and a neural decision feedback equalizer (NDFE) in terms of bit-error rate in nonlinear digital magnetic recording channels. Simulation results demonstrate that the proposed equalizer outperforms both DFE and NDFE     

针对判决反馈均衡器的部分ⅡR提前结构及其应用

给出一种可以用于高速数字接收的特殊的判决反馈均衡器结构。为减少FIR内多径传播影响到ⅡR内的多径响应，而将部分ⅡR提前于FIR，以得到更快的系数收敛速度。在此基础上的数据仿真，比较了提前结构同普通结构的性能差异，验证了该结构可以使均衡器在严重畸变的信道条件下得到更快的收敛速度。最后，介绍了提前结构的最新的高清晰度电视8VSB接收机中的应用。     

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     

MSK-type signals in the presence of adjacent channel interferenceand white noise

In this letter, the problem of adjacent channel interference (ACI) caused by the close packing of constant envelope MSK-type users in a given frequency band is considered. An optimal receiver filter, based on the theory of matched filtering, is found, and it serves as an upper bound on the signal-to-interference ratio. The intersymbol interference (ISI) caused by the time response of the matched filter is eliminated by a decision feedback equalizer (DFE) which, however, degrades performance. It was found that the matched-filter upper bound allows about 3-15 dB more ACI than the performance of a classical correlation detector (for additive white Gaussian noise only), depending on the frequency separation between channels. The DFE performance is only a little bit worse than that of the matched filter     

Electrical equalization for advanced optical communication systems

We investigate equalizers for electronic dispersion compensation (EDC) of dispersion limited optical fibre communication links in combination with different modulation formats. We show that the performance of conventional equalizers including feedforward equalizer (FFE) and decision feedback equalizer (DFE) are fundamentally limited by the nonlinearity of square-law detection of the photodiode in direct detection systems. Advanced modulation formats such as differential phase shift keying (DPSK) and optical duobinary further enhance this kind of nonlinearity and degrade further FFE/DFE performance. However, nonlinear FFE–DFE and maximum likelihood sequence estimation (MLSE) take into account the mitigation of nonlinear inter symbol interference (ISI) and hence can achieve much better performance. We show that in contrast to other modulation formats, optical single sideband modulation results in approximately linear distortions after detection and thus a simple linear FFE equalizer can achieve good compensation.     

基于多用户反馈的判决反馈均衡器的研究

本文提出的一种新颖的基于多用户反馈的判决反馈均衡器,解决了在CDMA多用户检测中传统自适应判决反馈均衡器误码率高、系统容量小的缺点.它由具有误差反馈滤波器的判决反馈均衡器(Decision Feedback Equalizer with Error Feedback Filter,DFE-EFF)构成,并在判决后反馈多用户数据抵消多址干扰(多用户反馈干扰抵消).文中给出其结构图,分析各种判决反馈均衡算法.理论证明,具有误差反馈滤波器的多用户反馈干扰抵消判决反馈均衡器(多用户反馈干扰抵消DFE-EFF)较各种判决反馈均衡器为最优,它能同时有效处理ISI,MAI和噪声的干扰.仿真结果表明,在误码率性能和系统容量两方面,多用户反馈干扰抵消DFE-EFF比DFE、DFE-EFF均有较大改善.     

A class of block-iterative equalizers for intersymbol interferencechannels: fixed channel results

A new and efficient class of nonlinear equalizers is developed for intersymbol interference (ISI) channels. These -"iterated-decision equalizers” use an optimized multipass algorithm to successively cancel ISI from a block of received data and generate symbol decisions whose reliability increases monotonically with each iteration. These equalizers have an effective complexity comparable to the decision-feedback equalizer (DFE), yet asymptotically achieve the performance of maximum-likelihood sequence detection (MLSD). We show that, because their structure allows cancellation of both precursor and postcursor ISI, iterated-decision equalizers outperform the minimum mean-square error DFE by 2.507 dB on severe ISI channels even with uncoded systems. Moreover, unlike the DFE, iterated-decision equalizers can be readily used in conjunction with error-control coding, making them attractive for a wealth of applications     

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     

A 35 Mb/s mixed-signal decision-feedback equalizer for disk drivesin 2-μm CMOS

A 35 Mb/s mixed-signal adaptive decision-feedback equalizer (DFE) has been implemented in a 2-μm CMOS technology. The DFE has four feedback taps for cancelling intersymbol interference (ISI) and one tap for cancelling dc offset. The ISI is cancelled using fully differential analog circuits. Coefficient adaptation is digital, and two adaptation rates are available. The DFE occupies 24 mm² and dissipates 165 mW     

