A new adaptive equalizer with channel estimator for mobile radiocommunication

For unknown mobile radio channels with severe intersymbol interference (ISI), a maximum likelihood sequence estimator, such as a decision feedback equalizer (DFE) having both feedforward and feedback filters, needs to handle both precursors and postcursors. Consequently, such an equalizer is too complex to be practical. This paper presents a new reduced-state, soft decision feedback Viterbi equalizer (RSSDFVE) with a channel estimator and predictor. The RSSDFVE uses maximum likelihood sequence estimation (MLSE) to handle the precursors and truncates the overall postcursors with the soft decision of the MLSE to reduce the implementation complexity. A multiray fading channel model with a Doppler frequency shift is used in the simulation. For fast convergence, a channel estimator with fast start-up is proposed. The channel estimator obtains the sampled channel impulse response (CIR) from the training sequence and updates the RSSDFVE during the bursts in order to track changes of the fading channel. Simulation results show the RSSDFVE has nearly the same performance as the MLSE for time-invariant multipath fading channels and better performance than the DFE for time-variant multipath fading channels with less implementation complexity than the MLSE. The fast start-up (FS) channel estimator gives faster convergence than a Kalman channel estimator. The proposed RSSDFVE retains the MLSE structure to obtain good performance and only uses soft decisions to subtract the postcursor interference. It provides the best tradeoff between complexity and performance of any Viterbi equalizers     

一种低复杂度聚类估计MLSE均衡器

给出了一种新的聚类估计最大似然序列均衡器(CBSE),避开了传统MLSE均衡需要估计信道脉冲响应(CIR)和卷积运算,由接收信号估计聚类中心,同时利用聚类中心之间的对称性,仅需估计其中部分中心,其余中心可通过简单运算获取,从而在缩短训练序列的同时减少了运算量.仿真表明,新方法在取得与RLS均衡器相近收敛性能的同时,计算量比LMS均衡器小.     

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.     

Adaptive MLSE equalizers with parametric tracking for multipathfast-fading channels

We use the parametric channel identification algorithm proposed by Chen and Paulraj (see Proc. IEEE Vehicular Technology Conf., p.710-14, 1997) and by Chen, Kim and Liang (see IEEE Trans. Veh. Technol., p.1923-35, 1999) to adaptively track the fast-fading channels for the multichannel maximum likelihood sequence estimation (MLSE) equalizer using multiple antennas. Several commonly-used channel tracking schemes, decision-directed recursive least square (DD/RLS), per-survivor processing recursive least square (PSP/RLS) and other reduced-complexity MLSE algorithms are considered. An analytic lower bound for the multichannel MLSE equalizer with no channel mismatch in the time-varying specular multipath Rayleigh-fading channels is derived. Simulation results that illustrate the performance of the proposed algorithms working with various channel tracking schemes are presented, and then these results are compared with the analytic bit error rate (BER) lower bound and with the conventional MLSE equalizers directly tracking the finite impulse response (FIR) channel tap coefficients. We found that the proposed algorithm always performs better than the conventional adaptive MLSE algorithm, no matter what channel tracking scheme is used. However, which is the best tracking scheme to use depends on the scenario of the system     

Low-complexity equalization for π/4 DQPSK signals based on themethod of projection onto convex sets

An equalizer adaptation technique for compensation of degradations caused by multipath Rayleigh fading channels to π/4 differential quadrature phase shift keying (DQPSK)-modulated signals is presented. The technique is applied to linear and nonlinear transversal-filter-type equalizers. It is based on the method of projection onto convex sets (POCS), realized in a particular form of the iterative least mean squares (LMS) procedure. The convergence speed of the proposed equalizer coefficient adaptation technique and its computational complexity depend on the newly introduced look-back parameter. Both can be tailored to the characteristics of the channel. For achieving convergence speeds comparable to speeds of recursive least squares (RLS) techniques, the computational load of the presented equalization is of the order of the load required of RLS techniques. However, its algorithmic implementation is notably simpler and its code and storage size requirements are smaller. The technique is numerically stable, and it is suitable for low-power implementations in digital signal processors or custom very large-scale integration (VLSI) circuits. Performed simulations verify good performance of the technique in various channel conditions for 900-MHz multipath fading radio channels     

