Showing papers on "Volterra series published in 2006"
04 Dec 2006
TL;DR: In this paper, a new representation of the Volterra series is proposed, which is derived from a previously introduced modified VOLTERRA series, but adapted to the discrete time domain and reformulated in a novel way.
Abstract: A new representation of the Volterra series is proposed, which is derived from a previously introduced modified Volterra series, but adapted to the discrete time domain and reformulated in a novel way. Based on this representation, an efficient model-pruning approach, called dynamic deviation reduction, is introduced to simplify the structure of Volterra-series-based RF power amplifier behavioral models aimed at significantly reducing the complexity of the model, but without incurring loss of model fidelity. Both static nonlinearities and different orders of dynamic behavior can be separately identified and the proposed representation retains the important property of linearity with respect to series coefficients. This model can, therefore, be easily extracted directly from the measured time domain of input and output samples of an amplifier by employing simple linear system identification algorithms. A systematic mathematical derivation is presented, together with validation of the proposed method using both computer simulation and experiment
399 citations
TL;DR: In this paper, the authors generalized the class of ARCH$(infty) models to the non-stationary class of RBMs with time-varying coefficients, leading to the notation locally stationary RBMs.
Abstract: In this paper the class of ARCH$(\infty)$ models is generalized to the nonstationary class of ARCH$(\infty)$ models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation ``locally stationary ARCH$(\infty)$ process.'' The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH$(p)$ processes ($p<\infty$) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the process is investigated. Moreover, a Taylor expansion of the nonstationary ARCH process in terms of stationary processes is given and it is proved that the time-varying ARCH process can be written as a time-varying Volterra series.
206 citations
TL;DR: In this article, the authors generalized the class of ARCH(oo) models to the nonstationary class of RBMs with time-varying coefficients, leading to the notation "locally stationary RBMs" and a Taylor expansion of the RBMs in terms of stationary processes.
Abstract: In this paper the class of ARCH(oo) models is generalized to the nonstationary class of ARCH(oo) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation "locally stationary ARCH(oo) process." The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH(p) processes (p < oo) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the process is investigated. Moreover, a Taylor expansion of the nonstationary ARCH process in terms of stationary processes is given and it is proved that the time-varying ARCH process can be written as a time-varying Volterra series.
173 citations
TL;DR: In this article, a Krylov subspace based projection method is presented for model reduction of large scale bilinear systems, which matches a desired number of moments of multivariable transfer functions corresponding to the kernels of Volterra series representation of the original system.
135 citations
TL;DR: It is shown that Volterra and Wiener series can be represented implicitly as elements of a reproducing kernel Hilbert space by using polynomial kernels.
Abstract: Volterra and Wiener series are perhaps the best-understood nonlinear system representations in signal processing. Although both approaches have enjoyed a certain popularity in the past, their application has been limited to rather low-dimensional and weakly nonlinear systems due to the exponential growth of the number of terms that have to be estimated. We show that Volterra and Wiener series can be represented implicitly as elements of a reproducing kernel Hilbert space by using polynomial kernels. The estimation complexity of the implicit representation is linear in the input dimensionality and independent of the degree of nonlinearity. Experiments show performance advantages in terms of convergence, interpretability, and system sizes that can be handled.
134 citations
TL;DR: In this paper, a low-noise amplifier (LNA) that achieves high third-order input intercept point (IIP3) at RF frequencies using a nonlinearity cancellation technique is proposed.
Abstract: A low-noise amplifier (LNA) that achieves high third-order input intercept point (IIP3) at RF frequencies using a nonlinearity cancellation technique is proposed. The circuit tackles the problem of the effect of the second-order nonlinearity on IIP3 at RF frequencies. The circuit functionality is analyzed using Volterra series. The linear LNA was designed and fabricated in a TSMC 0.35-mum CMOS process. An IIP3 of +21 dBm was achieved with a gain of 11.5 dB, noise figure of 2.95 dB, and a power consumption of 9 mA at 2.5 V
106 citations
TL;DR: This paper proposes a theoretical approach for evaluating distortion in the frequency domain of three-stage amplifiers adopting two commonly used compensation techniques, namely the nested Miller (NM) and the reversed NM, and provides useful design guidelines.
Abstract: This paper proposes a theoretical approach for evaluating distortion in the frequency domain of three-stage amplifiers adopting two commonly used compensation techniques, namely the nested Miller (NM) and the reversed NM. The analysis is based on appropriate amplifier modeling and on the assumption that the nonlinearity generated by each stage is static. Calculations are thus greatly simplified avoiding complex methods based on the Volterra series. Only dominant contributions need to be taken into account, thereby highlighting those mechanisms generating distortion and their features in the frequency domain. Moreover, the adopted approach provides useful design guidelines and explains why the NM compensation technique allows generally better linearity performance at low frequency and why the reversed NM is best suited to high frequencies. Simulation results with Spectre on two transistor-level CMOS circuits are also provided and found to be in very good agreement with expected results.
