Adaptive nonlinear filters equipped with polynomial models of nonlinearity are explained. The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion or a recursive nonlinear difference equation. The Volterra series expansion can model a large class of nonlinear systems and is attractive in adaptive filtering applications because the expansion is a linear combination of nonlinear functions of the input signal. The basic ideas behind the development of gradient and recursive least-squares adaptive Volterra filters are first discussed. Adaptive algorithms using system models involving recursive nonlinear difference equations are then treated. Such systems may be able to approximate many nonlinear systems with great parsimony in the use of coefficients. Also discussed are current research trends and new results and problem areas associated with these nonlinear filters. A lattice structure for polynomial models is described. >

Adaptive polynomial filters

Computer simulation is often used to estimate the bit error rate (BER) performance of digital communication systems. There are a number of distinct techniques in the simulation context that can be used to construct this estimate. A tutorial exposition of such techniques is provided, with particular reference to five specific methods which can be implemented in a simulation. These methods range from the traditional Monte Carlo trials to assumption of definite forms for the noise statistics. An attempt is made to show how these methods are related, and the specific assumptions that are invoked in order to apply them.

Techniques for Estimating the Bit Error Rate in the Simulation of Digital Communication Systems

An analytical solution to the problem of modeling bandpass nonlinear channels and evaluating the performance of digital communication systems operating on them is presented. A method based on a Volterra series representation of the overall channel is first proposed, which allows one to extend to nonlinearities with memory the well-known concepts of complex envelope of bandpass signals and low-pass equivalent of bandpass linear systems. The general results previously mentioned are then applied to digital satellite communication systems operating over nonlinear channels. The effect of a nonlinear amplifier located in the satellite is considered, in combination with that of transmitting and receiving filters located in the Earth stations. In addition, both uplink and downlink noise are taken into account. Basic advantages of this approach are the generality it offers to the analysis and the fact that it allows accurate evaluation of the error probability in a short computer time.

Modeling and Performance Evaluation of Nonlinear Satellite Links-A Volterra Series Approach

Conventional techniques attempting to compensate for the influence of linear and nonlinear distortion in digital satellite channels include optimization of channel filtering. With conventional linear filtering it has been experienced that there is still room for considerable improvement, so that it appears reasonable to investigate some forms of nonlinear filtering in an attempt to cope with those distortions. In this paper a nonlinear equalizer structure is proposed, and its performance is analyzed. It is shown, by some examples Of application to a 4-phase PSK satellite channel, that it can prove quite effective in terms of a tradeoff between performance improvement and hardware complexity.

Nonlinear Equalization of Digital Satellite Channels

https://www.dtc.umn.edu/s/resources/gg-se.pdf

A bibliography on nonlinear system identification

A good deal of effort has been spent, in the past few years, to devise numerical algorithms for evaluating the performance of digital communication systems over noisy linear channels, i.e., in the presence of intersymbol interference and noise. In this concise paper we present a method for computing the error probability of multilevel baseband digital modulation systems when the channel is nonlinear with memory. The algorithm is based on a Volterra series expansion of the nonlinearity; with this model, we show that the moments of the disturbance can be computed recursively, and the same techniques in use for linear channels can be applied for evaluating the error probability. This approach can be generalized to consider noise entering the nonlinear channel. The computing algorithms are described in detail, and a complete example is worked out.

Performance of Multilevel Baseband Digital Systems in a Nonlinear Environment

Performance prediction for digital satellite links - A Volterra series approach

An analytical solution totheproblem ofmodeling bandpass nonlinear channels andevaluating theperformance ofdigital communication systemsoperating on themispresented. A methodbasedon a Volterra series representation oftheoverall channel isfirst proposed, whichallows one toextendto nonlinearities withmemory thewell-known concepts ofcomplexenvelope ofbandpass signals andlow-pass equivalent of bandpass linear systems. Thegeneral results previously mentioned arethenapplied to digital satellite communication systemsoperating over nonlinear channels. Theeffect ofa nonlinear amplifier locatedinthe satellite isconsidered, incombination withthatoftransmitting andreceiving filters located intheEarthstations. Inaddition, bothuplink anddownlink noisearetakenintoaccount.Basic advantages ofthisapproach arethegenerality itofferstothe analysis andthefactthatitallowsaccurateevaluation ofthe errorprobability ina shortcomputertime.

R. Daffara

Papers

Modeling and Performance Evaluation of Nonlinear Satellite Links-A Volterra Series Approach

Performance of Multilevel Baseband Digital Systems in a Nonlinear Environment

Performance prediction for digital satellite links - A Volterra series approach

Modeling andPerformance Evaluation ofNonlinear Satellite Links-AVolterra Series Approach