A decision feedback equalizer with time-reversal structure

This work describes the use of a receiver with a time-reversal structure for low-complexity decision feedback equalization of slowly fading dispersive indoor radio channels. Time-reversal is done by storing each block of received signal samples in a buffer and reversing the sequential order of the signal samples in time prior to equalization. As a result, the equivalent channel impulse response as seen by the equalizer is a time-reverse of the actual channel impulse response. Selective time-reversal operation, therefore, allows a decision feedback equalizer (DFE) with a small number of forward filter taps to perform equally well for both minimum-phase and maximum-phase channel characteristics. The author evaluates the theoretical performance bounds for such a receiver and quantifies the possible performance improvement for discrete multipath channels with Rayleigh fading statistics. Two extreme cases of DFE examples are considered: an infinite-length DFE; and a DFE with a single forward filter tap. Optimum burst and symbol timing recovery is addressed and several practical schemes are suggested. Simulation results are presented. The combined use of equalization and diversity reception is considered     

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     

滑动窗快速横向滤波的自适应判决反馈均衡器算法

本文提出了一种基于滑动窗广义多路快速横向滤波（ＳＷＦＴＦ）的自适应判决反馈均衡器（ＤＦＦ）算法，它具有快速跟踪性能，故可用于快速时变多径衰落的信道。文中推导了ＳＷＦＴＦ－ＤＦＥ算法。在数字移动通信信道模型上，利用计算机模拟，在均方误差和误码率特性方面与其它均衡器算法进行了比较。     

A robust adaptive DFE receiver for DS-CDMA systems under multipathfading channels

This paper presents a novel receiver design from signal processing viewpoint for direct-sequence code-division multiple access (DS-CDMA) systems under multipath fading channels. A robust adaptive decision-feedback equalizer (DFE) is developed by using optimal filtering technique via minimizing the mean-square error (MSE). The multipath fading channels are modeled as tapped-delay-line filters, and the tap coefficients are described as Rayleigh distributions in order to imitate the frequency-selective fading channel. Then, a robust Kalman filtering algorithm is used to estimate the channel responses for the adaptation of the proposed DFE receiver under the situation of partially known channel statistics. The feedforward and feedback filters are designed by using not only the estimated channel responses but the uncertainties and error covariance of channel estimation as well. As shown in the computer simulations, the proposed adaptive DFE receiver is robust against the estimation errors and modeling dynamics of the channels. Hence, it is very suitable for receiver design in data transmissions through multipath fading channels encountered in most wireless communication systems     

稀疏多径信道的T/2间隔CFE均衡器研究

完全反馈均衡器(Complete Feedback Equalizer, CFE)是判决反馈均衡器(DFE)的改进。该文提出了一种T/2分数间隔稀疏CFE(T/2 Sparse CFE, T/2-SCFE)结构,以避免接收机对于符号定时误差的敏感性,并有效利用长时延扩展多径信道的稀疏性来降低均衡器的复杂度。理论分析与基于实测信道的计算机仿真表明, T/2-SCFE均衡器对符号定时误差保持了稳健性,总体性能优于符号间隔CFE及分数间隔DFE。     

Combined equalization and differential detection using precoding

A new transceiver for data transmission over multipath fading channels employing precoding and differential detection is investigated. This precoding scheme effectively functions as a decision feedback equalizer (DFE) for differentially coherent demodulation. The main advantage of the proposed scheme over the conventional DFE is its ability to compensate for fast channel phase variations     

Efficient bad equalizer in two-ray multipath fading channels

An efficient bidirectional arbitrated decision feedback (BAD) equalizer is presented in single-carrier block transmission system in the Two-Ray multipath fading channels, where the output from the bidirectional equalizers are combined together directly using maximal ratio combining (MRC) rule to improve the signal-to-noise ratio (SNR) before demodulation. The computational complexity of the BAD equalizer presented is linear with the channel length, which is the same as conventional decision feedback equalizer (DFE) and is significantly lower than that of conventional BAD equalizer as well as the maximum likelihood (ML) algorithm. While the performance of the new scheme depends on the specific channel characteristics, it is shown by simulation results that the performance of the new BAD can surpass the one of DFE dramatically in the minimum or non-minimum phase Two-Ray multipath fading channels.     

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.     