48 citations
TL;DR: In this paper, two nonlinear anelastic models with fractional derivatives, describing the properties of a series of materials as polymers, and polycrystalline materials are presented.
Abstract: Two nonlinear anelastic models with fractional derivatives, describing the properties of a series of materials as polymers, and polycrystalline materials are presented in this paper. These models are studied analytically, using a variational iteration method. The paper clarifies the different ways in which the fractional differentiation operator can be defined. A Volterra series method of model parameters identification from the experimental data is also presented.
46 citations
11 Jun 2006
TL;DR: A new deviation-reduction approach is proposed to simplify the structure of Volterra series based behavioral models, aimed at significantly reducing the complexity of this kind of model for RF/microwave power amplifiers.
Abstract: In this paper, a new deviation-reduction approach is proposed to simplify the structure of Volterra series based behavioral models, aimed at significantly reducing the complexity of this kind of model for RF/Microwave power amplifiers. The proposed model reduction method is based on a new format representation of the Volterra series, which is extended from a previously-introduced "Modified Volterra Series" but adapted to a complex baseband formulation in the discrete time-domain. This model can be easily extracted directly from measured time-domain samples of input and output signals of an amplifier by employing simple linear system identification algorithms.
40 citations
01 Dec 2006
TL;DR: In this paper, an overview of recently developed, simplified Volterra series based, behavioral modeling approaches for radio frequency and microwave power amplifiers is presented, together with a presentation of their comparative advantages and limitations.
Abstract: This paper presents an overview of recently-developed, simplified Volterra series based, behavioral modeling approaches for radio frequency and microwave power amplifiers. Various model topologies and model pruning strategies are discussed, together a presentation of their comparative advantages and limitations.
34 citations
TL;DR: An efficient way to obtain high- rate models and predistorters from low-rate models is discussed and the validity of the proposed scheme for a very-high-speed-digital-subscriber-line power amplifier, where an adjacent channel power supression of 20 dB is achieved.
Abstract: A novel identification and predistortion scheme of weakly nonlinear systems for mixed-signal devices, which takes into account practical implementation aspects, is presented. It is well known that for the identification of weakly nonlinear systems, despite the spectral regrowth, it suffices to sample the input-output (I/O) data of the system at the Nyquist rate of the input signal. Many applications such as linearization and mixed-signal simulations require system models at a higher sampling rate than Nyquist. Up to now, the construction of such high-rate models has been done by oversampling the corresponding I/O data. This leads to high computational complexity, ill posedness of the estimation, and high demand on the analog-to-digital-converter sampling rate for the implementation. This brief discusses an efficient way to obtain high-rate models and predistorters from low-rate models and shows the validity of the proposed scheme for a very-high-speed-digital-subscriber-line power amplifier, where an adjacent channel power supression of 20 dB is achieved
TL;DR: In this paper, a family of multi-wavelets is constructed from the classical finite element basis functions using the technique of intertwining, and the resulting multiwavelets are piecewise-polynomial, orthonormal, compactly-supported and can be constructed with arbitrary approximation order.
Abstract: The Volterra series is commonly used for the modeling of nonlinear dynamical systems. In general, however, a large number of terms are needed to represent Volterra kernels, with the number of required terms increasing exponentially with the order of the kernel. Therefore, reduced-order kernel representations are needed in order to employ the Volterra series in engineering practice. This paper presents an approach whereby multiwavelets are used to obtain low-order estimates of first-, second-, and third-order Volterra kernels. A family of multiwavelets is constructed from the classical finite element basis functions using the technique of intertwining. The resulting multiwavelets are piecewise-polynomial, orthonormal, compactly-supported, and can be constructed with arbitrary approximation order. Furthermore, these multiwavelets are easily adapted to the domains of support of the Volterra kernels. In contrast, most wavelet families do not possess this characteristic. Higher-dimensional multiwavelets can easily be constructed by taking tensor products of the original one-dimensional functions. Therefore, it is straightforward to extend this approach to the representation of higher-order Volterra kernels. This kernel identification algorithm is demonstrated on a prototypical oscillator with a quadratic stiffness nonlinearity. For this system, it is shown that accurate kernel estimates can be obtained in terms of a relatively small number of wavelet coefficients. These results indicate the potential of the multiwavelet-based algorithm for obtaining reduced-order models for a large class of weakly nonlinear systems.