Iterative Equalization using Improved Block DFE for Synchronous CDMA Systems

Iterative equalization using optimal multiuser detector and optimal channel decoder in coded CDMA systems improves the bit error rate (BER) performance tremendously. However, given large number of users employed in the system over multipath channels causing significant multiple-access interference (MAI) and intersymbol interference (ISI), the optimal multiuser detector is thus prohibitively complex. Therefore, the sub-optimal detectors such as low-complexity linear and non-linear equalizers have to be considered. In this paper, a novel low-complexity block decision feedback equalizer (DFE) is proposed for the synchronous CDMA system. Based on the conventional block DFE, the new method is developed by computing the reliable extrinsic log-likelihood ratio (LLR) using two consecutive received samples rather than one received sample in the literature. At each iteration, the estimated symbols by the equalizer is then saved as a priori information for next iteration. Simulation results demonstrate that the proposed low-complexity block DFE algorithm offers good performance gain over the conventional block DFE.     

Joint coding and decision feedback equalization for broadbandwireless channels

This paper introduces a new approach for joint convolutional coding and decision feedback equalization (DPE). To minimize error propagation, the DFE uses a combination of soft decisions and delayed tentative decisions to cancel intersymbol interference (ISI). Soft decisions are obtained by passing the DFE output through a (soft) nonlinear device. This simple method is shown to perform almost as well as an optimum soft feedback approach on wireless channels with diversity. Tentative decisions from the Viterbi decoder are used to cancel ISI due to multipath with large delays, thus remedying the increasing effect of error propagation in channels with large delay spreads. We consider the use of this soft/delayed feedback DFE (S/D-DFE) technique in broadband wireless channels (with delay spreads up to several tens of the symbol period) typical in high-bitrate mobile data applications. Simulation results indicate that the proposed joint coding and S/D-DFE technique performs to within 1-2 dB [in required signal-to-noise ratio (SNR)] of an ideal coded DFE without error propagation. When combined with antenna diversity and a reduced-complexity DFE concept with adaptive feedforward tap assignment, it provides high packet throughput against Rayleigh fading, severe delay spreads, and high Doppler rates     

Adaptive decision feedback equalization: can you skip the trainingperiod?

This paper presents a novel unsupervised (blind) adaptive decision feedback equalizer (DFE). It can be thought of as the cascade of four devices, whose main components are a purely recursive filter (ℛ) and a transversal filter (𝒯). Its major feature is the ability to deal with severe quickly time-varying channels, unlike the conventional adaptive DFE. This result is obtained by allowing the new equalizer to modify, in a reversible way, both its structure and its adaptation according to some measure of performance such as the mean-square error (MSE). In the starting mode, ℛ comes first and whitens its own output by means of a prediction principle, while 𝒯 removes the remaining intersymbol interference (ISI) thanks to the Godard (1980) (or Shalvi-Weinstein (1990)) algorithm. In the tracking mode the equalizer becomes the classical DFE controlled by the decision-directed (DD) least-mean-square (LMS) algorithm. With the same computational complexity, the new unsupervised equalizer exhibits the same convergence speed, steady-state MSE, and bit-error rate (BER) as the trained conventional DFE, but it requires no training. It has been implemented on a digital signal processor (DSP) and tested on underwater communications signals-its performances are really convincing     

Performance of trellis codes for a class of equalized ISI channels

The performance of trellis codes is examined for a class of intersymbol interference (ISI) channels that occur in high-frequency radio systems. The channels considered are characterized by in-band spectral nulls and by a rapid time variation. The baseline modulation technique is 4QAM (four-point quadrature amplitude modulation). When spectral nulls are absent, performance of fractionally spaced linear equalizers and trellis decoders is found to be near ideal and to be better than using symbol-spacing in the equalizer. However, error propagation in the feedback path, resulting from equalizer-based decisions, ruins the performance of the combination of decision-feedback equalizers and trellis decoders when spectral nulls are present. Their performance can be improved by using fractionally spaced feedforward equalizer sections and by designing the decoder to compensate for ISI. Rate 2/3 codes are found to outperform rate 1/2 codes in error performance