多电平PAM系统的最佳均衡理论

详细论述了多电平ＰＡＭ（脉冲幅度调制）系统的最佳均衡理论。首先建立了多电平ＰＡＭ系统的一种二进制码间干扰等效模型，将之视为二进制多路系统，从而说明其均稀可以用多个独立的二进制均衡器联事完成。在将均衡问题视为分类判决问题的基础上，根据贝叶斯准则导出了多电平ＰＡＭ系统的最佳均衡有达式和所能取得的最小符号概率的计算公式和近似计算公式。从最佳均衡解可以看到，无论是二进制通信系统还是多电平ＰＡＭ系统，其最佳     

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．     

Reconstruction of chaotic signals with application to channel equalization in chaos‐based communication systems

A number of schemes have been proposed for communication using chaos over the past years. Regardless of the exact modulation method used, the transmitted signal must go through a physical channel which undesirably introduces distortion to the signal and adds noise to it. The problem is particularly serious when coherent‐based demodulation is used because the necessary process of chaos synchronization is difficult to implement in practice. This paper addresses the channel distortion problem and proposes a technique for channel equalization in chaos‐based communication systems. The proposed equalization is realized by a modified recurrent neural network (RNN) incorporating a specific training (equalizing) algorithm. Computer simulations are used to demonstrate the performance of the proposed equalizer in chaos‐based communication systems. The Hénon map and Chua's circuit are used to generate chaotic signals. It is shown that the proposed RNN‐based equalizer outperforms conventional equalizers as well as those based on feedforward neural networks for noisy, distorted linear and non‐linear channels. Copyright © 2004 John Wiley & Sons, Ltd.     

Functional link neural network cascaded with Chebyshev orthogonal polynomial for nonlinear channel equalization

Nonlinear intersymbol interference (ISI) leads to significant error rate in nonlinear communication and digital storage channel. In this paper, therefore, a novel computationally efficient functional link neural network cascaded with Chebyshev orthogonal polynomial is proposed to combat nonlinear ISI. The equalizer has a simple structure in which the nonlinearity is introduced by functional expansion of the input pattern by trigonometric polynomial and Chebyshev orthogonal polynomial. Due to the input pattern and nonlinear approximation enhancement, the proposed structure can approximate arbitrarily nonlinear decision boundaries. It has been utilized for nonlinear channel equalization. The performance of the proposed adaptive nonlinear equalizer is compared with functional link neural network (FLNN) equalizer, multilayer perceptron (MLP) network and radial basis function (RBF) along with conventional normalized least-mean-square algorithms (NLMS) for different linear and nonlinear channel models. The comparison of convergence rate, bit error rate (BER) and steady state error performance, and computational complexity involved for neural network equalizers is provided.     

Blind equalization of nonlinear channels from second-orderstatistics

This paper addresses the blind equalization problem for single-input multiple-output nonlinear channels, based on the second-order statistics (SOS) of the received signal. We consider the class of "linear in the parameters" channels, which can be seen as multiple-input systems in which the additional inputs are nonlinear functions of the signal of interest. These models include (but are not limited to) polynomial approximations of nonlinear systems. Although any SOS-based method can only identify the channel to within a mixing matrix (at best), sufficient conditions are given to ensure that the ambiguity is at a level that still allows for the computation of linear FIR equalizers from the received signal SOS, should such equalizers exist. These conditions involve only statistical characteristics of the input signal and the channel nonlinearities and can therefore be checked a priori. Based on these conditions, blind algorithms are developed for the computation of the linear equalizers. Simulation results show that these algorithms compare favorably with previous deterministic methods     

Coaxial cable passive mesh networks

This paper presents a new type of fault-tolerant access network: an all-passive coaxial cable mesh network. The passive mesh network could have any topology, with cycles allowed. A technique for calculating the multipath response of the passive mesh network is presented. Both the delay and attenuation of a coaxial cable are represented by a single transform variable. The mesh network is modeled as a linear system with a state space that represents signal propagation. The channel responses of the individual sections of cable define the entries of a state-transition matrix. Using this theory, expressions are given for the overall mesh-network channel response. These expressions are manipulated to derive equalizer structures. The equalizers are zero-forcing and use decision feedback. It is shown that signals transmitted on any mesh network can be equalized. An example mesh topology, and equalizers for it, are presented. Signal and interference attenuation, and opposite-phase received carrier cancellation, are also discussed. The passive mesh network could be an inexpensive fault-tolerant architecture for residential access to telephony, cable TV, and future services     

Soft-Input Soft-Output Equalizers for Turbo Receivers: A Statistical Physics Perspective