A new channel estimator for fast start-up equalization

A novel noniterative algorithm is proposed for estimating the sampled impulse response of unknown channels. With the proper choice of the training sequence, implementation of the proposed channel estimator requires only additions and subtractions, i.e. no multiplications of the estimator is so simple that it can be easily implemented using an ordinary microprocessor with minimal storage. The channel estimate can serve to reduce the effects of intersymbol interference either by the maximum likelihood sequence estimator using the Viterbi algorithm or by channel equalization with a direct solution to obtain the optimum equalizer taps. A new procedure for the latter case is proposed using the Levinson-Trench algorithm for fast start-up of adaptive equalizers in noisy environments. The performance of the proposed algorithm is evaluated through simulation, and it is compared to some previous techniques. Computational efficiency is also taken into account. The results of the simulation show the superiority of the proposed scheme     

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 robust noncoherent equalizer receiver for fading channels with short memory .I. Basic structure

Traditional equalizers are very sensitive to carrier frequency offsets between the transmitter and receiver. Coherent receivers with frequency estimation algorithms can remove the offset to prevent the equalizer breakdown, but with a penalty in receiver complexity. On the other hand, noncoherent receivers such as differential detectors are inherently robust to the frequency offsets but cannot employ standard equalization techniques due to their nonlinear front-end. We introduce a simple noncoherent equalizer receiver structure for fading channel environments with short memory (up to two-bit intervals). The receiver consists of a whitened matched filter followed by a differential detector and a maximum likelihood sequence estimation (MLSE) equalizer. We examine the performance of this noncoherent equalizer by both analysis and simulation. It is shown that despite the simplicity, this receiver structure is capable of significant performance improvement as compared to an ordinary differential detector while operating with receiver frequency offsets two orders of magnitude greater than a traditional MLSE equalizer. This structure offers an attractive solution for high-bit-rate cordless transmission systems such as Digital Enhanced Cordless Telecommunications (DECT) that use simple noncoherent receivers whose performance can be constrained by channel dispersion. Using DECT as a case study, we show that the equalizer's performance limits are caused by the receiver nonlinearity and can be improved by adaptation of this nonlinearity to channel conditions.     

Novel spatiotemporal equalization based on cascaded connection of multibeam adaptive array and multi-input MLSE

This paper proposes a novel spatiotemporal equalizer using a cascaded connection of multibeam adaptive array and multi-input maximum likelihood sequence estimation (MLSE) based on single-user detection. The computational load for the proposed method is much lower than that of the optimal method, and computer simulations revealed that its bit-error-rate (BER) performance is identical to that of the optimal method. Theoretical analysis also supports equivalency between these methods.     

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     

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.     

Application of Sequential Estimation Algorithm Based on Branch Metric to Frequency-Selective Channel Equalization

In this work, a sequential estimation algorithm based on branch metric is used as channel equalizer to combat intersymbol interference in frequency-selective wireless communication channels. The bit error rate (BER) and computational complexity of the algorithm are compared with those of the maximum likelihood sequence estimation (MLSE), the recursive least squares (RLS) algorithm, the Fano sequential algorithm, the stack sequential algorithm, list-type MAP equalizer, soft-output sequential algorithm (SOSA) and maximum-likelihood soft-decision sequential decoding algorithm (MLSDA). The BER results have shown that whilst the sequential estimation algorithm has a close performance to the MLSE using the Viterbi algorithm, its performance is better than the other algorithms. Beside, the sequential estimation algorithm is the best in terms of computational complexity among the algorithms mentioned above, so it performs the channel equalization faster. Especially in M-ary modulated systems, the equalization speed of the algorithm increases exponentially when compared to those of the other algorithms.     

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.     

基于Hammerstein模型的非线性信道广义线性盲均衡算法

为了提高非线性信道盲均衡的性能、降低运算复杂度,本文以Hammerstein模型代替传统的Volterra级数模型来模拟非线性信道,利用非线性信道接收信号呈现非圆性的特点,构造了一种新的基于Wiener非线性模型的广义线性盲均衡器,并在常模准则的基础上提出了NCWL-CMA和NCWL-CMA Newton-like两种非线性信道广义线性盲均衡器抽头系数更新算法.理论分析和仿真实验结果表明,与传统盲均衡算法相比,新算法显著地降低了剩余码间干扰,提高了收敛速度.     

