Nonlinear channel equalization for QAM signal constellation usingartificial neural networks

Application of artificial neural networks (ANN's) to adaptive channel equalization in a digital communication system with 4-QAM signal constellation is reported in this paper. A novel computationally efficient single layer functional link ANN (FLANN) is proposed for this purpose. This network has a simple structure in which the nonlinearity is introduced by functional expansion of the input pattern by trigonometric polynomials. Because of input pattern enhancement, the FLANN is capable of forming arbitrarily nonlinear decision boundaries and can perform complex pattern classification tasks. Considering channel equalization as a nonlinear classification problem, the FLANN has been utilized for nonlinear channel equalization. The performance of the FLANN is compared with two other ANN structures [a multilayer perceptron (MLP) and a polynomial perceptron network (PPN)] along with a conventional linear LMS-based equalizer for different linear and nonlinear channel models. The effect of eigenvalue ratio (EVR) of input correlation matrix on the equalizer performance has been studied. The comparison of computational complexity involved for the three ANN structures is also provided.     

Nonlinear dynamic system identification using pipelined functional link artificial recurrent neural network

A computationally efficient pipelined functional link artificial recurrent neural network (PFLARNN) is proposed for nonlinear dynamic system identification using a modification real-time recurrent learning (RTRL) algorithm in this paper. In contrast to a feedforward artificial neural network (such as a functional link artificial neural network (FLANN)), the proposed PFLARNN consists of a number of simple small-scale functional link artificial recurrent neural network (FLARNN) modules. Since those modules of PFLARNN can be performed simultaneously in a pipelined parallelism fashion, this would result in a significant improvement in its total computational efficiency. Moreover, nonlinearity of each module is introduced by enhancing the input pattern with nonlinear functional expansion. Therefore, the performance of the proposed filter can be further improved. Computer simulations demonstrate that with proper choice of functional expansion in the PFLARNN, this filter performs better than the FLANN and multilayer perceptron (MLP) for nonlinear dynamic system identification.     

An adaptive decision feedback equalizer based on the combination of the FIR and FLNN

To compensate the linear and nonlinear distortions and to track the characteristic of the time-varying channel in digital communication systems, a novel adaptive decision feedback equalizer (DFE) with the combination of finite impulse response (FIR) filter and functional link neural network (CFFLNNDFE) is introduced in this paper. This convex nonlinear combination results in improving the convergence speed while retaining the lower steady-state error at the cost of a small increasing computational burden. To further improve the performance of the nonlinear equalizer, we derive here a novel simplified modified normalized least mean square (SMNLMS) algorithm. Moreover, the convergence properties of the proposed algorithm are analyzed. Finally, computer simulation results which support analysis are provided to evaluate the performance of the proposed equalizer over the functional link neural network (FLNN), radial basis function (RBF) neural network and linear equalizer with decision feedback (LMSDFE) for time-invariant and time-variant nonlinear channel models in digital communication systems.     

Communication channel equalization using complex-valued minimalradial basis function neural networks

A complex radial basis function neural network is proposed for equalization of quadrature amplitude modulation (QAM) signals in communication channels. The network utilizes a sequential learning algorithm referred to as complex minimal resource allocation network (CMRAN) and is an extension of the MRAN algorithm originally developed for online learning in real-valued radial basis function (RBF) networks. CMRAN has the ability to grow and prune the (complex) RBF network's hidden neurons to ensure a parsimonious network structure. The performance of the CMRAN equalizer for nonlinear channel equalization problems has been evaluated by comparing it with the functional link artificial neural network (FLANN) equalizer of J.C. Patra et al. (1999) and the Gaussian stochastic gradient (SG) RBF equalizer of I. Cha and S. Kassam (1995). The results clearly show that CMRANs performance is superior in terms of symbol error rates and network complexity.     

A channel equalizer using reduced decision feedback Chebyshev functional link artificial neural networks

In this paper, a reduced decision feedback Chebyshev functional link artificial neural network (RDF-CFLANN) is proposed for the design of a nonlinear channel equalizer. An RDF-CFLANN structure uses functional expansion utilities to nonlinearly transform its input signals into the output space. In most MLP structures, one or more hidden layers are needed to nonlinearly map the input signals to the output signal space. Therefore, the complexity of the RDF-CFLANN structure is generally much lower than that of an MLP structure. In addition, the required amount of computing at the training mode can also be reduced. The comparisons of the mean squared error (MSE) and the average transmission bit error rate (BER) among RDF-CFLANN, DF-CFLANN and CFLANN are presented in this paper. Simulation results demonstrate that RDF-CFLANN presents the best performance among the three structures.     

