Showing papers on "Volterra series published in 2004"

Behavioral modeling of RF power amplifiers based on pruned volterra series

Abstract: Behavioral modeling techniques provide a convenient and efficient means to predict system-level performance without the computational complexity of full circuit simulation or physics-level analysis of nonlinear systems, thereby significantly speeding up the analysis process. General Volterra series based models have been successfully applied for radio frequency (RF) power amplifier (PA) behavioral modeling, but their high complexity tends to limit their applications to "weakly" nonlinear systems. To model a PA with strong nonlinearities and long memory effects, for example, the general Volterra model involves a great number of coefficients. In this letter, we propose a new simplified Volterra series based model for RF power amplifiers by employing a "near-diagonality" pruning algorithm to remove the coefficients which are very small, or else not sensitive to the output error, therefore dramatically reducing the complexity of the behavioral model.

Digital Predistortion of Power Amplifiers for WirelessApplications

Abstract: For my family. iii ACKNOWLEDGEMENTS It is time to draw a period to my PhD endeavor. I feel extremely lucky to meet so many talented people during these years. I am grateful for their friendship, help, encouragement, and support. First, I would like to thank my advisor, Dr. G. Tong Zhou, for providing this opportunity for me to study at Georgia Tech. Her constant encouragement and valuable advices are essential for the completion of this thesis. I will be always inspired by the high standards she sets for herself and her sharp focus and deep devotion to whatever she works on.

Nonlinear Open-/Closed-Loop Aeroelastic Analysis of Airfoils via Volterra Series

Abstract: Determination of the subcritical aeroelastic response to arbitrary time-dependent external excitation and determination of the flutter instability of open/closed-loop two-dimensional nonlinear airfoils constitute the main topics. To address these problems, Volterra series and indicial aerodynamic functions are used, and, in the same context, the pertinent aeroelastic nonlinear kernels are determined. Flutter instability predictions obtained within this approach compared with their counterparts generated via the frequency eigenvalue analysis and via experiments reveal excellent agreements. Implications of a number of important parameters characterizing the lifting surface and control law on the aeroelastic response/flutter are discussed, and pertinent conclusions are outlined.

Filtered-X affine projection algorithm for multichannel active noise control using second-order Volterra filters

Abstract: A multichannel controller based on Volterra filters is described. A filtered-X affine projection algorithm is derived in detail for homogeneous quadratic filters. The proposed algorithm can be also extended to higher-order Volterra kernels and includes linear controllers as a particular case.

A nonlinear dynamic model for performance analysis of large-signal amplifiers in communication systems

Abstract: A new nonlinear dynamic model of large-signal amplifiers based on a Volterra-like integral series expansion is described. The new Volterra-like series is specially oriented to the modeling of nonlinear communication circuits, since it is expressed in terms of dynamic deviations of the complex modulation envelope of the input signal. The proposed model represents a generalization, to nonlinear systems with memory, of the widely-used amplitude/amplitude (AM/AM) and amplitude/phase (AM/PM) conversion characteristics, which are based on the assumption of a practically memoryless behavior. A measurement procedure for the experimental characterization of the proposed model is also outlined.

Volterra series for solving weakly non-linear partial differential equations: application to a dissipative Burgers' equation

Abstract: A method to solve weakly non-linear partial differential equations with Volterra series is presented in the context of single-input systems. The solution x(z,t) is represented as the output of a z-parameterized Volterra system, where z denotes the space variable, but z could also have a different meaning or be a vector. In place of deriving the kernels from purely algebraic equations as for the standard case of ordinary differential systems, the problem turns into solving linear differential equations. This paper introduces the method on an example: a dissipative Burgers'equation which models the acoustic propagation and accounts for the dominant effects involved in brass musical instruments. The kernels are computed analytically in the Laplace domain. As a new result, writing the Volterra expansion for periodic inputs leads to the analytic resolution of the harmonic balance method which is frequently used in acoustics. Furthermore, the ability of the Volterra system to treat other signals constitutes an improvement for the sound synthesis. It allows the simulation for any regime, including attacks and transients. Numerical simulations are presented and their validity are discussed.

Evaluation of signal-to-noise and distortion ratio degradation in nonlinear systems

Abstract: This paper presents a new figure-of-merit to evaluate signal-to-noise and distortion (SINAD) ratio degradation in nonlinear systems, herein referred to as the noise and distortion figure (NDF). In order to obtain a mathematical formula for this NDF, the best linear approximation calculation is presented for memoryless and dynamic nonlinear systems, which can be modeled by a finite Volterra series. To the best of the authors' knowledge, this is the first time such an attempt of calculating the NDF for a nonlinear and dynamic system is made. NDF results are discussed in both types of systems by means of numerical simulations of systems up to the third order.

Single-term walsh series method for the volterra integro-differential equations

Abstract: A method for the solution of Volterra integro-differential equations by using single-term Walsh series is presented Properties of single-term Walsh series are utilized to reduce the computation of Volterra integro-differential equations to some algebraic equations The method is computationally attractive, and applications are demonstrated through illustrative examples

Linear approximation of weakly nonlinear MIMO systems

Abstract: In this paper it is shown that a nonlinear MIMO system can be replaced by a linear system plus a nonlinear noise source. The optimized measurement strategy is proposed to measure the nonparametric FRF.

