Suppression of adjacent-channel, cochannel, and intersymbolinterference by equalizers and linear combiners

We describe the ability of a linear equalizer/combiner or decision-feedback equalizer to suppress all received adjacent-channel, intersymbol, and cochannel interference. The emphasis is on values among transmitter bandwidth, receiver bandwidth, carrier spacing, and antenna diversity which provide the best opportunities for interference suppression. Through analyses of the number of degrees of freedom and constraints in generalized zero-forcing equalizers, and partial comparisons to calculations of equalizer minimum-mean-square performance, four results are obtained. First, with one antenna and a linear equalizer, arbitrarily large receiver bandwidths allow for marginal improvements in spectral efficiency through decreased carrier spacing, because the carrier spacing cannot be reduced to a value below the symbol rate without incurring unsuppressible interference. Second, large receiver bandwidths assist multiple antennas in improving the spectral efficiency in that carrier spacing values may go below the symbol rate, even in the presence of cochannel interference. Third, the use of equalizers and linear combiners, together with large receiver bandwidths, allows large transmitter bandwidths to be used. Fourth, for cochannel interference and intersymbol interference, the number of interferers that may be suppressible by a generalized zero-forcing linear equalizer/combiner increases linearly with the product of the number of antennas and the truncated integer ratio of the total bandwidth to the symbol rate     

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.     

A Novel Interpolation Equalization Technique for Multicarrier Modulation/Demodulation Systems

This paper presents a novel multitap interpolation equalization technique for filter bank-based multicarrier modulation/demodulation systems. The proposed technique is based on the equalization of the channel fractional delay in each subchannel in time synchronization with the constituent receiver side decimator. The proposed synchronization is achieved by combining a subset of the polyphase components of the analysis filter output signal after having passed through a bank of interpolation equalizers. The resulting multitap interpolation equalization permits a trade-off between various equalization parameters, such as the number of used polyphase components, the length of the equalizer, and the interchannel interference terms, making it possible to achieve a high signal-to-noise ratio (SNR) involving moderate equalization cost or a moderate SNR involving very low equalization cost. Simulation results for the standard carrier serving area loop show that the proposed equalization technique gives rise to 15 dB improvement in SNR compared to the output combiner equalization technique and can achieve an SNR close to the matched-filter bound for the channel by employing a reasonable equalizer length. Compared to the output combiner equalization technique, the proposed equalization technique involves around three times less the storage requirement at the same computational cost or around three times less the computational cost at the same storage requirement for equalizer training. Two suboptimal solutions are also proposed to simplify the equalizer training at only a minor loss in SNR.     

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．     

The equivalence of two unified solutions for optimum space-timeprocessing

Ariyavisitakul et al. (IEEE Trans. Commun., vol.47, p.1073-83, 1999 July) provided a unified analysis of optimum space-time processors based on the following two analytical diversity receiver models: 1) a general model-with a linear filter on each diversity branch, and 2) a “matched filter” model-with a bank of matched filters on each branch, followed by common filter. Closed-form results were given for each receiver model, in terms of the minimum mean-square-error or maximum signal-to-noise ratio solutions for different types of equalizers, including a linear equalizer (LE), a decision-feedback equalizer (DFE), and a maximum-likelihood sequence estimator (MLSE). Although we implied that the two receiver models lead to the same optimum solutions, this requires some proof that is not directly obtainable from the results we presented. We therefore provide such a proof in the present paper for the completeness of the overall unified analysis     

Performance comparison of HSDPA downlink equalizers

To restore the orthogonality of the spreading code, an equalizer is adopted at the receiving site for a HSDPA system. In this paper, BER performance and complexity analysis of various equalizers are compared under different outdoor channels. Results show that with tapering technique, the fast FFT-circulant and Expand-truncate equalizers can ease the condition number problem at a high SNR multipath channel. Simulations also show that the CG method has a satisfactory BER improvement. However, its performance depends notably on the number of iterations.     