Adaptively Combined FIR and Functional Link Artificial Neural Network Equalizer for Nonlinear Communication Channel

This paper proposes a novel computational efficient adaptive nonlinear equalizer based on combination of finite impulse response (FIR) filter and functional link artificial neural network (CFFLANN) to compensate linear and nonlinear distortions in nonlinear communication channel. This convex nonlinear combination results in improving the speed while retaining the lower steady-state error. In addition, since the CFFLANN needs not the hidden layers, which exist in conventional neural-network-based equalizers, it exhibits a simpler structure than the traditional neural networks (NNs) and can require less computational burden during the training mode. Moreover, appropriate adaptation algorithm for the proposed equalizer is derived by the modified least mean square (MLMS). Results obtained from the simulations clearly show that the proposed equalizer using the MLMS algorithm can availably eliminate various intensity linear and nonlinear distortions, and be provided with better anti-jamming performance. Furthermore, comparisons of the mean squared error (MSE), the bit error rate (BER), and the effect of eigenvalue ratio (EVR) of input correlation matrix are presented.     

Efficient prediction of exchange rates with low complexity artificial neural network models

In recent years forecasting of financial data such as interest rate, exchange rate, stock market and bankruptcy has been observed to be a potential field of research due to its importance in financial and managerial decision making. Survey of existing literature reveals that there is a need to develop efficient forecasting models involving less computational load and fast forecasting capability. The present paper aims to fulfill this objective by developing two novel ANN models involving nonlinear inputs and simple ANN structure with one or two neurons. These are: functional link artificial neural network (FLANN) and cascaded functional link artificial neural network (CFLANN). These have been employed to predict currency exchange rate between US$ to British Pound, Indian Rupees and Japanese Yen. The performance of the proposed models have been evaluated through simulation and have been compared with those obtained from standard LMS based forecasting model. It is observed that the CFLANN model performs the best followed by the FLANN and the LMS models.     

Robust nonlinear channel equalization using WNN trained by symbiotic organism search algorithm

In the present world of ‘Big Data,’ the communication channels are always remaining busy and overloaded to transfer quintillion bytes of information. To design an effective equalizer to prevent the inter-symbol interference in such scenario is a challenging task. In this paper, we develop equalizers based on a nonlinear neural structure (wavelet neural network (WNN)) and train it's weighted by a recently developed meta-heuristic (symbiotic organisms search algorithm). The performance of the proposed equalizer is compared with WNN trained by cat swarm optimization (CSO) and clonal selection algorithm (CLONAL), particle swarm optimization (PSO) and least mean square algorithm (LMS). The performance is also compared with other equalizers with structure based on functional link artificial neural network (trigonometric FLANN), radial basis function network (RBF) and finite impulse response filter (FIR). The superior performance is demonstrated on equalization of two non-linear three taps channels and a linear twenty-three taps telephonic channel. It is observed that the performance of the gradient algorithm based equalizers fails in the presence of burst error. The robustness in the performance of the proposed equalizers to handle the burst error conditions is also demonstrated.     

Improved functional link artificial neural network via convex combination for nonlinear active noise control

A method relying on the convex combination of two normalized filtered-s least mean square algorithms (CNFSLMS) is presented for nonlinear active noise control (ANC) systems with a linear secondary path (LSP) and nonlinear secondary path (NSP) in this paper. The proposed CNFSLMS algorithm-based functional link artificial neural network (FLANN) filter, aiming to overcome the compromise between convergence speed and steady state mean square error of the NFSLMS algorithm, offers both fast convergence rate and low steady state error. Furthermore, by replacing the sigmoid function with the modified Versorial function, the modified CNFSLMS (MCNFSLMS) algorithm with low computational complexity is also presented. Experimental results illustrate that the combination scheme can behave as well as the best component and even better. Moreover, the MCNFSLMS algorithm requires less computational complexity than the CNFSLMS while keeping the same filtering performance.     