TL;DR: It is proved that the solution derived minimizes the upper bound of the squared norm of the error resulting from the practical truncation of the Laguerre series expansion into a finite number of functions.
01 Jan 2006
TL;DR: In this paper, the formalism of the Volterra series is used to represent the nonlinear Moog ladder filter and a discrete-time realization of the truncated seri es, which guarantees no aliasing, is performed.
Abstract: In this paper, we show how the formalism of the Volterra series can be used to represent the nonlinear Moog ladder filter. The ana log circuit is analyzed to produce a set of governing differenti al equations. The Volterra kernels of this system are solved from simple algebraic equations. They define an exact decomposition of the system. An identification procedure leads to structures composed of linear filters, sums and instantaneous products of s ignals. Finally, a discrete-time realization of the truncated seri es, which guarantees no aliasing, is performed.
24 May 2006
TL;DR: An adaptive extension of a least squares Volterra predistorter to compensate for the non-linearity of the high power amplifier (HPA) with memory effects in orthogonal frequency division multiplexing (OFDM) systems at the transmitter side is proposed.
Abstract: This paper proposes an adaptive extension of a least squares Volterra predistorter to compensate for the non-linearity of the high power amplifier (HPA) with memory effects in orthogonal frequency division multiplexing (OFDM) systems at the transmitter side. Specifically, the input and output of the nonlinear HPA are accessed in the feedback loop structure to obtain the Volterra kernel parameters using least mean square (LMS) and recursive least square (RLS) algorithms. Once the Volterra kernel is obtained and signals pass through the cascaded system of the predistorter and the HPA, overall linear system characteristics are achieved. The proposed method is non-parametric as it does not assume any specific model for the HPA and the signal structure. The performance of the proposed scheme is verified through computer simulations. The improvements in the reduction of out-of-band spectral regrowth and enhanced performance in terms of the bit error rate (BER) are documented for the traveling wave tube (TWT) HPA model.
24 Apr 2006
TL;DR: The results show that for the used pipeline ADC, the frequency dependence is significantly stronger for second order difference products than for sum products and the linear frequency dependence was not as pronounced as that of the second order Volterra kernel.
Abstract: Volterra theory can be used to mathematically model nonlinear dynamic components such as analog-to-digital converter (ADC). This paper describes how frequency domain Volterra kernels of an ADC are determined from measurements. The elements of Volterra theory are given and practical issues are considered, such as methods for signal conditioning, finding the appropriate test signals scenario and suitable sampling frequency. The results show that for the used pipeline ADC, the frequency dependence is significantly stronger for second order difference products than for sum products and the linear frequency dependence was not as pronounced as that of the second order Volterra kernel.
01 Jul 2006
TL;DR: The adaptive GA method suggested here addresses the problem of determining the proper Volterra candidates, which leads to the smallest error between the identified nonlinear system and the VolterRA model.
Abstract: In this paper, a floating-point genetic algorithm (GA) for Volterra-system identification is presented. The adaptive GA method suggested here addresses the problem of determining the proper Volterra candidates, which leads to the smallest error between the identified nonlinear system and the Volterra model. This is achieved by using variable-length GA chromosomes, which encode the coefficients of the selected candidates. The algorithm relies on sorting all candidates according to their correlation with the output. A certain number of candidates with the highest correlation with the output are selected to undergo the first evolution "era". During the process of evolution the candidates with the least significant contribution in the error-reduction process is removed. Then, the next set of candidates are applied into the next era. The process continues until a solution is found. The proposed GA method handles the issues of detecting the proper Volterra candidates and calculating the associated coefficients as a nonseparable process. The fitness function employed by the algorithm prevents irrelevant candidates from taking part in the final solution. Genetic operators are chosen to suit the floating-point representation of the genetic data. As the evolution process improves and the method reaches a near-global solution, a local search is implicitly applied by zooming in on the search interval of each gene by adaptively changing the boundaries of those intervals. The proposed algorithms have produced excellent results in modeling different nonlinear systems with white and colored Gaussian inputs with/without white Gaussian measurement noise
TL;DR: In this article, a new method for fast approximate calculation of quasi-steady states of cyclic processes is presented, based on the concept of higher-order frequency response functions.
