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     

Decision-feedback equalization of time-dispersive channels withcoded modulation

An extension is presented of the work of V.M. Eyubogin (see ibid., vol.36, p.401-9, Apr. 1988) on decision-feedback equalization (DFE) applied to coded systems with interleaving. The authors study the adaptive implementation of the DFE using recursive-least-squares algorithms (RLS). System performance on time-dispersive channels with nulls as well as on channels with relatively small intersymbol interference is investigated. A reference insertion method is used to improve system performance, and a two-stage processing technique is adopted to use the more reliable decisions from the decoder in equalizer coefficient adaptation. Simulation results show that the RLS-implemented DFE systems with coded modulation can successfully combat severe channel distortion while maintaining the coding gain over corresponding uncoded systems     

编码符号串扰信道的迭代判决反馈均衡算法

本文提出了编码符号串扰信道的两种迭代判决反馈均衡(DFE)算法.采用Turbo原则将卷积码Viterbi译码后的判决经重编码、交织后反馈到前端的判决反馈均衡部分,每次迭代时由于DFE中判决反馈部分来自于经Viterbi译码后的重编码值(因而更可靠),经多次迭代后,系统误码率能得到显著提高.由于采用了DFE算法及迭代硬判反馈结构,系统复杂度较低,从而具有较高的实用价值.     

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.     

Reduced-complexity equalization techniques for broadband wirelesschannels

This paper presents reduced-complexity equalization techniques for broadband wireless communications, both outdoors (fixed or mobile wireless asynchronous transfer mode (ATM) networks) and indoors [high-speed local-area networks (LANs)]. The two basic equalization techniques investigated are decision-feedback equalization (FE) and delayed decision-feedback sequence estimation (DDFSE). We consider the use of these techniques in highly dispersive channels, where the impulse response can last up to 100 symbol periods. The challenge is in minimizing the complexity as well as providing fast equalizer start-up for transmissions of short packets. We propose two techniques which, taken together, provide an answer to this challenge. One is an open-loop timing recovery approach (for both DFE and DDFSE) which can be executed prior to equalization; the other is a modified DFE structure for precanceling postcursors without requiring training of the feedback filter. Simulation results are presented to demonstrate the feasibility of the proposed techniques for both indoor and outdoor multipath channel models. The proposed open-loop timing recovery technique plays a crucial role in maximizing the performance of DFE and DDFSE with short feedforward spans (the feedforward section of DDFSE is a Viterbi sequence estimator). A feedforward span of only five is quite sufficient for channels with symbol rate-delay spread products approaching 100. The modified DFE structure speeds up the training process for these channels by 10-20 times, compared to the conventional structure without postcursor precancellation. The proposed techniques offer the possibility of practical equalization for broadband wireless systems     

On adaptive decision-feedback equalization of intersymbolinterference channels in coded modulation systems

Recently, Eyuboglu (1988) has shown that adaptive noise-predictive decision-feedback equalization (DFE) can be combined with coded modulation to achieve high-speed data transmission by periodic interleaving. In this paper, we present a new method of adaptive DFE with periodic interleaving for coded modulation systems. The method is an improved version of that proposed by Eyuboglu, where the deinterleaving operation is performed on a vector-by-vector basis, instead of a sample-by-sample basis. Unlike the original system in which the linear equalizer's coefficients can be adjusted only with hard decisions from the threshold detector, the improved structure updates the coefficients of both the linear equalizer and the noise predictor based on soft decisions from the most likely path in the soft decoder. The improved system achieves better error-rate performance than the original with a little increase in hardware complexity. As compared to another improved design reported by Zhou et al. (1990), the new structure also gains advantages in error-rate performance, hardware complexity, and throughput delay     

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.     

CCK demodulation via symbol decision feedback equalizer

A symbol decision feedback equalization (DFE) technique is developed for demodulating complementary code keying (CCK) signals. The efficacy of the proposed receiver is demonstrated on the physical layer (PHY) specified in the IEEE 802.11b wireless local area network (WLAN) standard. Packet error rate (PER) performance is compared with that of the conventional RAKE receiver. The proposed receiver structure and its low complexity variations demonstrate significant performance advantages over the RAKE receiver, especially in severe multipath channels. While a large delay spread can limit the performance of two low-complexity variations discussed here, performance of the optimal symbol DFE receiver is not limited by delay spread as long as the channel signal-to-noise ratio (SNR) is sufficiently high.     

Adaptive algorithms for channel equalization with soft decisionfeedback

A new approach based on joint entropy maximization (JEM) is taken and adaptive algorithms are developed for channel equalization with a decision feedback equalizer (DFE). The proposed work generalizes the existing algorithms for DFE with a hard decision device. Previous research has shown that when the hard decisions in a DFE are replaced with soft decisions, the performance of the adaptive algorithms [e.g., minimum mean square error (MMSE)] improves dramatically. The soft decisions can be introduced naturally via the viewpoint taken here. Additionally, constant modulus and other (blind) algorithms for DFE with soft decisions can be derived from this JEM approach     