Many algorithms in signal processing and digital communications must deal with the problem of computing the probabilities of the hidden state variables given the observations, i.e., the inference problem, as well as with the problem of estimating the model parameters. Such an inference and estimation problem is encountered, for e.g., in adaptive turbo equalization/demodulation where soft information about the transmitted data symbols has to be inferred in the presence of the channel uncertainty, given the received signal samples and a priori information provided by the decoder. An exact inference algorithm computes the a posteriori probability (APP) values for all transmitted symbols, but the computation of APPs is known to be an NP-hard problem, thus, rendering this approach computationally prohibitive in most cases. In this paper, we show how many of the well-known low-complexity soft-input soft-output (SISO) equalizers, including the channel-matched filter-based linear SISO equalizers and minimum mean square error (MMSE) SISO equalizers, as well as the expectation-maximization (EM) algorithm-based SISO demodulators in the presence of the Rayleigh fading channel, can be formulated as solutions to a variational optimization problem. The variational optimization is a well-established methodology for low-complexity inference and estimation, originating from statistical physics. Importantly, the imposed variational optimization framework provides an interesting link between the APP demodulators and the linear SISO equalizers. Moreover, it provides a new set of insights into the structure and performance of these widely celebrated linear SISO equalizers while suggesting their fine tuning as well.     

Performance bounds for multistep prediction-based blindequalization

Blind equalization attempts to remove the interference caused by a communication channel without using any known training sequences. Blind equalizers may be implemented with linear prediction-error filters (PEFs). For many practical channel types, a suitable delay at the output of the equalizer allows for achieving a small estimation error. The delay cannot be controlled with one-step predictors. Consequently, multistep PEF-based algorithms have been suggested as a solution to the problem. The derivation of the existing algorithms is based on the assumption of a noiseless channel, which results in zero-forcing equalization. We consider the effects of additive noise at the output of the multistep PEF. Analytical error bounds for two PEF-based blind equalizers in the presence of noise are derived. The obtained results are verified with simulations. The effect of energy concentration in the channel impulse response on the error bound is also addressed     

Performance of Reduced-Rank Equalization

We evaluate the performance of reduced-rank equalizers for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) frequency-selective channels. Each equalizer filter is constrained to lie in a Krylov subspace, and can be implemented as a reduced-rank multistage Wiener filter (MSWF). Both reduced-rank linear and decision-feedback equalizers (DFEs) are considered. Our results are asymptotic as the filter length goes to infinity. For SISO channels, the output mean-squared error (MSE) is expressed in terms of the moments of the channel spectrum. For MIMO channels, both successive and parallel interference cancellation are considered. The asymptotic performance in that case requires the computation of moments, which depend on shifted versions of the channel impulse response for different users. Those are also expressed in terms of the MIMO channel frequency response. Numerical results are presented, which show that near full-rank performance can be achieved with relatively low-rank equalizers     

The structure and design of realizable decision feedback equalizers for IIR channels with colored noise

A simple algorithm for optimizing decision feedback equalizers (DFEs) by minimizing the mean-square error (MSE) is presented. A complex baseband channel and correct past decisions are assumed. The dispersive channel may have infinite impulse response, and the noise may be colored. Consideration is given to optimal realizable (stable and finite-lag smoothing) forward and feedback filters in discrete time. They are parameterized as recursive filters. In the special case of transmission channels with finite impulse response and autoregressive noise, the minimum MSE can be attained with transversal feedback and forward filters. In general, the forward part should include a noise-whitening filter (the inverse noise model). The finite realizations of the filters are calculated using a polynomial equation approach to the linear quadratic optimization problem. The equalizer is optimized essentially by solving a system of linear equations Ax=B, where A contains transfer function coefficients from the channel and noise model. No calculation of correlations is required with this method. A simple expression for the minimal MSE is presented. The DFE is compared to MSE-optimal linear recursive equalizers. Expressions for the equalizer in the limiting case of infinite smoothing lags are also discussed.<>     

Diversity–Multiplexing Tradeoff in ISI Channels

The optimal diversity–multiplexing tradeoff curve for the intersymbol interference (ISI) channel is computed and various equalizers are analyzed using this performance metric. Maximum-likelihood signal decoding (MLSD) and decision feedback equalization (DFE) equalizers achieve the optimal tradeoff without coding, but zero forcing (ZF) and minimum mean-square-error (MMSE) equalizers do not. However if each transmission block is ended with a period of silence lasting the coherence time of the channel, both ZF and MMSE equalizers become diversity-multiplexing optimal. This suggests that the bulk of the performance gain obtained by replacing linear decoders with computationally intensive ones such as orthogonal frequency-division multiplexing (OFDM) or Viterbi, can be realized in much simpler fashion—with a small modification to the transmit scheme.      

基于复数径向基函数神经网络的自适应均衡器

本文对基于复数径向基函数网络（ＣＲＢＦＮ）的自适应均衡器作了研究；提出了两种新的复数径向基函数网络结构的均衡器；正交ＣＲＢＦＮ（ＯＣＲＢＦＮ）均衡器与非对称ＣＲＢＦＮ（ＡＣＲＢＦＮ）均衡器；并在此了提出了这两种自适应均衡器的训练算法，模拟结果表明对于线性信道或非线性信道定这两种基于ＣＲＢＦＮ均衡器的收敛性能比文献「２，５」中的元首衡器优越，具有一定的实用价值。     