Abstract: A new method for fast approximate calculation of quasi-steady states of cyclic processes is presented. The method is based on the concept of higher-order frequency response functions. The system input is represented in the form of Fourier series, whereas the output is presented in the form of Volterra series. For practical applications, both the input and the output series are approximated by finite-length sums. In this way, the approximate periodic quasi-steady state of the system output is calculated directly, without long numerical integrations. Cyclic operation of an adsorption column with periodic fluctuations of the inlet concentration or/and adsorbent temperature is used as a case study for testing the new method. The necessary frequency response functions (FRFs), up to the third order, are derived, based on the equilibrium dispersion model. The method is tested for sinusoidal and rectangular input changes. The approximate solutions based on the FRFs, up to the third order, and a finite number of input harmonics, are calculated for different input frequencies and amplitudes and compared with the numerical solutions. Very good agreement is obtained.
TL;DR: In this article, a single degree of freedom (sdof) analysis of a system's harmonic behavior is carried out for the single-degree-of-freedom (SDof) case.
30 May 2006
TL;DR: In this article, the effect of harmonic output terminations on intermodulation asymmetry has been clarified using a Volterra series approach applied to a power PHEMT device for X-band application.
Abstract: IMD asymmetry generation and its asymmetrical behaviour are discussed and clarified in this contribution using a Volterra series approach The approach has been applied to a power PHEMT device for X-band application The effects of harmonic terminations have been clarified, stressing the relevance of baseband terminations and in particular of the output susceptance Simplified expressions are inferred to clarify the effects of output terminations Finally, the opportunity to choose a suitable fundamental and second harmonic output termination to reduce intermodulation asymmetry is discussed
TL;DR: In this article, the mean upcrossing rate of stationary stochastic processes that can be represented as second order stochastically Volterra series (SVO) series is calculated.
TL;DR: In this paper, the authors proposed a graph-based approach for transient and distortion analysis of nonlinear analog circuits based on a frequency domain Volterra series representation of non-linear circuits.
Abstract: This paper presents a novel approach for transient and distortion analyses for time-invariant and periodically time-varying mildly nonlinear analog circuits. Our method is based on a frequency domain Volterra series representation of nonlinear circuits. It computes the nonlinear responses using a nonlinear current method that recursively solves a series of linear Volterra circuits to obtain linear and higher-order responses of a nonlinear circuit. Unlike existing approaches, where Volterra circuits are solved mainly in the time domain, the new method solves the linear Volterra circuits directly in the frequency domain via an efficient graph-based technique, which can derive transfer functions for any large linear network efficiently. As a result, both frequency domain characteristics, like harmonic and intermodulation distortion, and time domain waveforms can be computed efficiently. The new algorithm takes advantage of identical Volterra circuits for second- and higher-order responses, which results in significant savings in driving the transfer functions. Experimental results for two circuits—a low-noise amplifier and a switching mixer—are obtained and compared with SPICE3 to validate the effectiveness of this method.
01 Sep 2006
TL;DR: This paper combines the modeling of transmitted-reference systems with autocorrelation receivers as Volterra equivalent system models, and the statistical characterization of the inter-pulse-interference due to multipath propagation, to obtain the statistics of theVolterra model coefficients as a function of system and channel parameters.
Abstract: This paper combines the modeling of transmitted-reference (TR) systems with autocorrelation receivers as Volterra equivalent system models, and the statistical characterization of the inter-pulse-interference due to multipath propagation We obtain the statistics of the Volterra model coefficients as a function of system and channel parameters In its generic form, the analysis can be used for numerical performance evaluations of TR systems It is also expected to be useful for the optimization of signal processing tasks in TR receivers, where such statistical knowledge can be exploited Examples are Volterra channel estimation or synchronization Specializing the analysis to the elementary dual-pulse TR scheme, closed-form expressions are obtained for various performance metrics, which directly indicate the trade-off between different system choices
TL;DR: The validity and usefulness of the approach are demonstrated in numerical simulations as well as experiments applied to blindly identify the primary path of active-noise-control (ANC) systems in a practical scenario.
Abstract: This paper extends blind single-input single-output (SISO) Volterra-system identification from the second-order statistics (SOSs) domain into the third-order statistics domain. For the full-sized Volterra system with finite order and memory, which is excited by unobservable independent identically distributed (i.i.d.) stationary random sequences, it is known that blind identifiability is not possible in the SOS domain. Although this conclusion is also true in the higher order statistics (HOSs) domain, it will be shown that under some sufficient conditions, a larger set of sparse Volterra systems can be identified blindly in third-order moment (TOM) domain than in the SOS counterpart. This is due to the fact that (n+1)(3n+2)/2 terms of different statistical quantities can be used in the third-order-statistics domain while only (n+2) terms of statistical information are nonredundant for SOS-based blind identification, where n is the memory length of the system. The validity and usefulness of the approach are demonstrated in numerical simulations as well as experiments applied to blindly identify the primary path of active-noise-control (ANC) systems in a practical scenario.