Pipelined Chebyshev Functional Link Artificial Recurrent Neural Network for Nonlinear Adaptive Filter

A novel nonlinear adaptive filter with pipelined Chebyshev functional link artificial recurrent neural network (PCFLARNN) is presented in this paper, which uses a modification real-time recurrent learning algorithm. The PCFLARNN consists of a number of simple small-scale Chebyshev functional link artificial recurrent neural network (CFLARNN) modules. Compared to the standard recurrent neural network (RNN), those modules of PCFLARNN can simultaneously be performed in a pipelined parallelism fashion, and this would lead to a significant improvement in its total computational efficiency. Furthermore, contrasted with the architecture of a pipelined RNN (PRNN), each module of PCFLARNN is a CFLARNN whose nonlinearity is introduced by enhancing the input pattern with Chebyshev functional expansion, whereas the RNN of each module in PRNN utilizing linear input and first-order recurrent term only fails to utilize the high-order terms of inputs. Therefore, the performance of PCFLARNN can further be improved at the cost of a slightly increased computational complexity. In addition, due to the introduced nonlinear functional expansion of each module in PRNN, the number of input signals can be reduced. Computer simulations have demonstrated that the proposed filter performs better than PRNN and RNN for nonlinear colored signal prediction, nonstationary speech signal prediction, and chaotic time series prediction.      

Legendre神经网络非线性信道均衡

在分析Chebyshev正交多项式神经网络非线性滤波器的基础上，利用Legendre正交多项式快速逼近的优良特性以及判决反馈均衡器的结构特点，提出了两种新型结构的非线性均衡器，并利用NLMS算法，推导出自适应算法．仿真表明，无论通信信道是线性还是非线性，Legendre神经网络自适应均衡器与Chebyshev神经网络均衡器的各项性能均接近，而Legendre神经网络判决反馈自适应均衡器能够更有效地消除码间干扰和非线性干扰，误码性能也得到较好的改善．     

一种组合神经网络非线性判决反馈均衡器

1 引言数字通信系统的典型模型如图1所示,发送序列s(n)经信道传输后因发生失真及噪声v(n)的影响而成为畸变信号x(n),为此需用均衡器对其进行均衡以恢复发送序列。目前,自适应均衡已成为数字通信中一种非常重要的技术,自适应均衡器的构成也是多种多样,其中最简单的是线性横向均衡器(LTE)和判决反馈均衡器(DFE),它们都比较适用于线性信道。如果信道呈现非线性特性,两者的性能特别是LTE的均衡能力会大大下降,而利用径向基函数网络(RBFN)等构     

Decision feedback recurrent neural equalization with fast convergence rate

Real-time recurrent learning (RTRL), commonly employed for training a fully connected recurrent neural network (RNN), has a drawback of slow convergence rate. In the light of this deficiency, a decision feedback recurrent neural equalizer (DFRNE) using the RTRL requires long training sequences to achieve good performance. In this paper, extended Kalman filter (EKF) algorithms based on the RTRL for the DFRNE are presented in state-space formulation of the system, in particular for complex-valued signal processing. The main features of global EKF and decoupled EKF algorithms are fast convergence and good tracking performance. Through nonlinear channel equalization, performance of the DFRNE with the EKF algorithms is evaluated and compared with that of the DFRNE with the RTRL.     

Robust identification of nonlinear complex systems using low complexity ANN and particle swarm optimization technique

The paper introduces a novel method of adaptive robust identification of complex nonlinear dynamic plants including Box Jenkin, Mackey Glass and Sunspot series under the presence of strong outliers in the training samples. The identification model consists of a low complexity single layer functional link artificial neural network (FLANN) in the feed forward path and another on the feedback path. The connecting weights are iteratively adjusted by a population based particle swarm optimization technique so that a robust cost function (RCF) of the model-error is minimized. To demonstrate robust identification performance up to 50% random samples of the plant output is contaminated with strong outliers and are employed for training the model using PSO tool. Identification of wide varieties of benchmark complex static and dynamic plants is carried out through simulation study and the performance obtained are compared with those obtained from using standard squared error norm as CF. It is in general observed that, the Wilcoxon norm provides best identification performance compared to squared error and other RCFs based models.     

