Theory and Design of Transmission Line All-Pass Equalizers

A general theory of transmission line all-pass equalizers operating in either TEM, TE, or TM modes is presented. Application of the theory to practical problems is straightforward, and circuit realizations of the equalizers are often simply related to easily computed design curves. Although the theory, strictly speaking, is for commensurate transmission line networks, it is not essential that the network being equalized, or in narrow-band cases the equalizer itself, be of commensurate length lines. Design formulas for narrow-band equalizers of up to two cavities are presented, and a method for extending the design to a greater number of cavities is described. The effect of equalizer dissipation loss is investigated and briefly described. Two example designs are presented.     

Blind equalization for short burst wireless communications

In this paper, we propose a dual mode blind equalizer based on the constant modulus algorithm (CMA). The blind equalizer is devised for short burst transmission formats used in many current wireless TDMA systems as well as future wireless packet data systems. Blind equalization is useful for such short burst formats, since the overhead associated with training can be significant when only a small number of bits are transmitted at a time. The proposed equalizer overcomes the common problems associated with classic blind algorithms, i.e., slow convergence and ill-convergence, which are detrimental to applying blind equalization to short burst formats. Thus, it can eliminate the overhead associated with training sequences. Also, the blind equalizer is extended to a two branch diversity combining blind equalizer. A new initialization for fractionally spaced CMA equalizers is introduced. This greatly improves the symbol timing recovery performance of fractionally spaced CMA equalizers with or without diversity, when applied to short bursts. Through simulations with quasi-static or time-varying frequency selective wireless channels, the performance of the proposed equalizer is compared to selection diversity and conventional equalizers with training sequences. The results indicate that its performance is far superior to that of selection diversity alone and comparable to the performance of equalizers with short training sequences. Thus, training overhead can be removed with no performance degradation for fast time-varying channels, and with slight performance degradation for static channels     

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.     

Chip-Level MMSE Equalization for CDMA Downlink

1IntroductionNext generation standards support high data rate ser-vices,in which users are only assigned a smaller-orderspreading code . This leads to a necessity for the tech-niques that suppress Inter-Chip Interference (ICI) aswell as Multi-Access Interference ( MAI) . The tradi-tional RAKE receiver experiences difficulty because theorthogonality decays when signal transmits over multi-path frequency selective fading channels . The RAKEreceiver cannot overcome the serious MAI and I…     

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     

Convergence analysis of finite length blind adaptive equalizers

The paper presents some new analytical results on the convergence of two finite length blind adaptive channel equalizers, namely, the Godard equalizer and the Shalvi-Weinstein equalizer. First, a one-to-one correspondence in local minima is shown to exist between the Godard and Shalvi-Weinstein equalizers, hence establishing the equivalent relationship between the two algorithms. Convergence behaviors of finite length Godard and Shalvi-Weinstein equalizers are analyzed, and the potential stable equilibrium points are identified. The existence of undesirable stable equilibria for the finite length Shalvi-Weinstein equalizer is demonstrated through a simple example. It is proven that the points of convergence for both finite length equalizers depend on an initial kurtosis condition. It is also proven that when the length of equalizer is long enough and the initial equalizer setting satisfies the kurtosis condition, the equalizer will converge to a stable equilibrium near a desired global minimum. When the kurtosis condition is not satisfied, generally the equalizer will take longer to converge to a desired equilibrium given sufficiently many parameters and adequate initialization. The convergence analysis of the equalizers in PAM communication systems can be easily extended to the equalizers in QAM communication systems     

Non-uniformly spaced tapped-delay-line equalizers

A systematic way to design nonuniformly spaced tapped-delay-line (TDL) equalizers is described, and the performance of such equalizers is compared to that of uniformly spaced TDL equalizers with the same number of tap coefficients. It is shown that the signal-to-mean-squared-error ratio at the output of a TDL equalizer can be improved by optimally choosing the positions of the tap weights. An algorithm to find both the tap positions and the corresponding tap weights for a given delay span and a given minimum tap spacing of the equalizer is presented. Typical results are illustrated by using, as an example, the magnetic recording channel. For two target waveforms at different densities of recording, it is shown that there is a potential for saving up to seven equalizer taps     