Amplifier linearization using compact microstrip resonant cell-theory and experiment

Abstract: This paper presents a novel technique for reducing the intermodulation distortions (IMDs) in power amplifiers. In this method, both second- and third-harmonic components generated by the transistor are reflected back simultaneously by the compact microstrip resonant cell (CMRC) at the input port with proper phases to mix with the fundamental signal for the reduction of IMDs. A rigorous mathematical analysis on the effectiveness of multiharmonic reflections has been formulated and derived using the Volterra series. Moreover, the delay mismatch factor of the proposed method is analytically studied and the result shows that a better tolerance to the delay error can be achieved by using CMRC circuitry. Standard two-tone test measurements reveal 32- and 22-dB reductions for the third-order IMD and fifth-order IMD, respectively, without affecting the fundamental signal at 2.45 GHz. Meanwhile, the proposed approach gives a peak power added efficiency of 53% with 11.5 dB transducer gain and 15 dBm output power for a single-stage SiGe bipolar junction transistor. The adjacent channel power ratio (ACPR) is -55dBc for a data rate of 384-kb/s quadrature phase shift keyed modulated signal with 2-MHz spanning bandwidth, and this ACPR is maintained for a broad range of output power level.

Towards a Volterra series representation from a Neural Network model

Abstract: We have developed a Neural Network model able to reproduce some nonlinear characteristics of an electronic device. However, electronic devices nonlinear analysis requires an analytical model, that allows to draw conclusions about the device behavior. Such a model can be the Volterra series representation, which is a series that has some particular terms, named the “Volterra kernels”. We want to show in this work how a Volterra model can be built using the parameters of the proposed Neural Network model. We present a method for estimating the Volterra kernels using the Neural Network parameters and some simulation results.

Volterra series and neural networks to model an electronic device nonlinear behavior

Abstract: Electronic devices that have a dynamic nonlinear behavior are generally modeled by the so-called Volterra series model. The construction of such analytical model, however, is a complex and time-consuming task. In this work we propose a new approach to help in the building of a Volterra series model for modeling an electronic device, using a very simple neural network model. As an initial case of study, the proposed approach is applied to the modeling of a diode and the simulation results are presented. Conclusions are drawn from the comparison of the results obtained with different kernels approximations and network topologies.

Identification of PARAFAC-Volterra cubic models using an Alternating Recursive Least Squares algorithm

Abstract: A broad class of nonlinear systems can be modelled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filters structure. This paper is concerned with the problem of identification of third-order Volterra kernels. A tensorial decomposition called PARAFAC is used to represent such a kernel. A new algorithm called the Alternating Recursive Least Squares (ARLS) algorithm is applied to identify this decomposition for estimating the Volterra kernels of cubic systems. This method significantly reduces the computational complexity of Volterra kernel estimation. Simulation results show the ability of the proposed method to achieve a good identification and an important complexity reduction, i.e. representation of Volterra cubic kernels with few parameters.

Identifying the main nonlinear contributions: use of multisine excitations during circuit design

Abstract: Modeling and understanding the nonlinear behavior of analog and RF circuits is essential for good design of telecommunication systems. Classical Volterra series give the designer this necessary insight, but they are only valid for weakly nonlinear systems and they are difficult to edit. To overcome these limitations, we developed a technique to identify, quantify and qualify the sources of nonlinear behavior in analog and RF circuits by combining the information obtained by a set of simulations that use periodic excitation signals with a given power spectrum and arbitrary phases. The paper describes and demonstrates this approach by the analysis of the cascade of a BiCMOS power preamplifier and power amplifier with adaptive biasing for 5 GHz wireless local area networks (WLAN). The approach is applicable to weakly and strongly nonlinear systems, which is demonstrated by pushing the amplifier into compression. Furthermore, it provides useful design information, such as the contribution of each subcircuit to the overall nonlinear behavior.

Volterra−Laguerre Models for Nonlinear Process Identification with Application to a Fluid Catalytic Cracking Unit

Abstract: Volterra series models are attractive for use in model-based control of nonlinear processes because they are direct extensions of linear impulse response models commonly used in process control. However, a limitation in their use is the fact that higher than second-order nonlinearities and/or multi-input multi-output Volterra models involve very large numbers of parameters. Here we address the problem with a parameter reduction method that utilizes a Laguerre basis function expansion of the Volterra kernels and orthogonal regression analysis for the determination of the dominating terms in the model. The conditions under which a nonlinear system can be approximated by a Volterra−Laguerre model are investigated. The technique is then applied to the identification of a 3 × 3 third-order nonlinear model for a simulated model IV fluid catalytic cracking unit.

