Showing papers on "Volterra series published in 2002"

Distortion Analysis in Analog Integrated Circuits

Abstract: This paper reviews different techniques used in the litera ture to analyze distortion in analog integrated circuits. It concentrates on analytical techniques rather than on numerical techniques. Techniques such as Volterra series, harmonic injection method, and modeling of circuit non-linearities, are discussed with emphasis on the last tw o techniques. The theory behind each technique is e xplained, and they are compared together.

The RP method: a new tool for the iterative solution of the nonlinear Schrodinger equation

Abstract: An original approach to the solution of the nonlinear Schrodinger equation (NLSE) is pursued in this paper, following the regular perturbation (RP) method. Such an iterative method provides a closed-form approximation of the received field and is thus appealing for devising nonlinear equalization/compensation techniques for optical transmission systems operating in the nonlinear regime. It is shown that, when the nonlinearity is due to the Kerr effect alone, the order n RP solution coincides with the order 2n + 1 Volterra series solution proposed by Brandt-Pearce and co-workers. The RP method thus provides a computationally efficient way of evaluating the Volterra kernels, with a complexity comparable to that of the split-step Fourier method (SSFM). Numerical results on 10 Gb/s single-channel terrestrial transmission systems employing common dispersion maps show that the simplest third-order Volterra series solution is applicable only in the weakly nonlinear propagation regime, for peak transmitted power well below 5 dBm. However, the insight in the nonlinear propagation phenomenon provided by the RP method suggests an enhanced regular perturbation (ERP) method, which allows the first order ERP solution to be fairly accurate for terrestrial dispersion mapped systems up to launched peak powers of 10 dBm.

A modified Volterra series approach for nonlinear dynamic systems modeling

Abstract: This paper describes a modeling approach for nonlinear dynamic systems based on a modified Volterra series; by comparing the truncation error of this series with that of the classical Volterra one, we outlined that, under the assumption of short-term nonlinear memory effects, the modified series enables a single-fold nonlinear convolution integral to be adopted also in the presence of strong nonlinearities. The measurement-based identification of the first terms of the modified Volterra series is described; experimental and simulation results which confirm the theoretical considerations are also provided.

On the modeling of memory nonlinear effects of power amplifiers for communication applications

Abstract: Understanding power amplifier (PA) nonlinearity is a first step towards linearization efforts We first explore the passband and baseband PA input/output relationships and show that they manifest differently when the PA exhibits long-term, short-term, or no memory effects We then explain the various memory effects in the context of AM/AM and AM/PM responses The so-called quasi-memoryless case is especially clarified Four particular nonlinear models with memory are further investigated

Complex-bilinear recurrent neural network for equalization of a digital satellite channel

Abstract: Equalization of satellite communication using complex-bilinear recurrent neural network (C-BLRNN) is proposed. Since the BLRNN is based on the bilinear polynomial, it can be used in modeling highly nonlinear systems with time-series characteristics more effectively than multilayer perceptron type neural networks (MLPNN). The BLRNN is first expanded to its complex value version (C-BLRNN) for dealing with the complex input values in the paper. C-BLRNN is then applied to equalization of a digital satellite communication channel for M-PSK and QAM, which has severe nonlinearity with memory due to traveling wave tube amplifier (TWTA). The proposed C-BLRNN equalizer for a channel model is compared with the currently used Volterra filter equalizer or decision feedback equalizer (DFE), and conventional complex-MLPNN equalizer. The results show that the proposed C-BLRNN equalizer gives very favorable results in both the MSE and BER criteria over Volterra filter equalizer, DFE, and complex-MLPNN equalizer.

An adaptive Volterra predistorter for the linearization of RF high power amplifiers

Abstract: An efficient digital baseband predistortion linearizer is presented to compensate for nonlinear distortions induced by RF high power amplifiers in wireless communication systems. The proposed approach utilizes an indirect learning architecture with a fast recursive least squares (RLS) filtering algorithm, implemented using V-vector algebra, to update the coefficients of a Volterra-based predistorter. There is no requirement for an initial identification of the nonlinear characteristics of HPA as in linearizers based on conventional pth-order inverse methods. Simulation results show that that good performance and low computational complexity are achieved in the linearization of both narrow and wide bandwidth systems.