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。     

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     

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     

Bounding performance and suppressing intercarrier interference in wireless mobile OFDM

While rapid variations of the fading channel cause intercarrier interference (ICI) in orthogonal frequency-division multiplexing (OFDM), thereby degrading its performance considerably, they also introduce temporal diversity, which can be exploited to improve performance. We first derive a matched-filter bound (MFB) for OFDM transmissions over doubly selective Rayleigh fading channels, which benchmarks the best possible performance if ICI is completely canceled without noise enhancement. We then derive universal performance bounds which show that the time-varying channel causes most of the symbol energy to be distributed over a few subcarriers, and that the ICI power on a subcarrier mainly comes from several neighboring subcarriers. Based on this fact, we develop low-complexity minimum mean-square error (MMSE) and decision-feedback equalizer (DFE) receivers for ICI suppression. Simulations show that the DFE receiver can collect significant gains of ICI-impaired OFDM with affordable complexity. In the relatively low Doppler frequency region, the bit-error rate of the DFE receiver is close to the MFB.     

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     

Upper-bound performance of a wide-band adaptive modem

Adaptive modulation is applied in conjunction with a decision-feedback equalizer (DFE) in order to mitigate the effects of the slowly varying wide-band multipath Rayleigh fading channel in a noise-limited environment. An upper-bound mean bit-error rate and bits per symbol performance is introduced for this scheme by utilizing the pseudo signal-to-noise ratio at the output of the DFE in order to switch the modulation schemes on a burst-by-burst basis     

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。     

Importance sampling simulation for evaluating lower-bound symbolerror rate of the Bayesian DFE with multilevel signaling schemes

For the class of equalizers that employs a symbol-decision finite-memory structure with decision feedback, the optimal solution is known to be the Bayesian decision feedback equalizer (DFE). The complexity of the Bayesian DFE, however, increases exponentially with the length of the channel impulse response (CIR) and the size of the symbol constellation. Conventional Monte Carlo simulation for evaluating the symbol error rate (SER) of the Bayesian DFE becomes impossible for high channel signal-to-noise ratio (SNR) conditions. It has been noted that the optimal Bayesian decision boundary separating any two neighboring signal classes is asymptotically piecewise linear and consists of several hyperplanes when the SNR tends to infinity. This asymptotic property can be exploited for efficient simulation of the Bayesian DFE. An importance sampling (IS) simulation technique is presented based on this asymptotic property for evaluating the lower bound SER of the Bayesian DFE with a multilevel pulse amplitude modulation (M-PAM) scheme under the assumption of correct decisions being fed back. A design procedure is developed, which chooses appropriate bias vectors for the simulation density to ensure asymptotic efficiency (AE) of the IS simulation     

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     

时域自适应均衡技术的分析与应用

概述了频率选择性衰落信道的传输特性,论述了采用均衡技术的必要性。通过对各种均衡器结构和自适应均衡算法在抵抗符号间干扰能力、收敛速度以及运算复杂度等方面的分析与比较,选择了判决反馈作为均衡器结构、最小均方自适应算法作为自适应准则的均衡器方案。仿真及试验结果证实了设计的时域自适应均衡器不仅具有较强的抵抗符号间干扰能力,而且能够获得隐分集增益,在频率选择性衰落信道中具有良好的应用效果。     

Performance analysis of a single-user MISO ultra-wideband time reversal system with DFE

This paper presents an analysis of the performance of a baseband multiple-input single-output (MISO) time reversal ultra-wideband system (TR-UWB) incorporating a symbol spaced decision feedback equalizer (DFE). A semi-analytical performance analysis based on a Gaussian approach is considered, which matched well with simulation results, even for the DFE case. The channel model adopted is based on the IEEE 802.15.3a model, considering correlated shadowing across antenna elements. In order to provide a more realistic analysis, channel estimation errors are considered for the design of the TR filter. A guideline for the choice of equalizer length is provided. The results show that the system’s performance improves with an increase in the number of transmit antennas and when a symbol spaced equalizer is used with a relatively small number of taps compared to the number of resolvable paths in the channel impulse response. Moreover, it is possible to conclude that due to the time reversal scheme, the error propagation in the DFE does not play a role in the system’s performance.     

Digital Transmission Performance on Fading Dispersive Diversity Channels

The reception and detection of a single digit under known channel conditions are investigated. The probability of error for an optimum one-shot receiver instantaneously matched to the channel state is averaged over an ensemble of dispersive diversity channels. The average probability of error as a function of energy to noise ratio is found to be solely dependent on the ratio of rms dispersion width to data symbol width. For these dispersive channels an implicit diversity effect is qualitatively explained in terms of eigenvalues that depend on the ensemble statistic. The one-shot receiver performance provides a bound for practical receivers. In a comparison with a decision feedback equalizer, it is shown that on moderately dispersive channels the equalizer nearly achieves optimum one-shot performance. Since an adaptive version of this equalizer exists, this means data transmission on slowly fading channels is possible at rates above the natural rate suggested by the channel dispersion spread without bandwidth expansion and with small intersymbol interference penalty. The use of one-shot receiver performance curves can also be used as estimates of equalizer performance in situations where computation of the latter is impractical.