Nonlinear Behaviour of Structures Using the Volterra Series—Signal Processing and Testing Methods

Abstract: To extend modal analysis to nonlinear structures, and adopting the Volterra series as a mathematical framework, we present some new routes together with progress on signal processing. The closed form expressions of higher-order transfer function on the other hand would permit one to obtain eigenvalues of various orders and eigenvectors. Existing signal processing analyzers are initially devoted to linear systems. Programs treating input and output signals of systems are tailored for one-time (or frequency) variable functions. Nonlinear systems can indeed be analyzed by one-dimensional (direct or inverse) Fourier transforms. However, the experimenter rapidly discovers their limitation when dealing with coupling phenomena that require functions with many time (or frequency) variables. In this framework, multidimensional Fourier transforms are necessary.

Performance analysis of sampling switches in voltage and frequency domains using Volterra series

Abstract: In any data converter system, the linearity of the sampling switch is a very critical parameter, especially for wideband sigma-delta modulators. Distortion introduced in the sampling instance directly degrades the quality of the input signal. In this paper we present analyses of a set of sampling switches in the frequency and voltage domains in order to find the most linear type for wide baseband excitation. Volterra series analysis is adopted to find the frequency behavior of the switches. The theoretical results are verified by circuit simulations in a 0.35 /spl mu/m CMOS process. It is found that the bootstrap sampling switch is a very attractive candidate, especially for frequencies near f/sub s//2.

Selection of a time-varying quadratic Volterra model using a wavelet packet basis expansion

Abstract: We consider the identification of a time-varying nonlinear system based on a single realization of the system input-output. To enable identification, the system's time variation is approximated by a weighted sum of known basis sequences. Using wavelet packet basis sequences increases the flexibility of the model, allowing a suitable basis to be selected. A basis selection procedure is formulated using the Best Basis algorithm to choose the minimum entropy wavelet packet basis. The statistical significance of each of the chosen basis sequences is then tested using a multiple hypothesis testing procedure. Selecting individual sequences in this way achieves a specified level of confidence that the final model contains only those sequences that are significant. As an alternative, we also propose a search procedure, based on an information theoretic criterion, to select basis sequences.

Large-signal HBT model requirements to predict nonlinear behaviour

Abstract: Measurements and simulations are carried out in order to determine the requirements for a HBT model to predict the generation of harmonics. Unlike, investigations based on Volterra series, also the case of large excitations is investigated, where the load-line reaches through wide ranges of currents and voltages, and self-biasing effects take place. It turns out that in class A operation, it is absolutely necessary for the model to account for the current dependence of the base collector capacitance and collector transit time, even in a set-up where fundamental power and bias points are predicted well also without.

Volterra-series-based analytic technique to assess the power density spectrum of nonlinearly distorted OFDM signals

Abstract: A Volterra-series-based analytic technique is developed to assess the power density spectrum of orthogonal frequency division multiplexing (OFDM) signals distorted by frequency- independent or frequency-dependent nonlinearities. The nonlinearly distorted OFDM signal power density spectrum is expressed in terms of the non-distorted OFDM signal harmonic power density spectra and the nonlinearity transfer functions. The effectiveness of the technique in both the frequency-independent and the frequency-dependent cases is established by comparing analysis and simulation. It is shown that if the OFDM signal is modelled rigorously as a cyclostationary stochastic process, analysis agrees perfectly with simulation. Further, it is also shown that if the OFDM signal is modelled as a stationary stochastic process, the developed mathematical expressions reduce to the familiar Bedrosian-Rice expressions. The appropriateness of this approximation for many practical purposes is verified by the very close agreement obtained between the simplified analytic and simulation results.

Fitting of 2-dimensional polynomial device model based on simulated voltage and current spectra

Abstract: This paper presents a fitting technique for polynomial 2-dimensional nonlinearity, based on voltage current spectra. It will be shown that despite the strongly correlating controlling voltages, the nonlinear 2-dimensional drain-source current (I/sub DS/) of the 30 W RF power transistor model can be fitted. Furthermore, a simplified Volterra presentation of the 3rd order intermodulation distortion (IM3) contributors of I-V and Q-V sources can be constructed. The results match well with the data simulated using harmonic balance. Also IM3 phasors of the input and output of the device are presented. The analysis shows that the total output IM3 current is dominated by the distortion from I/sub DS/. Also a significant portion of the IM3 current is caused by the fact that output IM3 voltage appears across linear but large drain-source capacitance (C/sub DS/).

Harmonic distortion in three-stage nested-Miller-compensated amplifiers

Abstract: A simplified approach for evaluating high-frequency distortion of three-stage amplifiers compensated with the nested-Miller technique is presented. The analysis exploits a proper amplifier modeling and, by suitable assumptions avoids complex methods based on the Volterra series, while providing simple equations useful even for design. Besides, the most important mechanisms generating distortion and their features in the frequency domain are clearly highlighted. Simulations on a CMOS circuit are found in excellent agreement with expected results.

Model reduction for process control using iterative nonlinear identification

Abstract: Given a complex first principles model of a process, a strategy for model complexity reduction is developed, such that the model obtained is suitable for process control. The system is assumed to have a Volterra representation that can be parametrized in terms of basis functions with fixed poles. The approach taken consists of an iteratively using system identification techniques on the complex system model, while at the same time optimizing the inputs used. The results are tested on a copolymerization reactor example.