Pipelined functional link artificial recurrent neural network with the decision feedback structure for nonlinear channel equalization

This paper presents a computationally efficient nonlinear adaptive filter by a pipelined functional link artificial decision feedback recurrent neural network (PFLADFRNN) for the design of a nonlinear channel equalizer. It aims to reduce computational burden and improve nonlinear processing capabilities of the functional link artificial recurrent neural network (FLANN). The proposed equalizer consists of several simple small-scale functional link artificial decision feedback recurrent neural network (FLADFRNN) modules with less computational complexity. Since it is a module nesting architecture comprising a number of modules that are interconnected in a chained form, its performance can be further improved. Moreover, the equalizer with a decision feedback recurrent structure overcomes the unstableness thanks to its nature of infinite impulse response structure. Finally, the performance of the PFLADFRNN modules is evaluated by a modified real-time recurrent learning algorithm via extensive simulations for different linear and nonlinear channel models in digital communication systems. The comparisons of multilayer perceptron, FLANN and reduced decision feedback FLANN equalizers have clearly indicated the convergence rate, bit error rate, steady-state error and computational complexity, respectively, for nonlinear channel equalization.     

Identification of nonlinear dynamic systems using functional linkartificial neural networks

We have presented an alternate ANN structure called functional link ANN (FLANN) for nonlinear dynamic system identification using the popular backpropagation algorithm. In contrast to a feedforward ANN structure, i.e., a multilayer perceptron (MLP), the FLANN is basically a single layer structure in which nonlinearity is introduced by enhancing the input pattern with nonlinear functional expansion. With proper choice of functional expansion in a FLANN, this network performs as good as and in some cases even better than the MLP structure for the problem of nonlinear system identification.     

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.     

Using recurrent neural networks for adaptive communication channelequalization

Nonlinear adaptive filters based on a variety of neural network models have been used successfully for system identification and noise-cancellation in a wide class of applications. An important problem in data communications is that of channel equalization, i.e., the removal of interferences introduced by linear or nonlinear message corrupting mechanisms, so that the originally transmitted symbols can be recovered correctly at the receiver. In this paper we introduce an adaptive recurrent neural network (RNN) based equalizer whose small size and high performance makes it suitable for high-speed channel equalization. We propose RNN based structures for both trained adaptation and blind equalization, and we evaluate their performance via extensive simulations for a variety of signal modulations and communication channel models. It is shown that the RNN equalizers have comparable performance with traditional linear filter based equalizers when the channel interferences are relatively mild, and that they outperform them by several orders of magnitude when either the channel's transfer function has spectral nulls or severe nonlinear distortion is present. In addition, the small-size RNN equalizers, being essentially generalized IIR filters, are shown to outperform multilayer perceptron equalizers of larger computational complexity in linear and nonlinear channel equalization cases.     

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.     

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.     

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.     

Communication channel equalization using wavelet network

Wavelet network (WN) based on wavelet decomposition principle is applied to channel equalization for both linear and non-linear channels. The WN is trained by extended Kalman filter (EKF) based recursive algorithm and is compared with EKF based multi-layered perceptron (MLP) and radial basis function neural network (RBFNN). Exhaustive simulation study reveals the superiority of the WN based equalizer in terms of bit error rate performance, compared to the above equalizer scheme.     

Nonlinear dynamic system identification using Chebyshev functionallink artificial neural networks

A computationally efficient artificial neural network (ANN) for the purpose of dynamic nonlinear system identification is proposed. The major drawback of feedforward neural networks, such as multilayer perceptrons (MLPs) trained with the backpropagation (BP) algorithm, is that they require a large amount of computation for learning. We propose a single-layer functional-link ANN (FLANN) in which the need for a hidden layer is eliminated by expanding the input pattern by Chebyshev polynomials. The novelty of this network is that it requires much less computation than that of a MLP. We have shown its effectiveness in the problem of nonlinear dynamic system identification. In the presence of additive Gaussian noise, the performance of the proposed network is found to be similar or superior to that of a MLP. A performance comparison in terms of computational complexity has also been carried out.     

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．     

Artificial Neural Network trained by Particle Swarm Optimization for non-linear channel equalization

In this paper, we apply Artificial Neural Network (ANN) trained with Particle Swarm Optimization (PSO) for the problem of channel equalization. Existing applications of PSO to Artificial Neural Networks (ANN) training have only been used to find optimal weights of the network. Novelty in this paper is that it also takes care of appropriate network topology and transfer functions of the neuron. The PSO algorithm optimizes all the variables, and hence network weights and network parameters. Hence, this paper makes use of PSO to optimize the number of layers, input and hidden neurons, the type of transfer functions etc. This paper focuses on optimizing the weights, transfer function, and topology of an ANN constructed for channel equalization. Extensive simulations presented in this paper shows that, as compared to other ANN based equalizers as well as Neuro-fuzzy equalizers, the proposed equalizer performs better in all noise conditions.     