基于UKF的自适应DFE信道均衡

针对信道的线性和非线性失真,在分析简化的非线性滤波的基础上,利用判决反馈的结构特点对其进行扩展,提出了基于UKF滤波的判决反馈均衡器,仿真表明,UKF滤波算法能降低系统均方误差性能。     

基于外积FLNN的非线性系统辨识

函数型连接神经网络通过对输入模式预先进行非线性扩展,增强了输入信号的模式表达,从而大大简化网络结构,降低计算复杂度。本文提出一种外积扩展型连接神经网络,用于辨识幂函数非线性系统,并与MLP和CFLNN网络对比,仿真结果表明,外积型辨识幂函数非线性系统结构简单、计算量低、性能最优。     

Complex-bilinear recurrent neural network for equalization of adigital satellite channel

Equalization of satellite communication using complex-bilinear recurrent neural network (C-BLRNN) is proposed. Since the BLRNN is based on the bilinear polynomial, it can be used in modeling highly nonlinear systems with time-series characteristics more effectively than multilayer perceptron type neural networks (MLPNN). The BLRNN is first expanded to its complex value version (C-BLRNN) for dealing with the complex input values in the paper. C-BLRNN is then applied to equalization of a digital satellite communication channel for M-PSK and QAM, which has severe nonlinearity with memory due to traveling wave tube amplifier (TWTA). The proposed C-BLRNN equalizer for a channel model is compared with the currently used Volterra filter equalizer or decision feedback equalizer (DFE), and conventional complex-MLPNN equalizer. The results show that the proposed C-BLRNN equalizer gives very favorable results in both the MSE and BER criteria over Volterra filter equalizer, DFE, and complex-MLPNN equalizer.     

Performance of fuzzy logic-based slope tuning of neural equaliser for digital communication channel

Adaptive equalisation in digital communication systems is a process of compensating the disruptive effects caused mainly by intersymbol interference in a band-limited channel and plays a vital role for enabling higher data rate in modern digital communication system. Designing efficient equalisers having low structural complexity and faster learning algorithms is also an area of much research interest in the present scenario. This paper presents a novel technique of improving the performance of conventional multilayer perceptron (MLP)-based decision feedback equaliser (DFE) of reduced structural complexity by adapting the slope of the sigmoidal activation function using fuzzy logic control technique. The adaptation of the slope parameter increases the degrees of freedom in the weight space of the conventional feedforward neural network (CFNN) configuration. Application of this technique provides faster learning with less training samples and significant performance gain. This research work also proposes adaptive channel equalisation techniques on recurrent neural network framework. Exhaustive simulation studies carried out prove that by replacing the conventional sigmoid activation functions in each of the processing nodes of recurrent neural network with multilevel sigmoid activation functions, the bit error rate performance has significantly improved. Further slopes of different levels of the multilevel sigmoid have been adapted using fuzzy logic control concept. Simulation results considering standard channel models show faster learning with less number of training samples and performance level comparable to the their conventional counterparts. Also, there is scope for parallel implementation of slope adaptation technique in real-time implementation, which saves the computational time.     

Equalization of nonlinear time-varying channels using type-2 fuzzyadaptive filters

Presents a kind of adaptive filter: type-2 fuzzy adaptive filter (FAF); one that is realized using an unnormalized type-2 Takagi-Sugeno-Kang (TSK) fuzzy logic system (FLS). We apply this filter to equalization of a nonlinear time-varying channel and demonstrate that it can implement the Bayesian equalizer for such a channel, has a simple structure, and provides fast inference. A clustering method is used to adaptively design the parameters of the FAF. Two structures are used for the equalizer: transversal equalizer (TE) and decision feedback equalizer (DFE). A decision tree structure is used to implement the decision feedback equalizer, in which each leaf of the tree is a type-2 FAF. This DFE vastly reduces computational complexity as compared to a TE. Simulation results show that equalizers based on type-2 FAFs perform much better than nearest neighbor classifiers (NNC) or equalizers based on type-1 FAFs     

振动筒式压力传感器的FLANN非线性校正

采用函数链神经网络方法对振动筒式压力传感器进行非线性校正．与BP算法相比，函数链神经网络结构明了、算法简单、易于收敛。文中介绍了函数链神经网络解决振动筒式压力传感器的非线性原理和建模方法，仿真实验结果证明了该方法的可行性和有效性。