Radial Basis Function Equalizer Research Articles

An Efficient ANN Interference Cancelation for High Order Modulation over Rayleigh Fading Channel

High order modulation (HOM) presents a key challenge in increasing spectrum efficiency in 4G and upcoming 5G communication systems. In this paper, two non-linear adaptive equalizer techniques based on multilayer perceptron (MLP) and radial basis function (RBF) are designed and applied on HOM to optimize its performance despite its high sensitivity to noise and channel distortions. The artificial neural network’s (ANN) adaptive equalizer architectures and learning methods are simplified to avoid more complexity and to ensure greater speed in symbol decision making. They will be compared with the following popular adaptive filters: least mean square (LMS) and recursive least squares (RLS), in terms of bit error rate (BER) and minimum square error (MSE) with 16, 64, 128, 256, 512 and 1024 quadrature amplitude modulation (QAM). By that, this work will show the advantage that the MLP equalizer has, in most cases, over RBF and traditional linear equalizers.

RBF equalizer based on adaptive niche hierarchy genetic algorithm

It is the fact that only one optimum individual can be determined by the Hierarchy Genetic Algorithm(HGA).This paper proposed a new improved hierarchy Genetic Algorithm(GA) based on the niche,in which the range of the niche could be determined by the information of the evolution.The best structure of the Radial Basis Function(RBF) neural network equalizer could be selected from several optimal solutions with the criterion of the lowest bit error rate and the best clustering degree of the hidden centers.The simulation results demonstrate that the validity and the stability of the new algorithm.

Radial Basis Function Network Equalizer for Optical Communication OOK System

In this paper, we introduce a nonlinear equalizer using the radial basis function (RBF) network for electronic dispersion compensation in optical communication systems with on-off keying and a direct-detection receiver. The RB method introduces a nonlinear equalization technique that is suitable for optical communication direct-detection systems that include nonlinear transformation at the photodetector. A bit error rate performance comparison shows that the RBF equalizer outperforms the conventional linear feedforward equalizer. In addition, it is shown that, in optically amplified systems, the RBF equalizer improvement is increased even further. Finally, the feasibility of the RBF method is validated by experimental results.

Nonlinear channel equalizer design using directional evolutionary multi-objective optimization

In this paper, a new equalizer learning scheme is introduced based on the algorithm of the directional evolutionary multi-objective optimization (EMOO). Whilst nonlinear channel equalizers such as the radial basis function (RBF) equalizers have been widely studied to combat the linear and nonlinear distortions in the modern communication systems, most of them do not take into account the equalizers’ generalization capabilities. In this paper, equalizers are designed aiming at improving their generalization capabilities. It is proposed that this objective can be achieved by treating the equalizer design problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets, followed by deriving equalizers with good capabilities of recovering the signals for all the training sets. Conventional EMOO which is widely applied in the MOO problems suffers from disadvantages such as slow convergence speed. Directional EMOO improves the computational efficiency of the conventional EMOO by explicitly making use of the directional information. The new equalizer learning scheme based on the directional EMOO is applied to the RBF equalizer design. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good generalization capabilities, i.e., good performance on predicting the unseen samples.

Design of a blind spatial and temporal RBF equalizer using a genetic algorithm

This paper describes a new solution to channel intersymbol interference and nonlinear distortion by means of an adaptive array antenna and radial basis function (RBF) equalizer. The RBF equalizer can reduce the influence of intersymbol interference and additive noise in the digital communication system. It is also well known to eliminate nonlinear distortion effectively. However, conventional RBF equalizers including our previous proposed equalizer, a spatial and temporal RBF equalizer using adaptive array antenna, need training data to learn channel states, which incurs a decline in the data rate. In this paper, without training data, we construct a blind spatial and temporal RBF equalizer using genetic algorithm. We also describe a method of synthesizing Bayesian decision variables of RBF equalizers in order to obtain better performance. The RBF equalizer based on the proposed method can achieve a remarkable improvement in BER characteristics and its performance is demonstrated by computer simulations. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 152(4): 50–56, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20123

A Design Method of Blind Spatial and Temporal RBF Equalizer Using Genetic Algorithm

This paper describes a new solution to the channel intersymbol interference and the nonlinear distortion by means of adaptive array antenna and radial basis function (RBF) equalizer. RBF equalizer can reduce the influence of intersymbol interference and additive noise in the digital communication system. It is also well known to eliminate the nonlinear distortion effectively. But the conventional RBF equalizers including our previous proposed equalizer, spatial and temporal RBF equalizer using adaptive array antenna, need training data to learn channel states, which incurs decline in the data rate. In this paper, without training data, we construct a blind spatial and temporal RBF equalizer using genetic algorithm. Furthermore, we also describe a method of synthesizing Bayesian decision variables of RBF equalizers in order to obtain better performance. The RBF equalizer based on the proposed method can present a remarkable improvement in BER characteristics and its performance is demonstrated by computer simulations.