Aeroelastic Response of Nonlinear Wing Sections Using a Functional Series Technique

Abstract: This paper addresses the problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via indicial functions and Volterra series approach. The related aeroelastic governing equations are based upon the inclusion of structural and damping nonlinearities in plunging and pitching, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of the considered nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

Modified Volterra series transfer function method

Abstract: In this letter, we offer a modified version of the Volterra series transfer function (VSTF) method that has been previously proposed as an analytical solution to the nonlinear Schrodinger equation for single-mode fibers. The modified VSTF provides a simple closed-form expression of the output of a mildly nonlinear fiber. It gives orders more accurate result than the original VSTF method and can successfully solve the energy divergence problem experienced by the original method. The result is a stronger analytical tool for modeling signal propagation in optical communication systems.

On rewriting the imaging mechanism of underwater bottom topography by synthetic aperture radar as a Volterra series expansion

Abstract: Ocean surface current gradients can be imaged by real and synthetic aperture radar (RAR/SAR) due to the so-called hydrodynamic modulation mechanism. This is the reason why underwater bottom topography and internal waves are visible on radar images. Several physical models exist for this imaging mechanism. When trying to obtain current information from SAR images, a problem arises: the imaging mechanism can be nonlinear. We propose to rewrite the classical modeling of the SAR underwater bottom topography imaging mechanism by using a Volterra series expansion. The Volterra model can be seen as a tool allowing us to study whether the imaging mechanism can be inverted or not. It is a transposition of a well-studied physical problem into a more explicit expression. The conditions for the inversion of the Volterra model are presented and a scheme for estimating the bathymetry from SAR images is described. The main property of the inversion algorithm is its independence from the physical model used for the mechanism.

Linearity analysis and design optimisation for 0.18 /spl mu/m CMOS RF mixer

Abstract: Equations for the 1dB compression point and third-order intermodulation point as a function of circuit and technology parameters are derived using a Volterra series expansion. The linearity analysis for both single- and double-balanced CMOS Gilbert mixers is examined. The relation between the input third-order intercept point and source inductance is studied in depth. The gate to drain overlap capacitance, which is one of the dominant nonlinear elements in a MOSFET, is included in the model. The design methodology to satisfy the mixer noise figure and conversion gain while optimising linearity is summarized. The analytical predictions are verified with the Cadence SpectreRF circuit simulation and experimental data. Good agreement between the model predictions and experimental data is obtained.

Extraction of a nonlinear AC FET model using small-signal S-parameters

Abstract: The nonlinearities of an RF FET can be obtained by a set of small-signal circuit elements extracted over a range of terminal voltages and temperatures. This study used pulsed S-parameter measurements on a 3 /spl times/ 3 DC-bias-point grid at two different temperatures to obtain electrical and electrothermal nonlinearity coefficients up to the third order. The extracted nonlinear AC model can be used in a Volterra analysis to gain an insight into the distortion mechanisms. The measurement results were in good agreement with the calculated third-order intermodulation values.

Identification of Volterra kernels using interpolation

Abstract: This paper presents a new method for the identification of frequency-domain Volterra kernels. Since the nonlinear kernels often play a secondary role compared to the dominant, linear component of the system, it is worth establishing a balance between the degree of liberty of these components and their effect on the overall accuracy of the model. This is necessary in order to reduce the model complexity, hence the required measurement length. Based on the assumption that frequency-domain kernels are locally smooth, the kernel surfaces can be approximated by interpolation techniques, thus reducing the complexity of the model. Similarly to the unreduced (Volterra) model, this smaller model is also i) linear in the unknowns; ii) only locally sensitive to its parameters; and iii) free of structural assumptions about the system. The parameter estimation boils down to solving a linear system of equations in the least-squares (LS) sense. The design of the interpolation scheme is described and the performance of the approximation is analyzed and illustrated by simulation. The algorithm allows a significant saving in measurement time compared to other kernel estimation methods.

Nonlinear model predictive control of a continuous bioreactor using approximate data-driven models

Abstract: An analytical solution to the nonlinear model predictive control (NMPC) problem is developed for a class of nonlinear systems Process input-output behavior is captured using Volterra and Volterra-Laguerre nonlinear polynomial models By employing the traditional 2-norm squared NMPC objective function, the prediction equations, and hence the objective function, are explicitly constructed for an arbitrary prediction horizon of length p Minimization of this objective function is equivalent to solving the set of polynomial equations resulting from differentiation of the objective with respect to the future manipulated variable moves over a horizon of length m A reduced Grobner basis is constructed for the resulting polynomials, and roots of the basis polynomials represent candidate sets of solutions for the manipulated variable profile Results from a continuous-flow bioreactor case study demonstrate the superior performance of this algorithm versus previous analytical solution methods that were limited to single-input single-output problems with a move horizon of unity