On the least-squares performance of a novel efficient center estimation method for clustering-based MLSE equalization

Recently, a novel maximum-likelihood sequence estimation (MLSE) equalizer was reported that avoids the explicit estimation of the channel impulse response. Instead, it is based on the fact that the (noise-free) channel outputs, needed by the Viterbi algorithm, coincide with the points around which the received (noisy) samples are clustered and can thus be estimated directly with the aid of a supervised clustering method. Moreover, this is achieved in a computationally efficient manner that exploits the channel linearity and the symmetries underlying the transmitted signal constellation. The resulting computational savings over the conventional MLSE equalization scheme are significant even in the case of relatively short channels where MLSE equalization is practically applicable. It was demonstrated, via simulations, that the performance of this algorithm is close to that using a least-squares (LS) channel estimator, although its computational complexity is even lower than that of the least-mean squares (LMS)-trained MLSE equalizer. This paper investigates the relationship of the center estimation (CE) part of the proposed equalizer with the LS method. It is proved that, when using LS with the training sequence employed by CE, the two methods lead to the same solution. However, when LS is trained with random data, it outperforms CE, with the performance difference being proportional to the channel length. A modified CE method, called MCE, is thus developed, that attains the performance of LS with perfectly random data, while still being much simpler computationally than classical LS estimation. Through the results of this paper, CE is confirmed as a methodology that combines high performance, simplicity, and low computational cost, as required in a practical equalization task. An alternative, algebraic viewpoint on the CE method is also provided.     

基于非单点模糊支持向量机的判决反馈均衡器

该文提出了一种具有较强抗突发干扰能力的非单点模糊支持向量机判决反馈均衡器。该方法以支持向量机为框架,采用具有前置滤波特性的非单点模糊高斯核函数,利用梯度下降法调整核函数中的可调参数。通过仿真实验,并与支持向量机判决反馈均衡器和传统判决反馈均衡器进行比较,结果证明该方法具有优良的非线性均衡能力和抗突发干扰能力。     

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     

基于非单点模糊RBF网络的判决反馈均衡器

提出了一种具有较强抗突发干扰能力的非单点模糊径向基函数（Radial Basis Function,RBF）网络判决反馈均衡器.该方法将具有前置滤波特性的非单点模糊化技术引入RBF网络,利用梯度下降法自适应调整参数.通过仿真实验,并与基于径向基函数网络的判决反馈均衡器（Radial Basis Function Network-Decision Feedback Equalizer,RBFN-DFE）和传统判决反馈均衡器（Decision Feedback Equalizer,DFE）进行比较,结果证明该方法抗突发干扰能力强,误码性能好.     

Low-Complexity Block Turbo Equalization for OFDM Systems in Time-Varying Channels

We propose low-complexity block turbo equalizers for orthogonal frequency-division multiplexing (OFDM) systems in time-varying channels. The presented work is based on a soft minimum mean-squared error (MMSE) block linear equalizer (BLE) that exploits the banded structure of the frequency-domain channel matrix, as well as a receiver window that enforces this banded structure. This equalization approach allows us to implement the proposed designs with a complexity that is only linear in the number of subcarriers. Three block turbo equalizers are discussed: two are based on a biased MMSE criterion, while the third is based on the unbiased MMSE criterion. Simulation results show that the proposed iterative MMSE BLE achieves a better bit error rate (BER) performance than a previously proposed iterative MMSE serial linear equalizer (SLE). The proposed equalization algorithms are also tested in the presence of channel estimation errors.      

A NEW ADAPTIVE EQUALIZER STRUCTURE FOR NONLINEAR CHANNELS

Based on the analysis of nonlinear channel models,a new connectionist model ofadaptive equalizer is constructed.Comparing with the connectionist model using the Volterraseries to extend the input vector space,the number of weights with the new structure is reducedsignificantly.It is shown by simulations that the weight values of the new scheme converge to theoptimal values closely for non-minimum phase channels as well minimum phase channels,if thechannel noise is small enough.Testing results of the BER(Bit Error Rate)tell us that the newadaptive equalizer for nonlinear channels is superior to the conventional linear equalizers in theequalization performances.