In this paper, a new complex-valued neural network based on adaptive activation functions is proposed. By varying the control points of a pair of Catmull–Rom cubic splines, which are used as an adaptable activation function, this new kind of neural network can be implemented as a very simple structure that is able to improve the generalization capabilities using few training samples. Due to its low architectural complexity (low overhead with respect to a simple FIR filter), this network can be used to cope with several nonlinear DSP problems at a high symbol rate. In particular, this work addresses the problem of nonlinear channel equalization. In fact, although several authors have already recognized the usefulness of a neural network as a channel equalizer, one problem has not yet been addressed: the high complexity and the very long data sequence needed to train the network. Several experimental results using a realistic channel model are reported that prove the effectiveness of the proposed network on equalizing a digital satellite radio link in the presence of noise, nonlinearities, and intersymbol interference (ISI).

Several researchers have demonstrated how neural networks can be trained to compensate for nonlinear signal distortion in e.g. digital satellite communications systems. These networks, however, require that both the original signal and its distorted version are known. Therefore, they have to be trained off-line, and they cannot adapt to changing channel characteristics. In this paper, a novel dual reinforcement learning approach is proposed that can adapt on-line while the system is performing. Assuming that the channel characteristics are the same in both directions, two predistorters at each end of the communication channel co-adapt using the output of the other predistorter to determine their own reinforcement. Using the common Volterra Series model to simulate the channel, the system is shown to successfully learn to compensate for distortions up to 30%, which is significantly higher than what might be expected in an actual channel. 1 Introduction In a satellite communication sys...

Gaussian mixture probability density functions (pdfs) have been popular for modeling nonGaussian noise. The majority of non-Gaussian noise research has been restricted to independent and identically distributed observation sequences due to the difficulty in characterizing multidimensional pdf's. There has been very few studies on the ability of Gaussian mixture pdfs to model correlated non-Gaussian noise processes. In this paper, we initiate such a study and demonstrate that in practical cases, Gaussian mixture pdfs with a small number of mixing terms can give good approximations to non-Gaussian noise pdfs. Some general models for correlated non-Gaussian interference and noise are reviewed. The focus is on three approaches. The first is the Gaussian mixture model approach. The second is an approach based on spherically invariant random vectors. The final approach involves the combination of linear filters and nonlinearities, generally in an ad-hoc manner. The three approaches...

Since many signal processing problems can be posed as sample-based decision and estimation tasks, we discuss how studies from other fields such as neural networks might suggest improved architectures (models) and algorithms for these types of problems. We then concentrate on PAM equalization, showing that a reordering of the equivalent classification problem generates a 'staircase ' which, while retaining the simplicity of the classical equalizer, allows modifications to made in the outputs and in the training objectives which provide advantages even in the least complex cases.We go on to demonstrate that these advantages increase when one considers, for example, nonlinear channels with memory. From our simulations we draw conclusions and suggest futher related research. We also present two new avenues of inquiry, offering significant practical advantages, which are motivated by the discussions. 1.

LUNSFORD II, PHILIP J. The Frequency Domain Behavioral Modeling and Simulation of Nonlinear Analog Circuits and Systems. (Under the direction of Michael B. Steer.) A new technique for the frequency-domain behavioral modeling and simulation of nonautonomous nonlinear analog subsystems is presented. This technique extracts values of the Volterra nonlinear transfer functions and stores these values in binary files. Using these files, the modeled substem can be simulated for an arbitrary periodic input expressed as a finite sum of sines and cosines. Furthermore, the extraction can be based on any circuit simulator that is capable of steady state simulation. Thus a large system can be divided into smaller subsystems, each of which is characterized by circuit level simulations or lab measurements. The total system can then be simulated using the subsystem characterization stored as tables in binary files.

This paper proposes a trigonometric functional extension, hereafter named the Fourier model, as an alternative framework to the Volterra approach for non-linear systems modelling. This work is focused on the general advantages that trigonometric functionals show in adaptive implementations and also on the possibility they provide to reuse well-known linear processing tools in a non-linear context. The performance of the Fourier model is compared in a set of simulations that cover companders for audio and radio frequency amplifiers, Probability Density Function (PDF) whitening and PDF estimation.

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