Mohamed Ibnkahla

Neural network modeling and identification of nonlinear channels with memory: algorithms, applications, and analytic models

This paper proposes a neural network (NN) approach for modeling nonlinear channels with memory. Two main examples are given: (1) modeling digital satellite channels and (2) modeling solid-state power amplifiers (SSPAs). NN models provide good generalization performance (in terms of output signal-to-error ratio). NN modeling of digital satellite channels allows the characterization of each channel component. Neural net models represent the SSPA as a system composed of a linear complex filter followed by a nonlinear memoryless neural net followed by a linear complex filter. If the new algorithms are to be used in real systems, it is important that the algorithm designer understands their learning behavior and performance capabilities. Some simplified neural net models are analyzed in support of the simulation results. The analysis provides some theoretical basis for the usefulness of NNs for modeling satellite channels and amplifiers. The analysis of the simplified adaptive models explains the simulation results qualitatively but not quantitatively. The analysis proceeds in several steps and involves several novel ideas to avoid solving the more difficult general nonlinear problem.

Analytic behavior of the LMS adaptive line enhancer for sinusoids corrupted by multiplicative and additive noise

The least mean squares adaptive line enhancer (LMS ALE) has been widely used for the enhancement of coherent sinusoids in additive wideband noise. This paper studies the behavior of the LMS ALE when applied to the enhancement of sinusoids that have been corrupted by both colored multiplicative and white additive noise. The multiplicative noise decorrelates the sinusoid, spreads its power spectrum, and acts as an additional corrupting noise. Closed-form expressions are derived for the optimum (Wiener filter) ALE output SNR as a function of the residual coherent sine wave power, the noncoherent sine wave power spectrum, and the background additive white noise. When the coherent to noncoherent sine wave power ratio is sufficiently small, it is shown that a nonlinear (e.g., square law) transformation of the ALE input results in a larger optimum ALE output SNR.

Statistical analysis of a two-layer backpropagation algorithm used for modeling nonlinear memoryless channels: the single neuron case

Neural networks have been used for modeling the nonlinear characteristics of memoryless nonlinear channels using backpropagation (BP) learning with experimental training data. In order to better understand this neural network application, this paper studies the transient and convergence properties of a simplified two-layer neural network that uses the BP algorithm and is trained with zero mean Gaussian data. The paper studies the effects of the neural net structure, weights, initial conditions, and algorithm step size on the mean square error (MSE) of the neural net approximation. The performance analysis is based on the derivation of recursions for the mean weight update that can be used to predict the weights and the MSE over time. Monte Carlo simulations display good to excellent agreement between the actual behavior and the predictions of the theoretical model.

Vector neural networks for digital satellite communications

Conventional techniques used for identification and equalization of nonlinear M-ary PSK digital satellite channels are based on linear or nonlinear filtering devices (e.g. tapped delay line equalizers, Volterra series approaches). This paper uses a new technique based on the vector neural network (VNN) and Kohonen (1989) self organizing feature map. We have used a VNN for adaptive equalization and identification of the satellite channel. The decision process is performed by a Kohonen map.

Equalization of satellite UMTS channels using neural network devices

The presence of nonlinear devices in several communication channels, such as satellite channels, causes distortions of the transmitted signal. These distortions are more severe for non-constant envelope modulations such as 16-QAM. Over the last years neural networks (NN) have emerged as competitive tools for linear and nonlinear channel equalization. However, their main drawback is often slow convergence speed which results in poor tracking capabilities. The present paper combines simple NN structures with conventional equalizers. The NN techniques are shown to efficiently approximate the optimal decision boundaries which results in good symbol error rate (SER) performance. The paper gives simulation examples (in the context of satellite mobile channels) and compares neural network approaches to classical equalization techniques.

Equalization of satellite mobile communication channels using combined self-organizing maps and RBF networks

The paper proposes a neural network approach to equalize time varying nonlinear channels. The approach is applied to a satellite UMTS channel composed of time invariant linear filters, a non-linear memoryless amplifier and a time varying multipath propagation channel. The neural network equalizer has a radial basis function structure. The usual k-mean clustering algorithm is replaced by a Kohonen (1995) learning rule. This results in an RBF-SOM equalizer which outperforms the LMS equalizer, and which has better recovering abilities (after passing through a high fading area) than the former RBF equalizer.

Fluctuation analysis of a two-layer backpropagation algorithm used for modeling nonlinear memoryless channels

Neural networks have previously been used for modelling the nonlinear characteristics of memoryless nonlinear channels using the backpropagation learning (BP) with experimental training data (Ibnkahla et al. 1997). The mean transient and convergence behavior of a simplified two-layer neural network have also been studied (Bershad et al. 1997). The network was trained with zero mean Gaussian data. This paper extends these results to include the effects of the weight fluctuations upon the mean-square-error (MSE). A new methodology is presented which can be extended to other nonlinear learning problems. The new mathematical model is able to predict the MSE learning behavior as a function of the algorithm step size /spl mu/. Linear recursions are derived for the variance and covariance of the weights which depend nonlinearly upon the mean weights. As in linear gradient search problems (LMS, etc.), there exists an optimum /spl mu/ (minimizing the MSE) which is the trade-off between fast learning and small weight fluctuations. Monte Carlo simulations display excellent agreement with the theoretical predictions for various /spl mu/.

On the influence of the number of layers on the performance and convergence behavior of the back propagation algorithm

In many neural network applications to signal processing, the back propagation (BP) algorithm is used for the training process. Recently, several authors have analyzed the behavior of the BP algorithm and studied its properties. The influence of the number of layers on the performance and convergence behavior of the BP algorithm remains, however, not well known. The paper tries to investigate this problem by studying a simplified multilayer neural network used for adaptive filtering. The analysis is based upon the derivation of recursions for the mean weight update which can be used to predict the weights and mean squared error over time. The paper shows also the effects of the algorithm step size and the initial weight values upon the algorithm behavior. Computer simulations display good agreement between the actual behavior and the predictions of the theoretical model. The properties of the BP algorithm are illustrated through several simulation examples and compared to the classical LMS algorithm.

Equalization of satellite UMTS channels using RBF networks

The paper proposes a radial basis function (RBF) neural network (NN) approach to satellite universal mobile telecommunication system (S-UMTS) channel equalization. Two main problems arise in S-UMTS communications: (i) non-linear distortions which are caused by the onboard nonlinear power amplifiers, and (ii) multipath propagation. This paper shows that RBF networks are particularly well suited to overcome these problems. The paper presents several simulation results which show that RBF networks outperform classical equalization techniques for different configurations of the mobile channel (mobile speed, noise level, number of paths, etc.).

Fluctuation analysis of a two-layer backpropagation algorithm used for modelling nonlinear memoryless channels

Neural networks have previously been used for modelling the nonlinear characteristics of memoryless nonlinear channels using the backpropagation learning (BP) with experimental training data (Ibnkahla et al. 1997). The mean transient and convergence behavior of a simplified two-layer neural network have also been studied (Bershad et al. 1997). The network was trained with zero mean Gaussian data. This paper extends these results to include the effects of the weight fluctuations upon the mean-square-error (MSE). A new methodology is presented which can be extended to other nonlinear learning problems. The new mathematical model is able to predict the MSE learning behavior as a function of the algorithm step size /spl mu/. Linear recursions are derived for the variance and covariance of the weights which depend nonlinearly upon the mean weights. As in linear gradient search problems (LMS, etc.), there exists an optimum /spl mu/ (minimizing the MSE) which is the trade-off between fast learning and small weight fluctuations. Monte Carlo simulations display excellent agreement with the theoretical predictions for various /spl mu/.