Least bit error rate adaptive nonlinear equalisers for binary signalling

The paper considers the problem of constructing adaptive minimum bit error rate (MBER) neural network equalisers for binary signalling. Motivated from a kernel density estimation of the bit error rate (BER) as a smooth function of training data, a stochastic gradient algorithm called the least bit error rate (LBER) is developed for adaptive nonlinear equalisers. This LBER algorithm is applied to adaptive training of a radial basis function (RBF) equaliser in a channel intersymbol interference (ISI) plus co-channel interference setting. A simulation study shows that the proposed algorithm has good convergence speed, and a small-size RBF equaliser trained by the LBER can closely approximate the performance of the optimal Bayesian equaliser. The results also demonstrate that the standard adaptive algorithm, the least mean square (LMS), performs poorly for neural network equalisers because the minimum mean square error (MMSE) is clearly suboptimal in the equalisation setting.

Burst-by-burst adaptive turbo-coded radial basis function-assisted decision feedback equalization

The performance of the proposed radial basis function (RBF) assisted turbo-coded adaptive modulation scheme is characterized in a wideband channel scenario. We commence by introducing the novel concept of the Jacobian RBF equalizer, which is a reduced-complexity version of the conventional RBF equalizer. Specifically, the Jacobian logarithmic RBF equalizer generates its output in the logarithmic domain and hence it can be used to provide soft outputs for the turbo-channel decoder. We propose using the average magnitude of the log-likelihood ratio (LLR) of the bits in the received transmission burst before channel decoding as the channel quality measure for controlling the mode-switching regime of our adaptive scheme.

A complex valued radial basis function network for equalization of fast time varying channels

This paper presents a complex valued radial basis function (RBF) network for equalization of fast time varying channels. A new method for calculating the centers of the RBF network is given. The method allows fixing the number of RBF centers even as the equalizer order is increased so that a good performance is obtained by a high-order RBF equalizer with small number of centers. Simulations are performed on time varying channels using a Rayleigh fading channel model to compare the performance of our RBF with an adaptive maximum-likelihood sequence estimator (MLSE) consisting of a channel estimator and a MLSE implemented by the Viterbi algorithm. The results show that the RBF equalizer produces superior performance with less computational complexity.

A practical radial basis function equalizer

A radial basis function (RBF) equalizer design process has been developed in which the number of basis function centers used is substantially fewer than conventionally required. The reduction of centers is accomplished in two-steps. First an algorithm is used to select a reduced set of centers that lie close to the decision boundary. Then the centers in this reduced set are grouped, and an average position is chosen to represent each group. Channel order and delay, which are determining factors in setting the initial number of centers, are estimated from regression analysis. In simulation studies, an RBF equalizer with more than 2000-to-1 reduction in centers performed as well as the RBF equalizer without reduction in centers, and better than a conventional linear equalizer.

Extended adaptive RBF equaliser for overcoming co-channel interference

The authors investigate the problem of nonlinear adaptive equalisation in the presence of intersymbol interference, additive white Gaussian noise and co-channel interference. An extended radial basis function (RBF) network is proposed, in which regression weights are used in the output layer and the hidden unit is defined to have the Gaussian formula with the Mahalanobis distance. It is shown by simulation that the proposed structure gives reduced computational complexity without performance degradation, compared to that of the conventional RBF equaliser.

Overcoming co-channel interference using an adaptive radial basis function equaliser

Abstract The paper investigates the problem of adaptive equalisation in the presence of intersymbol interference, additive white Gaussian noise and co-channel interference. The radial basis function network is designed to realise a sophisticated nonlinear adaptive equaliser capable of operating under poor signal to interference ratio and signal to noise ratio conditions. A two-stage learning strategy is derived by exploiting the nature of the data structure and this enables the radial basis function network to realise the optimal Bayesian symbol-decision equaliser. At the first stage of the learning, a supervised clustering algorithm is employed to model the effects of the channel intersymbol interference. This learning stage is extremely simple and robust, and it is capable of producing a very good approximation to the optimal Bayesian solution. At the second stage of the learning, the network structure is expanded and an unsupervised clustering algorithm is added into the learning procedure so that the network can model the full effects of the co-channel interference and achieve the full optimal equalisation solution.