Grouped signed power-of-two algorithms for low-complexity adaptive equalization

With increasing demand for higher data rate, modern communication systems have grown more complex. Equalization has become more and more important as it is effective in mitigating the multipath fading often occurred in high-data-rate communication systems. However, the implementation complexity of adaptive equalizers is usually too high for mobile communication applications. In this paper, a novel adaptive equalization algorithm and its low-complexity architecture are proposed. This algorithm employs a new grouped signed power-of-two (GSPT) number representation. The GSPT algorithm and several enhanced versions are simulated as adaptive equalizers in a phase-shift keying communication receiver for several practical channels and the GSPT-based equalizers perform as well as the least mean square (LMS) equalizer. Moreover, for comparison, two GSPT-based equalizers and two other equalizers are implemented in field-programmable gate arrays. The GSPT-based equalizers require only about 25%-30% of the hardware resources needed in the LMS equalizer. Also the GSPT-based equalizers are more than twice as fast as the LMS equalizer.     

Nonlinear Electrical Equalization for Different Modulation Formats With Optical Filtering

Based on bit-error-ratio simulations, we investigate electrical-dispersion-compensation performance by using a nonlinear electrical equalizer based on nonlinear Volterra theory for different modulation formats. This nonlinear equalizer is compared to conventional decision-feedback equalizer as well as to maximum-likelihood sequence estimation. Especially, we show that nonlinear equalizers, in conjunction with narrowband optical filtering of the light signal, result in improved performance. First of all, the system can benefit from the noise reduction due to narrowband filtering. Second, interacting with chromatic dispersion, nonlinear equalizers benefit from the improved dispersion tolerance through spectrum reshaping by narrowband optical filtering. Finally, nonlinear equalizers can efficiently mitigate the distortion resulting from strong optical filtering     

Optimum space-time processors with dispersive interference: unifiedanalysis and required filter span

We consider optimum space-time equalizers with unknown dispersive interference, consisting of a linear equalizer that both spatially and temporally whitens the interference and noise, followed by a decision-feedback equalizer or maximum-likelihood sequence estimator. We first present a unified analysis of the optimum space-time equalizer, and then show that, for typical fading channels with a given signal-to-noise ratio (SNR), near-optimum performance can be achieved with a finite-length equalizer. Expressions are given for the required filter span as a function of the dispersion length, number of cochannel interferers, number of antennas, and SNR, which are useful in the design of practical near-optimum space-time equalizers     

Fractional Tap-Spacing Equalizer and Consequences for Clock Recovery in Data Modems

Adaptive equalizers are usually realized in the form of a transversal filter with variable tap gains and tap spacing equal to the symbol spacingT. The performance of these equalizers depends critically on the symbol-clock phase derived in the receiver, due to the clock-phase dependent aliasing of the spectral roll-off components, upon which the conventional equalizer has no influence. In this paper we study the possibility of overcoming this difficulty by making the tap spacing of the equalizer somewhat smaller thanT(fractional tap spacing). It is shown that this leads to satisfactory performance of the equalizer for a broad continuous range of clock phases, without penalizing the speed of convergence. Furthermore, it allows the application of a simple clock recovery scheme which derives a phase control signal from the equalizer tap-gain values.     

基于JUMMSE准则的前向分数间隔判决反馈均衡器

研究了前向分数间隔判决反馈均衡器的原理与结构,并推导了基于联合无偏差MMSE(JUMMSE)准则设计的最优解。文中讨论了均衡器长度对误符号率(SER)性能的影响。仿真结果表明,在较高的信噪比、选择恰当的均衡器长度时,这种均衡器对于高频信道的均衡效果是显著的。     

复值的MBER非线性均衡器用于QAM信号

本文提出一种复值的最低误码率非线性滤波器用于非线性信道中QAM信号的均衡.推导了针对QAM信号的最低误码率准则训练算法的目标函数,并用Voherra序列来实现复值的非线性均衡器.为使非线性均衡器能在线自适应训练并增加训练算法的数值稳定性,提出～种滑窗随机梯度算法.大量仿真表明,对于非线性信道中QAM信号的均衡,最低误码率非线性均衡器的性能优于最小均方误差准则.     

Quasi-Resonant Zero-Current-Switching Bidirectional Converter for Battery Equalization Applications

A systematic approach to reform and analyze a soft-switching bidirectional dc-to-dc converter is proposed for cell voltage balancing control in a series connected battery string. quasi-resonant converter circuits have been designed to achieve the zero-current-switching (ZCS) to reduce the switching loss in bidirectional battery equalizers. The results indicate that the switching loss and energy transfer efficiency can be substantially improved using the quasi-resonant ZCS (QRZCS) technology in a battery charging system with an individual cell equalizer (ICE). The validity of the battery equalization is further verified using an experimental installation involving a battery string of three lithium–ion cells. The simulation and experimental results show that the proposed QRZCS battery equalization schemes can achieve bidirectional battery equalization performance and reduce the MOSFET transistor switch power losses by more than 96% and increase the efficiency by around 20%$sim$30% compared with the conventional battery equalizer during an identical equalization process.     