Performance of equalization techniques in a radio interferenceenvironment

The performance of equalization techniques for digital radio systems in the presence of sinusoidal and modulated interference signals is investigated. Linear and nonlinear equalizers, as well as synchronous and T/2-spaced structures, are considered. It is shown that synchronous decision-feedback equalizers are powerful countermeasure devices for radio channels affected by both selective fading and sinusoidal interferers, and that both T/2-spaced linear and nonlinear equalizers can provide a significant improvement of the adjacent channel interference margin, whether the channel is selective or not, especially in the case of multicarrier interleaved frequency arrangements     

Kalman Filter-Trained Recurrent Neural Equalizers for Time-Varying Channels

Recurrent neural networks have been successfully applied to communications channel equalization because of their modeling capability for nonlinear dynamic systems. Major problems of gradient-descent learning techniques commonly employed to train recurrent neural networks are slow convergence rates and long training sequences required for satisfactory performance. This paper presents decision-feedback equalizers using a recurrent neural network trained with Kalman-filtering algorithms. The main features of the proposed recurrent neural equalizers, using the extended Kalman filter and the unscented Kalman filter, are fast convergence and good performance using relatively short training symbols. Experimental results for various time-varying channels are presented to evaluate the performance of the proposed approaches over a conventional recurrent neural equalizer.     

Eigenanalysis-based blind methods for identification, equalization,and inversion of linear time-invariant channels

Some blind algorithms are presented for estimation of equalizers for linear time invariant (LTI) channels from the eigenvectors of certain rank-one matrices constructed from the second-order statistics of the oversampled received signal. It is shown that the channel can also be identified from the same matrices. It can be shown that in multipath dominated environments, equalizers with symbol spread of only one (referred to as inverters) can be used when sufficient diversity is available. Because of the manner in which structure in the channel distortion is exploited, the proposed identification and equalization algorithms are also applicable to this case. For the same reason, the proposed algorithms do not require estimation of the channel memory (only an upper bound is required). Equalizers of desired delay are estimated directly independent of others     

Blind turbo equalization in Gaussian and impulsive noise

We consider the problem of simultaneous parameter estimation and restoration of finite-alphabet symbols that are blurred by an unknown linear intersymbol interference (ISI) channel and contaminated by additive Gaussian or non-Gaussian white noise with unknown parameters. Non-Gaussian noise is found in many wireless channels due to the impulsive phenomena of radio-frequency interference. Bayesian inference of all unknown quantities is made from the blurred and noisy observations. The Gibbs sampler, a Markov chain Monte Carlo procedure, is employed to calculate the Bayesian estimates. The basic idea is to generate ergodic random samples from the joint posterior distribution of all unknowns and then to average the appropriate samples to obtain the estimates of the unknown quantities. Blind Bayesian equalizers based on the Gibbs sampler are derived for both Gaussian ISI channel and impulsive ISI channel. A salient feature of the proposed blind Bayesian equalizers is that they can incorporate the a priori symbol probabilities, and they produce as output the a posteriori symbol probabilities. (That is, they are “soft-input soft-output” algorithms.) Hence, these methods are well suited for iterative processing in a coded system, which allows the blind Bayesian equalizer to refine its processing based on the information from the decoding stage and vice versa-a receiver structure termed as blind turbo equalizer     

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.     

Advanced Time- and Frequency-Domain Adaptive Equalization in Multilevel QAM Digital Radio Systems

Digital radio systems employing multilevel QAM are at least optionally equipped with adaptive time- and/or frequency-domain equalizers. Their purpose is to reduce the vulnerability of these systems to linear distortion caused by multipath propagation. Linear transversal filters are prominent candidates for the realization of time-domain equalizers, especially for high-capacity applications. They are well known for their good performance and their relatively easy implementation at a high data rate. On the other hand, decision feedback equalizers are known to be very capable of eliminating linear distortion, especially of the so-called minimum-phase type. But realization problems are likely to occur in a high-speed application. A solution is proposed which merges the relative advantages of both the linear transversal and the decision feedback approaches. The goal of a frequency-domain equalizer, which is the restoration of the shape of the power density spectrum of the received signal without any recovered carrier and timing signals, can also be achieved with the aid of a transversal filter. The performance obtained with the joint utilization of the novel timeand frequency-domain equalizers is described.     

Blind fractionally spaced equalization of noisy FIR channels:direct and adaptive solutions

Blind fractionally spaced equalizers reduce intersymbol interference using second-order statistics without the need for training sequences. Methods for finding FIR zero-forcing blind equalizers directly from the observations are described, and adaptive versions are developed. In contrast, most current methods require channel estimation as a first step to estimating the equalizer. The direct methods can be zero-forcing, minimum mean-square error, or even minimum mean square error (MMSE) within the class of zero-forcing equalizers. Performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels, including an empirically measured digital microwave channel     

A decision feedback recurrent neural equalizer as an infiniteimpulse response filter

An adaptive decision feedback recurrent neural equalizer (DFRNE), which models a kind of an IIR structure, is proposed. Its performance is compared with the traditional linear and nonlinear equalizers with FIR structures for various communication channels. The small size and high performance of the DFRNE makes it suitable for high-speed channel equalization