Reduced complexity decision feedback equalization for digitalsubscriber loops

Decision feedback equalizers (DFEs) are widely used in modern local network digital transmission systems to remove the intersymbol interference caused by slowly decaying pulse tails. A gradient descent algorithm for adapting a coefficient to model the slowly decaying portion of the tail is described. An equalization strategy is described that exploits prior knowledge of the nature of the subscriber loop channel, together with the new adaptation algorithm, to give reduced complexity DFE structures. The use of this algorithm in FIR and IIR equalizer structures is described. The use of this algorithm in FIR and IIR equalizers is quantitatively compared to a conventional DFE in terms of performance and implementation complexity. An analysis is presented describing the operation of the adaptation algorithm in the presence of noise. Simulation results illustrate the training of the algorithm and its stability in the presence of near-end crosstalk noise     

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.     

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     

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     

基于DFE均衡器的线性化拆分算法的研究和应用

利用DFE非线性均衡器,通过数学处理对其进行线性化拆分,拆分后的两个线性均衡器分别置于信道的接收和发送端,使其能用于强多径干扰的信号传输环境(如存在强多径干扰的隧道中的高速信号传输).该方法降低了实现的复杂度,同时保持了高抗干扰性,且这种相互对称的均衡器结构有利于系统双向传输的实现.计算机仿真结果验证了该方法的有效性.     

On the performance of the electrical equalization technique in MMF links for 10-gigabit ethernet

In this paper, the electrical equalization technique utilized in multimode fiber (MMF) links for 10-Gigabit Ethernet is reported. This paper presents and compares three kinds of equalizers: linear equalizer, decision feedback equalizer (DFE), and a nonlinear finite-impulse-response DFE (NL-FIR-DFE) based on the analysis of nonlinear operations of direct modulation and detection in MMF links. Computer simulations reveal that NL-FIR-DFE exhibits superior performance in comparison with normal DFE. The equalization performance for an MMF channel with bandwidth 500 MHz-km as well as 160 MHz-km is demonstrated. It is demonstrated that with direct modulation of cost-effective vertical-cavity surface-emitting laser (VCSEL) or Fabry-Perot laser, the transmission distance for installed MMF with a bandwidth of 500 MHz-km at 10 Gb/s can be extended to 300 m with an appropriate offset restricted mode launch condition by utilizing normal DFE and to more than 650 m for NL-FIR-DFE. Moreover, it is shown that the transmission distance for an MMF with a bandwidth of 160 MHz-km can reach 300 m with more than seven times bandwidth improvement by using NL-FIR-DFE.     

MLSE Equalizers for Frequency Discrimination Receiver of MSK Optical Transmission System

We propose maximum-likelihood sequence estimator (MLSE) equalizers based on either Viterbi algorithm or template matching temple matching (TM) for the equalization of impairments imposed on the minimum shift keying (MSK) modulation formats in long haul transmission without optical dispersion compensation. The TM-MLSE equalizer is proposed as a simplified alternative for the Viterbi-MLSE equalizer. It is verified that the Viterbi-MLSE equalizer can operate optimally when noise approaches a Gaussian distribution. Simulation results of the performances of the two MLSE equalizers for optical frequency discrimination receiver-based optical MSK systems are described. The transmission performance is evaluated in terms of: (1) the chromatic dispersion (CD) tolerance for both Viterbi-MLSE and TM-MLSE equalizers; (2) transmission distance limits of Viterbi-MLSE equalizers with various number of states; (3)the robustness to fiber polarization mode dispersion (PMD) of Viterbi-MLSE equalizers; and (4) performance improvements for Viterbi-MLSE equalizers when utilizing sampling schemes with two and four samples per bit over the conventional single sample per bit. With a small number of states (64 states), the non-compensating optical link can equivalently reach up to approximately 928 km SSMF for 10 Gb/s transmission or 58 km SSMF for 40 Gb/s. The performance of 16-state Viterbi-MLSE equalizers for optical frequency discrimination receiver (OFDR)-based optical MSK transmission systems for PMD mitigation is also numerically investigated. The performance of Viterbi-MLSE equalizers can be further improved by using the sampling schemes with multiple samples per bit compared to the conventional single sample bit. The equalizer also offers high robustness to fiber PMD impairment.     

Equalizers for transmultiplexers in orthogonal multiple carrier data transmission

Orthogonal multiple carrier data transmission systems are efficiently realized using modified dft transmultiplexer filter banks. In data transmission applications, a non-ideal transmission channel causes distortions such as intersymbol interference and crosstalk between the subrate bands of the transmultiplexer. Hence, in order to equalize these distortions, subband equalizers, which affect the intersymbol interference and crosstalk behavior, are considered for implementation. The special structure of modified dft transmultiplexers requires a discussion concerning the various possibilities of placing the subband equalizers at the receiver. Wiener solutions and lms adaptive algorithms for various new subband equalizer structures are derived and compared by means of simulation results.     

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.     

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.     

自适应均衡算法在信道均衡技术中的应用研究

文中描述了两种非线性均衡器分别为判决反馈均衡器(DFE)和最大似然序列估计(MLSE)均衡器.所用信道模型为加性白高斯噪声信道,在DFE和线性均衡器(LE)中都是使用递归最小二乘(RLS)算法和最小均方(LMS)算法对数据进行分块处理.MLSE均衡器中使用了维特比最佳译码算法.就误比特性能来做以比较,DFE远好于LE,MLSE均衡器又明显优于DFE,并且它能达到几乎最优的性能.     