An efficient transient analysis algorithm for mildly nonlinear circuits

Abstract: This paper presents a new and efficient transient analysis method for mildly nonlinear circuits. The method is based on Volterra series representation of nonlinear circuits. It characterizes nonlinear circuits using a set of linear circuits called Volterra circuits. The input of the first-order Volterra circuit is identical to that of the nonlinear circuit, whereas that of higher order Volterra circuits is obtained from the response of lower order Volterra circuits. Fourier series interpolation is employed to approximate the input of higher order Volterra circuits. These circuits are analyzed using the sampled-data simulation of linear circuits for computational efficiency and the response of nonlinear circuits is obtained at equally spaced intervals of time. The accuracy of the method is. controlled by the order of Volterra and interpolating Fourier series. Various sources contributing to the error are analyzed. The method has been implemented in a computer program. Numerical results on example circuits demonstrate that the accuracy of the method is comparable to that of linear multistep predictor-corrector algorithms, but with greatly improved speed.

A Volterra Series Approach to the Approximation of Stochastic Nonlinear Dynamics

Abstract: A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system isapproximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this series. The parameters of the bilinear system are determined by minimizing, in a statistical sense,the difference between the original system and the bilinear system. Application to a piecewise linear modelof a beam with a nonlinear one-sided supportillustrates the effectiveness of this approach in approximatingtruly nonlinear, stochastic response phenomena in both the statistical momentsand the power spectral density of the response of this system in case ofa white noise excitation.

5th order multi-tone Volterra simulator with component-level output

Abstract: In this paper, a Matlab software performing numerical Volterra distortion analysis of a weakly nonlinear circuit with arbitrary multiport topology is described. Due to numerical convolution of signal spectrums, the degree of nonlinearity is relatively easy to increase, and the amount of signal tones is not limited to one or two. Distortion products are displayed graphically as vector sums of all different contributions. This makes it easy to recognize the dominant distortion source and possible cancellation mechanisms, and aids the designer to improve the design.

Volterra Equalizer for Electrical Compensation of Dispersion and Fiber Nonlinearities

Abstract: An electrical equalizer for fiber communication systems with direct receivers has to cope with various forms of nonlinear distortions arising from dispersion and fiber nonlinearities like self-phase-modulation. A transversal filter structure according to a discrete Volterra series can serve as an equalizer for general fiber communication systems. While a complete volterra series requires a large amount of coefficients, even a filter with a highly reduced number of coefficients can yield superior results compared to a linear equalizer. On the basis of two fiber system examples the equalizer performance and its dependence on the choice of the appropriate filter coefficients is evaluated.

Analysis of the SAR imaging process of the ocean surface using Volterra models

Abstract: The synthetic aperture radar (SAR) process of the ocean surface mapping is studied using a decomposition based on a Volterra model. By a mathematical expansion of the complex exponential of the complete SAR transform, these models decompose the nonlinear distortion mechanisms of the SAR spectrum over different spectra of polynomial interactions. Thus, they offer an alternative modeling (to the exact SAR transform) giving a theoretical separation between the SAR Fourier components linearly derived from the sea surface elevation and the artifacts created by nonlinearities of the SAR mapping of the ocean surface. The paper gives a systematic assessment of such an approximation of the ocean surface SAR imaging process. Higher order statistics (HOS) of the SAR transform and their calculus and implementation are presented. In fact, nonlinearity detection, location (in the Fourier domain) and quantification can only be performed by HOS, reduced to a second-order Volterra model. The Volterra expansion of the SAR imaging process opens new theoretical inversion schemes since under certain conditions on the linear part, Volterra models are easily invertible. Our method is first tested on simulated SAR images in order to validate the HOS tools. We then show results of this nonlinearity analysis performed on images from the ERS-1 satellite and we present cases of nonlinearity detection.

Modelling and performance assessment of OFDM communication systems in the presence of non-linearities