A new training scheme for neural networks and application in non-linear channel equalization

This paper deals with the problem of equalization of channels in a digital communication system. In the literature, artificial neural network (ANN) has been increasingly used for the said problem. However, traditional methods of ANN training fall short of desired performance in the problem of equalization. In this paper, we propose a recently proposed training method for ANN for the problem. This training uses directed search optimization (DSO) as a trainer to neural networks. Then, we apply the same to the problem of nonlinear channel equalization and in that way, this paper introduces a novel strategy for equalization of nonlinear channels. Proposed method of channel equalization performs better than contemporary equalization methods used in the literature, as evident from extensive simulation results presented in this paper.     

Nonlinear magnetic storage channel equalization using minimalresource allocation network (MRAN)

This letter presents the application of the recently developed minimal radial basis function neural network called minimal resource allocation network (MRAN) for equalization in highly nonlinear magnetic data storage channels. Using a realistic magnetic channel model, MRAN equalizer's performance is compared with the nonlinear neural equalizer of Nair and Moon (1997), referred to as maximum signal-to-distortion ratio (MSDR) equalizer. MSDR equalizer uses a specially designed neural architecture where all the parameters are determined theoretically. Simulation results indicate that MRAN equalizer has better performance than that of MSDR equalizer in terms of higher signal-to-distortion ratios.     

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.     

Multilayer perceptron-based DFE with lattice structure

The severely distorting channels limit the use of linear equalizers and the use of the nonlinear equalizers then becomes justifiable. Neural-network-based equalizers, especially the multilayer perceptron (MLP)-based equalizers, are computationally efficient alternative to currently used nonlinear filter realizations, e.g., the Volterra type. The drawback of the MLP-based equalizers is, however, their slow rate of convergence, which limit their use in practical systems. In this work, the effect of whitening the input data in a multilayer perceptron-based decision feedback equalizer (DFE) is evaluated. It is shown from computer simulations that whitening the received data employing adaptive lattice channel equalization algorithms improves the convergence rate and bit error rate performances of multilayer perceptron-based DFE. The adaptive lattice algorithm is a modification to the one developed by Ling and Proakis (1985). The consistency in performance is observed in both time-invariant and time-varying channels. Finally, it is found in this work that, for time-invariant channels, the MLP DFE outperforms the least mean squares (LMS)-based DFE. However, for time-varying channels comparable performance is obtained for the two configurations.     

Performance Evaluation of GAP-RBF Network in Channel Equalization

A Growing and Pruning Radial Basis Function (GAP-RBF) network has been recently proposed by Huang et al. [IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics, 34(6) (2004), 2284–2292]. However, its performance in signal processing areas is not clear yet. In this paper, GAP-RBF network is used for solving the communication channel equalization problem. The simulation results demonstrate that GAP-RBF equalizer outperforms other equalizers such as recurrent neural network and MRAN on linear and nonlinear channel model in terms of bit error rate.     

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.     

Development and performance evaluation of neural network classifiers for Indian internet shoppers

The rapid growth of usage of internet has paved the way towards the use of online shopping. Consumers’ behavior is one of the significant aspects that is considered by the service providers for the improvement of various services. Consumers are generally satisfied if their needs are fulfilled. In this paper an in depth investigation is made on the behavior of Indian consumers towards online shopping. Factor analysis is carried out to extract significant factors that affect online shopping of Indian consumers and these consumers are clustered based on their behavior, towards online shopping using hierarchical clustering. Employing the results of clustering in training of multilayer perceptron (MLP), functional link artificial neural network (FLANN) and radial basis function (RBF) networks efficient classifier models are developed. The performance of these classifiers are evaluated and compared with those obtained by conventional statistical based discriminant analysis. The simulation study demonstrates that the RBF network provides best classification performance of internet shoppers compared to those given by the FLANN, MLP and discriminant analysis based methods. The simulation study on the impact of different combination of inputs demonstrates that demographic input has least effect on classification performance. On the other hand the combination of psychological and cultural inputs play the most significant role in classification followed by psychological and then cultural inputs alone.     

Neural equalization applied to systems with bidimensional digital modulation

A new equalization model for digital communication systems is proposed, based on a multi-layer perceptron (MLP) artificial neural network with a backpropagation algorithm. Unlike earlier techniques, the proposed model, called the bidimensional neural equalizer, is composed of two independent MLP networks that operate in parallel for each dimension of the digital modulation scheme. A heuristic method to combine the errors of the two MLP networks is also proposed, with the aim of reducing the convergence time. Simulations performed for linear and nonlinear channels demonstrated that the new model could improve performance in terms of the bit error rate and the convergence time, compared to existing models.     

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.