Aspects of PCM Regenerator Design for Crosstalk Limited Environments

The design of PCM regenerators for crosstalk limited environments is considered. A Regenerator Noise Figure is introduced and used to compare various regenerator equalizer designs. An optimum equalizer is derived to provide a basis for the comparison. The major conclusion is that cosine rolloff equalizers provide better crosstalk tolerance than Gaussian equalizers and that with particular rolloff factors they achieve near optimum performance. AMI, HDB3, and Class 4 partial response line codes are considered and results placed into practical context by examining regenerator eye diagrams.     

Adaptive bit rate maximizing time-domain equalizer design for DMT-based systems

The classical discrete multitone receiver as used in, e.g., digital subscriber line (DSL) modems, combines a channel shortening time-domain equalizer (TEQ) with one-tap frequency-domain equalizers (FEQs). In a previous paper, the authors proposed a nonlinear bit rate maximizing (BM) TEQ design criterion and they have shown that the resulting BM-TEQ and the closely related BM per-group equalizers (PGEQs) approach the performance of the so-called per-tone equalizer (PTEQ). The PTEQ is an attractive alternative that provides a separate complex-valued equalizer for each active tone. In this paper, the authors show that the BM-TEQ and BM-PGEQ, despite their nonlinear cost criterion, can be designed adaptively, based on a recursive Levenberg-Marquardt algorithm. This adaptive BM-TEQ/BM-PGEQ makes use of the same second-order statistics as the earlier presented recursive least-squares (RLS)-based adaptive PTEQ. A complete range of adaptive BM equalizers then opens up: the RLS-based adaptive PTEQ design is computationally efficient but involves a large number of equalizer taps; the adaptive BM-TEQ has a minimal number of equalizer taps at the expense of a larger design complexity; the adaptive BM-PGEQ has a similar design complexity as the BM-TEQ and an intermediate number of equalizer taps between the BM-TEQ and the PTEQ. These adaptive equalizers allow us to track variations of transmission channel and noise, which are typical of a DSL environment.     

基于概率软切换的两级双模盲均衡器

文中提出一种基于概率软切换的两级双模盲均衡器。它实时统计两级盲均衡器输出硬判决值相同的概率,并利用它切换盲均衡算法。该均衡器结合了级联两级均衡结构和双模算法的优点。仿真表明,它能够纠正相位偏移,相对于波特间隔（BSE）的并发常模＋判决导引（CMA＋DD）盲均衡器,以非常小的计算复杂度代价,获得稳态均方误差（MSE）性能和误比特率（BER）性能的较大提高。     

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     

Performance of smart lightwave receivers with linear equalization

Signal processing techniques can be used to reduce linear and nonlinear distortion in high-speed lightwave systems caused by fiber dispersion and nonideal responses of optoelectronic and electronic components. The improvement in the performance of 2.5 and 10 Gb/s intensity modulation, direct detection systems is assessed for receivers which utilize an analog taped delay line equalizer to compensate for signal distortion. Synchronous and fractionally spaced equalizers are evaluated. Smart receivers that jointly optimize the decision time, decision threshold, and equalizer tap weights under a minimum bit error ration criterion are considered. This yields the optimum system performance and allows consideration of both reduced distortion and enhanced noise arising from the signal processing. The effectiveness of the equalization is determined as a function of several important system parameters. Three-tap and five-tap synchronous equalizers yield virtually the same improvement in receiver sensitivity. Depending on the system, a five-tap fractionally spaced equalizer with half-bit-period tap spacing may or may not be significantly more effective than a three-tap synchronous equalizer     

一种新的神经网络均衡器:结构、算法与性能

本文根据克服数字通信中码间干扰（ISI）的最佳均衡解一般表达式，提出了一种新的自适应神经网络均衡器结构，然后导出了基于该结构的一种自适应算法和相应的学习规则，最后对提出的自适应神经网络均衡器性能进行了计算机模拟，模拟结果与分析表明：本文提出的神经网络均衡器用于实现最佳信道均衡非常有效，比传统线性均衡器和Gibson等人[1]提出的多层感知均衡器（MLPE）性能更优越，更具实用性．