Abstract: This thesis is concerned with the development of analytic techniques to assess the impact of non-linearides on the performance of orthogonal frequency division multiplexing (OFDM) signals in fibre-radio based wireless networks. Volterra series are used to model both the frequency independent and the frequency dependent behaviour exhibited by fibre-radio system non-linearities. Expressions to determine the power density spectrum (PDS) of non-linearly distorted OFDM signals are derived and validated by comparing analytic to simulation results. Such expressions relate the PDS of the distorted signal to the harmonic power density spectra (HPDS) of the non-distorted signal and the transfer functions of the non-linearity. Expressions to determine the error probability of non-linearly distorted OFDM signals in additive white Gaussian noise (AWGN) are also derived and validated by comparing analytic to simulation results. Such expressions relate the error probability of the OFDM signal to the error probabilities of the OFDM sub-channels, each of which is given as the expectation with respect to the intermodulation distortion (IMD) random variable (RV) of the error probability in AWGN conditioned by a given value of the IMD RV. To calculate the error probability expectations, an investigation of appropriate approximations/estimations for the IMD distribution based on a limited number of moments of the IMD RV is carried out. Finally, the analytic techniques are applied to two different intensity modulation/direct detection (IM/DD) fibre-radio systems. One of the systems is based on the direct modulation of a laser source and exhibits frequency dependent non-linear behaviour. The other system is based on the external modulation of a laser source and exhibits frequency independent non-linear behaviour. Merits and demerits of the techniques are discussed by comparing analytic to simulation results. Overall, this thesis provides a range of analytical tools to assess the performance of fibre-radio based wireless networks employing OFDM signalling as well as further insight into the behaviour of non-linearly distorted OFDM signals.

System and method for active sonar signal detection and classification

Abstract: A sonar system and method are provided to extract and identify information about a particular target illuminated by an active sonar system. The present invention utilizes a Volterra Series Expansion in conjunction with a least squares procedure to estimate channel and target responses, which may be linear or nonlinear. The system estimates the channel and target responses for different orders of the Volterra Series Expansion and then selects the order for which a minimum error is determined with respect to a measured acoustic return signal. The system requires as inputs only the excitation waveform and the measured acoustic return signal.

Analytical expressions for intermodulation distortion of a MESFET small-signal amplifier using the nonlinear Volterra series

Abstract: Using the nonlinear Volterra series representation, analytical expressions for the third-order intermodulation distortion power and intercept point for a MESFET small-signal amplifier are derived when its equivalent circuit is bilateral and includes the gate-to-drain capacitance ( C gd ) explicitly as a nonlinear element. Previously developed analytical expressions treated C gd as a linear element or incorporated it as a part of gate-to-source and drain-to-source capacitances ( C gs and C ds ). These new analytical expressions are then compared with experimental data and good agreement is obtained. The analytical expressions are also used to study the variation of intermodulation distortion with input power and frequency, and the effect of the individual nonlinear elements in the MESFET’s equivalent circuit.

/spl Ropf//sub +/ fading memory and extensions of input-output maps

Abstract: Much is known about time-invariant nonlinear systems with inputs and outputs defined on /spl Ropf//sup +/ that possess approximately finite memory. For example, under mild additional conditions, they can be approximated arbitrarily well by the maps of certain interesting simple structures. An important fact that gives meaning to results concerning such systems is that the approximately finite memory condition is known to be often met. Here we consider the known proposition that if a causal time-invariant continuous-time input-output map H has fading memory on a certain set of bounded functions defined on all of /spl Ropf/, then H can be approximated arbitrarily well by a finite Volterra series operator. We show that in a certain sense, involving the existence of extensions of system maps, this result too has wide applicability.

Predicting Nonlinear Distortion in Common-Emitter Stages for Amplifier Design Using Volterra Series

Abstract: In this paper we present a method for predicting nonlinear distortion in electronic circuits using the Volterra series. Simple expressions for the distortion in a Common-Emitter stage are determined. Designers may use these expressions to get a quick insight in both qualitative and quantitative aspects of the distortion. Also predictors are given for the maximum distortion in different situations.

Analysis of FET Resistive Mixers with a Double Volterra Series Approach

Abstract: In this communication a double Volterra series approach is applied to the analysis of FET resistive mixers. Starting with a general description of double Volterra series, recursion formulas and closed-form expressions for nonlinear transfer functions of a FET resistive mixer are obtained from a generalized nonlinear current method for two-input port systems. Conversion loss is evaluated following this approach and results show a good correspondence with published data.

Nonlinear system modelling: how to estimate the highest significant order

Abstract: A new method for estimating the highest significant order of nonlinearity of Volterra type systems is presented. The method is based on the use of multisine signals and the possibility of testing the system at three different amplitudes. The performance of the proposed method is demonstrated in simulation and it is shown that it is possible to estimate the highest order of nonlinearity of Volterra type systems very accurately. The method can be used to provide essential prior knowledge about the nonlinearity and thus aid the accurate representation of the system under test.

Practical notes on two Volterra filter identification direct methods

Abstract: A survey of direct methods for identification of discrete Volterra systems is given. The Lee-Schetzen method and Korenberg's fast orthogonal algorithm (FOA) are reviewed. These methods are still useful and can be used as reference for other methods. We give practical considerations and suggestions for optimal use of these two methods coming up from the study of statistical simulations up to the third order.