Equalization concepts for Alamouti's space-time block code

In this paper, we develop receiver concepts for transmission with space-time block codes (STBCs) over frequency-selective fading channels. The focus lies on Alamouti's space-time block-coding scheme, but the results may be generalized to other STBCs as well. We show that a straightforward combination of conventional equalizers and a space-time block decoder is only possible if at least as many receive antennas as transmit antennas are employed, but not for the practically interesting case of pure transmit diversity, for which space-time coding had been originally developed. This restriction is circumvented by our approach. Here, the structural properties of the transmit signal of space-time block coding, which is shown to be improper (rotationally variant), are fully used. For this, equalizers with widely linear (WL) processing are designed, such as a WL equalizer, a decision-feedback equalizer with WL feedforward and feedback filtering, and a delayed decision-feedback sequence estimator with WL prefiltering. Simulation results demonstrate that the proposed concepts may be successfully employed in an enhanced data rates for GSM evolution (EDGE) receiver, especially for pure transmit diversity. Here, significant gains can be observed, compared with a conventional single-input single-output transmission.     

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。     

Performance of a hybrid decision feedback equalizer structure forCAP-based DSL systems

We study the performance of a class of derision feedback equalizer (DFE) structures for high-speed digital transmission systems. We first present mathematical formulation of minimum mean-square error (MMSE) and the optimum tap coefficients for various finite-length phase-splitting equalizers over the loop in the presence of colored noise, such as near-end crosstalk (NEXT) and far-end crosstalk (FEXT). The performance of the equalizers is also analyzed in the presence of narrowband interference and the channel reflections introduced by bridged taps. The hybrid-type DFE (H-DFE) is presented as a practical equalizer structure for these applications. The results of analysis show that the H-DFE has advantages in the performance and/or in the implementation complexity as compared with the existing DFE structures. An additional advantage of the H-DFE is in the transmission systems that employ the precoding technique. The precoding for the H-DFE allows the system to track small changes in the channel     

A bandwidth-optimized reduced-complexity equalized multicarriertransceiver

A bandwidth-optimized and equalized multicarrier transceiver that achieves near-optimum performance at a practical complexity level is described. The equalizer used is a relatively short FIR filter whose taps and delay are set to optimize the performance of the multicarrier transceiver. Simulation results on a set of carrier-serving-area digital subscriber loops are also presented to demonstrate the separate and joint effects of bandwidth optimization and equalization on performance. Finally, the intriguing idea of using a pole-zero equalizer to achieve the high performance of long FIR equalizers at a much lower implementation cost is investigated     

Application of Fast Kalman Estimation to Adaptive Equalization

Very rapid initial convergence of the equalizer tap coefficients is a requirement of many data communication systems which employ adaptive equalizers to minimize intersymbol interference. As shown in recent papers by Godard, and by Gitlin and Magee, a recursive least squares estimation algorithm, which is a special case of the Kalman estimation algorithm, is applicable to the estimation of the optimal (minimum MSE) set of tap coefficients. It was furthermore shown to yield much faster equalizer convergence than that achieved by the simple estimated gradient algorithm, especially for severely distorted channels. We show how certain "fast recursive estimation" techniques, originally introduced by Morf and Ljung, can be adapted to the equalizer adjustment problem, resulting in the same fast convergence as the conventional Kalman implementation, but with far fewer operations per iteration (proportional to the number of equalizer taps, rather than the square of the number of equalizer taps). These fast algorithms, applicable to both linear and decision feedback equalizers, exploit a certain shift-invariance property of successive equalizer contents. The rapid convergence properties of the "fast Kalman" adaptation algorithm are confirmed by simulation.     