Decision-feedback equalization via separating hyperplanes

The design of finite-length decision-feedback equalization (DFE) forward and feedback filters under the assumption of genie-aided feedback and independent and equally likely transmitted symbols is considered. It is shown that the problem of determining DFE filters that minimize the probability of symbol error at high signal-to-noise ratio (SNR) is equivalent to finding the hyperplane that maximally separates two given finite groups of points in a finite-dimensional Euclidean space. The latter task can be formulated as a quadratic program which is readily solved numerically. It is also shown that the problem of finding finite-length DFE filters that minimize the probability of symbol error at any SNR subject to a certain separation condition is a convex optimization problem. The case where the transmitted data is coded using a runlength-limited code is also investigated. Examples show that this criterion yields a performance that is better than zero-forcing DFE on severely distorted channels at high SNR     

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     

Near-optimum soft decision equalization for frequency selective MIMO channels

In this paper, we develop soft decision equalization (SDE) techniques for frequency selective multiple-input multiple-output (MIMO) channels in the quest for low-complexity equalizers with error performance competitive to that of maximum likelihood (ML) sequence detection. We demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered and linear in the signal constellation size. Building on the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. The first SDE algorithm adopts a zero-padded transmission structure to convert the challenging sequence detection problem into a block-by-block least-square formulation. It introduces key enhancement to the original PDA to enable applications in rank-deficient channels and for higher level modulations. The second SDE algorithm takes advantage of the Toeplitz channel matrix structure embodied in an equalization problem. It processes the data samples through a series of overlapping sliding windows to reduce complexity and, at the same time, performs implicit noise tracking to maintain near-optimum performance. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Simulation comparisons of our SDE methods with minimum-mean-square error (MMSE)-based MIMO DFE and sphere decoded quasi-ML detection are presented.     

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。     

频选衰落MIMO信道的Turbo均衡

针对Turbo编码频选慢衰落MIMO信道,提出基于滑窗式概率数据辅助(Probabilistic Data Association)的软输出判决反馈均衡和软输入软输出Turbo信道解码器间迭代处理的Turbo均衡算法。充分利用已获得的信息,实现信道均衡与信道解码的迭代更新,克服传统判决反馈均衡器误差传播的缺陷。仿真表明,该系统经3次迭代就可获得较为满意的符号间干扰消除效果。     

Equalization and semi-blind channel estimation for space-time block coded signals over a frequency-selective fading channel

In this paper, we investigate the equalization and channel identification for space-time block coded signals over a frequency-selective multiple-input multiple-output (MIMO) channel. The equalization has been considered by taking into account the cyclostationarity of space-time block coded signals. The minimum mean square error (MMSE) solutions have been derived for the linear and decision feedback (DF) equalizers. The channel estimation is required for the equalization. With known symbols (as pilot symbols), MIMO channels can be estimated. In addition, due to the redundancy induced by space-time block code, it is possible to identify MIMO channels blindly using the subspace method. We consider both blind and semi-blind channel estimation for MIMO channels. It is shown that the semi-blind channel estimate has fewer estimation errors, and it results in less (bit error rate) performance degradation of the MMSE linear and DF equalizers.     

Comparison of DFE and MLSE Receiver Performance on HF Channels

Data communication at rates near or above 2 kbits/s on 3 kHz-baadwidth HF radio channels is subject to impairment from severe linear dispersion, rapid channel time variation, and severe fading. In this investigation, recorded 2.4 kbit/s QPSK signals received from HF channels were processed to extract a time-varying estimate of the channel impulse response. From the estimated channel impulse responses, performance-related parameters were computed for ideal matched filter reception, maximum-likelihood sequence-estimation (MLSE), and decision feedback equalization (DFE). The results indicated that the simpler DFE receiver suffered only a small theoretical performance degradation relative to the more complex MLSE receiver. Other HF channel impulse response statistics were also obtained to shed light on equalization and filter adaptation techniques.     

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.     

Combined equalization and coding for high-density saturationrecording channels

Combined equalization and coding approaches which significantly outperform previous techniques are presented for the binary Lorentzian channel with additive Gaussian noise. The authors develop a technique based on the concatenation of standard trellis codes with an equalization code and a block decision feedback equalizer (BDFE). Signal sets for the trellis code are generated by partitioning BDFE output vectors according to four- and eight-dimensional lattices. They also investigate the combination of a decision feedback equalizer (DFE) and a convolutional code (CC) and find that this system provides theoretical coding gains from 1 to 3 dB in the high linear recording density range of 2⩽pw₅₀/T⩽3. Although the BDFE with the trellis code system does not perform as well as the DFE with CC system at high densities, it does produce substantial coding gains at low linear recording densities     

A 6.0-mW 10.0-Gb/s Receiver With Switched-Capacitor Summation DFE

A low-power receiver with a one-tap decision feedback equalization (DFE) was fabricated in 90-nm CMOS technology. The speculative equalization is performed using switched-capacitor-based addition at the front-end sample-hold circuit. In order to further reduce the power consumption, an analog multiplexer is used in the speculation technique implementation. A quarter-rate-clocking scheme facilitates the use of low-power front-end circuitry and CMOS clock buffers. The receiver was tested over channels with different levels of ISI. The signaling rate with BER<10^-12 was significantly increased with the use of DFE for short- to medium-distance PCB traces. At 10-Gb/s data rate, the receiver consumes less than 6.0 mW from a 1.0-V supply. This includes the power consumed in all quarter-rate clock buffers, but not the power of a clock recovery loop. The input clock phase and the DFE taps are adjusted externally     

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