Francis Castanie

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.

Adaptive MLSE receiver over rapidly fading channels

Abstract This paper develops an adaptive maximum likelihood sequence estimator (MLSE) for rapidly fading channels corrupted by additive white Gaussian noise. This estimator is based on an explicit incorporation of the time-varying characteristics in channel modelling. When the multipath is caused by a few strong reflectors, the channel is shown to be poly-periodically time varying. The channel impulse response is then approximated by a linear combination of a finite set of complex exponential functions whose frequencies are termed Doppler frequencies. This modelling is well motivated in aeronautical radio communications and cellular telephony. During the training period, a cyclic statistics-based approach is developed to estimate the Doppler frequencies. An eigenvector approach as well as a maximum likelihood method are proposed to estimate the coefficients of linear expansion. After this initialization, the channel parameters are updated using a modified version of the LMS algorithm. Computer simulations are carried out to evaluate the proposed receiver performance. The new approach exhibits a large saving in computational complexity and offers superior performance over conventional adaptive MLSE in rapidly fading environment.

Stochastic analysis of adaptive gradient identification of Wiener-Hammerstein systems for Gaussian inputs

This correspondence investigates the statistical behavior of two adaptive gradient search algorithms for identifying an unknown Wiener-Hammerstein system (WHS) with Gaussian inputs. The first scheme attempts to identify the WHS with an LMS adaptive filter. The LMS algorithm identifies a scaled version of the convolution of the input and output linear filters of the WHS. The second scheme attempts to identify the unknown WHS with a gradient adaptive WHS when the shape of the nonlinearity is known a priori. The mean behavior of the gradient recursions are analyzed when the WHS nonlinearity is modeled by an error function. The mean recursions yield very good agreement with Monte Carlo simulations for slow learning.

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.

Comparison of neural network adaptive predistortion techniques for satellite down links

In this paper, we present adaptive predistortion techniques for two satellite down links. The first link is a memoryless amplifier that gives two kind of distortions: amplitude distortion (AM/AM conversion) and phase distortion (AM/PM conversion). The second link is an amplifier with memory modeled by a memoryless amplifier followed by a linear filter. Predistortions are realized with multilayer perceptron (MLP) neural networks (NN) associated with the backpropagation (BP) algorithm. For the first down link we compare two adaptive predistorsions whereas only one predistorsion technique is applied to the second down link.

Time-scale analysis of abrupt changes corrupted by multiplicative noise

Multiplicative Abrupt Changes (ACs) have been considered in many applications. These applications include image processing (speckle) and random communication models (fading). Previous authors have shown that the Continuous Wavelet Transform (CWT) has good detection properties for ACs in additive noise. This work applies the CWT to AC detection in multiplicative noise. CWT translation invariance allows to define an AC signature. The problem then becomes signature detection in the time-scale domain. A second-order contrast criterion is defined as a measure of detection performance. This criterion depends upon the first- and second-order moments of the multiplicative processs CWT. An optimal wavelet (maximizing the contrast) is derived for an ideal step in white multiplicative noise. This wavelet is asymptotically optimal for smooth changes and can be approximated for small AC amplitudes by the Haar wavelet. Linear and quadratic suboptimal signature-based detectors are also studied. Closed-form threshold expressions are given as functions of the false alarm probability for three of the detectors. Detection performance is characterized using Receiver Operating Characteristic (ROC) curves computed from Monte-Carlo simulations.

Mean Value Jump Detection: A Survey of Conventional and Wavelet Based Methods

Abstract Many problems in signal processing are concerned with the detection of abrupt changes in the parameters of signals or systems. We focus our attention on the simple case of a mean value jump of a stationary random process, as it includes various other cases. The aim of the present study is to compare the performances of two classes of detectors, the first based on conventional segmentation algorithms and the second on the Continuous Wavelet Transform (CWT). The first section gives a brief overview of the methods, and highlights the 2-D wavelet detectors such as the sum of fixed scales slices or the 2-D correlation with the CWT jump signature. According to previous results [4,6], the optimal wavelet maximizes the signal to noise ratio in the (time, scale) plane. Unlike the usual representations, these detectors take advantage of information redundancy in the plane. The second section is devoted to the comparison between the different methods, by means of the detectors characteristics in terms of probability of false alarm and non-detection. A common criterion of detection delay is taken into account, as well as the accuracy of the detection date, or the possibility of detecting two close jumps. Finally, we give some indications relating to the performance of non-abrupt changes with the new optimal wavelet, and evaluate the possibility of those methods to deal with other jumps.