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     

Capacity bound analysis for FIR Be/spl acute/zout equalizers in ISI MIMO channels

We provide a quantitative analysis for the capacity performance of zero-forcing equalizers, also known as Be/spl acute/zout equalizers, in a multiple antenna, frequency-selective fading environment with either parallel or sequential structure. The capacity upper bound of the equalizers, when there is no restriction on the filter length, is derived by directly extending the flat-fading results in a previous paper by the present authors. The parallel structure presents an inherent capacity loss quantified as a function of the channel couplings, which can be avoided by adopting an interference cancellation procedure in the sequential structure. For practical implementation, two approaches are investigated for finite impulse response (FIR) sequential equalizers-truncated LaBe/spl acute/st (Layered Be/spl acute/zout Space-Time) and perfect LaBe/spl acute/st equalizers. For truncated LaBe/spl acute/st equalizers, the percentage of achievable capacity is derived as a function of the filter length in analytical form, and the empirical optimum delay is also provided. For perfect LaBe/spl acute/st equalizers, we demonstrate that the filter choice that yields an optimum signal-to-noise ratio (SNR) can also asymptotically achieve the optimum infinite impulse response (IIR) capacity bound. Both of the two designs can approach the IIR capacity upper bound arbitrarily closely, provided there are an adequate number of FIR taps.     

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     

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.     

Nonlinear equalization of multipath fading channels withnoncoherent demodulation

A nonlinear decision-based adaptive equalizer compatible with differentially coherent phase shift keying (PSK) is proposed for frequency-selective fading channels. This equalization scheme is appropriate whenever conventional equalizers are not capable of tracking phase variations in selective fading channels. The received signal is first converted to a baseband signal and then sent through a differential detector. A nonlinear processor before the equalizer generates the needed nonlinear terms that are weighted and summed in the equalizer. Nonlinear intersymbol interference at the output of the differential detector is dealt with by minimizing an error signal between the output of the equalizer and the detected data. The adaptation algorithm can be any algorithm currently used for conventional equalizers. Our simulation results confirm that for channels with spectral nulls, equalization is achieved successfully with the proposed scheme, whereas, linear equalizers, either with coherent or noncoherent detection, fail     

Equalizer design with integrated envelope-error criterion

Results concerning the design of an equalizer with an integrated envelope-error criterion using the known IF optimum equalizer are presented. The upper bound of envelope error is shown to be twice the IF error. The necessary and sufficient condition for the optimum equalizer among a class of equalizers is derived.     

A novel expression for the achievable MSE performance obtained by blind adaptive equalizers

In this paper, I propose for the noisy, real, and two independent quadrature carrier case, an approximated closed-form expression for the achievable minimum mean square error (MSE) performance obtained by blind equalizers where the error that is fed into the adaptive mechanism which updates the equalizer’s taps can be expressed as a polynomial function of the equalized output of order three like in Godard’s algorithm. The proposed closed-form expression for the achievable MSE is based on the step-size parameter, on the equalizer’s tap length, on the channel power, on the signal to noise ratio (SNR), on the nature of the chosen equalizer, and on the input signal statistics. Since the channel power is measurable or can be calculated if the channel coefficients are given, there is no need anymore to carry out any simulation with various step-size parameters, different values for the signal to noise ratio (SNR) and equalizer’s tap length for a given equalization method, and input signal statistics in order to find the MSE performance in the convergence state.     

Static and dynamic convergence behavior of adaptive blindequalizers

This paper presents a theoretical analysis of the static and dynamic convergence behavior for a general class of adaptive blind equalizers. We first study the properties of prediction error functions of blind equalization algorithms, and then, we use these properties to analyze the static and dynamic convergence behavior based on the independence assumption. We prove in this paper that with a small step size, the ensemble average of equalizer coefficients will converge to the minimum of the cost function near the channel inverse. However, the convergence is not consistent. The correlation matrix or equalizer coefficients at equilibrium are determined by a Lyapunov equation. According to our analysis results, for a given channel and stepsize, there is an optimal length for an equalizer to minimize the intersymbol interference. This result implies that a longer-length blind equalizer does not necessarily outperform a shorter one, which is contrary to what is conventionally conjectured. The theoretical analysis results are confirmed by computer simulations     

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