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.     

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     

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.     

Phase precoding for frequency-selective Rayleigh and Rician slowlyfading channels

This paper presents a novel phase precoding (pre-equalization) technique to equalize frequency-selective Rayleigh and Rician slowly fading channels for personal communication systems using phase modulation. In order to achieve intersymbol interference (ISI)-free transmission, the precoding technique pre-distorts the signal transmitted from a base station to a portable unit. The novelty of the technique lies in using a spiral curve design: (1) to ensure the stability of the precoder even in equalizing a non-minimum-phase channel; (2) to obtain an ISI-free received signal; and (3) to keep a constant transmitted signal amplitude. Using the precoder can improve the bit-error-rate (BER) transmission performance without increasing the complexity of the portable unit receiver. The BER performance of coherent quadrature phase-shift-keying (QPSK) with the channel pre-equalization is analyzed theoretically for both Rayleigh and Rician fading channels. Analytical and simulation results demonstrate that coherent QPSK using the proposed channel precoder has a significantly lower BER than that using a conventional decision-feedback equalizer (DFE) because the precoder does not suffer from error propagation     

Performance of Volterra and MLSD receivers for nonlinearband-limited satellite systems

This paper evaluates the performance of Volterra equalizers and maximum-likelihood sequence detection (MLSD) receivers for compensation of signal distortion in nonlinear band-limited satellite systems. In addition, the performance of a receiver with a fractionally-spaced equalizer followed by a Volterra equalizer is studied (FSE-Volterra equalizer). For the equalizers, adaptation of the equalizer weights is considered including a multiple-step LMS algorithm which improves the convergence characteristics. Two MLSD receiver structures are considered: the optimum receiver consisting of a matched-filter bank followed by a Viterbi (1967) detector and a suboptimum receiver consisting of a single receiver filter followed by a Viterbi detector. The performance of the MLSD receivers is then compared to that of the equalizers     

Multiuser Diffuse Indoor Wireless Infrared Communication Using Equalized Synchronous CDMA

We propose an indoor wireless infrared downlink scheme for high-data-rate multiuser connectivity with diffuse channels. The scheme is based on synchronous code-division multiple access with unipolar Hadamard codes. The orthogonality of unipolar Hadamard codes enables multiuser operation with relatively short codes. Thus, practical downlink rates of tens of Mb/s for each user can be obtained. However, multipath reflections in diffuse channels cause strong multipath dispersion and, consequently, severe distortion. This distortion becomes even more severe in a multiuser environment, as the dispersed incoherent infrared radiation of all users aggregates together. To mitigate this distortion, we use a novel adaptive multilevel serial composite decision feedback and feedforward equalizer. We investigate the system's performance with the proposed equalizer, and compare it with the performance of the same system, both composite decision-feedback and feedforward equalizers, and with a conventional decision-feedback equalizer (DFE). Our results show that the proposed scheme enables a high-data-rate multiaccess link and eliminates most of the multiuser distortion. Furthermore, it improves system performance in a multiaccess environment, as compared with the other composite equalizers and DFE for the same complexity. We also compare other coding schemes, and show that Hadamard codes are on top of the other codes.     

Combined coding and precoding for PAM and QAM HDSL systems

A system is described for high-speed digital subscriber line (HDSL) applications. It uses trellis coding combined with Tomlinson (1971) precoding. Theoretical performance results are provided for uncoded pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) assuming an ideal decision feedback equalizer (DFE) that includes an optimum feedforward filter. The similarities and differences in behavior are explained. It is shown that combined coding and Tomlinson precoding can achieve the equalization performance of the DFE and full coding gain of the trellis code. Simulation results are given to show that about 3.4 dB additional margin is obtained by using a four-dimensional eight-state trellis code. The receiver complexity is increased by it is quite manageable     

Electrical Joint Equalization for PMD-Induced Performance Degradation in Direct-Detection Polarization-Multiplexed Transmission Systems

Polarization-division-multiplexed (PDM) systems are sensitive to polarization-mode dispersion (PMD), since PMD induces not only intersymbol distortion but also interchannel crosstalk. Electrical equalization for individual channels is not sufficient for the lack of information from another channel. In this letter, electrical joint equalization including both the decision-feedback equalizer and Viterbi equalizer for PMD compensation in direct-detection PDM systems is investigated. Simulation shows that joint equalizers can effectively combat PMD-induced performance degradation and lower the requirement for dynamic polarization control.     

Electrical Mitigation of Penalties Caused by Group Delay Ripples for Different Modulation Formats

Electrical equalizers are proposed to mitigate the distortions caused by group delay ripples (GDRs) of cascaded optical filters (e.g., fiber Bragg gratings for chromatic dispersion (CD) compensation). Different electrical equalizers including feedforward equalizer (FFE), decision-feedback equalizer (DFE), nonlinear FFE-DFE, and maximum-likelihood sequence estimator are investigated and compared comprehensively for four different modulation formats: ON-OFF keying, optical duobinary, optical single sideband, and differential phase-shift keying. Especially, we find that the relationship of electrical equalization performance on the modulation format is very similar for the mitigation of GDR and CD.