22 Mar 2006
TL;DR: In this article, a novel identification method for time-varying Volterra systems (TVVS) is proposed, where the system identification problem is converted to a state estimation problem of a dynamic system.
Abstract: Most nonlinear system identification methods based on Volterra model assume that the underlying system is time-invariant. In this paper, a novel identification method for time-varying Volterra systems (TVVS) is proposed. We view this problem from a different perspective in the sense that the system identification problem is converted to a state estimation problem of a dynamic system. The time-varying Volterra kernels are governed by a Gauss-Markov stochastic difference equation upon which a state-space representation of time-varying Volterra systems is built. The state transition matrix and noise covariance of the underlying state equations are usually unknown. Therefore, we develop a method to estimate these unknown quantities. Finally, a Kalman filtering scheme is utilized to identify and track the time-varying Volterra system. Simulation examples are given to illustrate the better performance of the proposed method as compared with other adaptive identification methods such as the LMS and RLS algorithms.
21 May 2006
TL;DR: An automatic synthesis tool for RFIC design that incorporates built-in numerical simulators for fast evaluation of the performance metrics and nonlinearity is modeled using Volterra series method.
Abstract: An automatic synthesis tool for RFIC design is demonstrated The tool incorporates built-in numerical simulators for fast evaluation of the performance metrics Nonlinearity is modeled using Volterra series method The tool additionally provides the dimensions of the on-chip inductors along with their values To validate this approach, a low noise amplifier (LNA) at 900MHz is synthesized using a 035/spl mu/m CMOS process The synthesis results are verified with the simulation data, obtained from Cadence SPECTRE circuit simulator
01 Sep 2006
TL;DR: In this article, the minimisation of the asymmetry between lower and upper sideband intermodulation products is discussed, using a Volterra series approach, and new conditions to minimise IMD asymmetry are obtained and verified through the design of a C-band 2nd harmonic tuned hybrid power amplifier using a GaN PHEMT device.
Abstract: In this contribution the minimisation of the asymmetry between lower and upper sideband intermodulation products is discussed, using a Volterra series approach. From the inferred relationships new conditions to minimise IMD asymmetry are obtained and verified through the design of a C-band 2nd harmonic tuned hybrid power amplifier using a GaN PHEMT device. The proposed approach, without linearization schemes, achieves the minimisation of AM-PM conversion and asymmetry up to 400 MHz tone spacing, with a minimum 32.5 dBm output power and over 60 % drain efficiency @ 5.5 GHz
01 Jan 2006
TL;DR: This paper is divided into two parts, the first part presents a method to implement the Volterra and nonlinear impulse response models in Matlab/Simulink environment and a co-simulation interface between Matlab / Simulink and Xepedion/Goldengate circuit simulator.
Abstract: The verification of the system performances becomes of prime importance and notably with the emergence of the SoC, in which, the spurious couplings between the functional circuits can be critical. The needs in terms of system simulation tools become thus very important. This paper is divided into two parts, the first part presents a method to implement the Volterra and nonlinear impulse response models in Matlab/Simulink environment. The second part presents a co-simulation interface between Matlab/Simulink and Xepedion/Goldengate circuit simulator.
TL;DR: This example suggests that the use of two tones widely separated in frequency to model the interferers provides sufficiently accurate results compared to a multitone approximation of the spurious free dynamic range.
Abstract: The spurious free dynamic range (SFDR) is commonly used as a measure of dynamic range for the radio frequency and microwave front-end receivers. Although well defined in narrow-band systems, the definition becomes less clear in wide-band systems, when the nonlinearity is memoryless and the the noise figure is frequency dependent. To generalize the SFDR to wide-band systems, a meaningful physical interpretation of the conventional two-tone test is first developed. Based on this interpretation, the upper bound of the wide-band SFDR is obtained by applying a multitone test, while the lower bound is computed using the effective noise figure. The multitone test in both the memoryless and memory nonlinear Volterra systems is considered. A practical measurement technique to characterize the Volterra kernel is also provided. A realistic example based on a low noise amplifier shows a significant difference between the conventional and wide-band SFDR values. In this example, our results suggest that the use of two tones widely separated in frequency to model the interferers provides sufficiently accurate results compared to a multitone approximation.
01 Sep 2006
TL;DR: This paper presents a novel approach to estimating the optimum memory length required for accurate behavioral modeling of RF power amplifiers from the measured input and output signals of the PA in the time domain.
Abstract: In RF power amplifier (PA) behavioral modeling, special emphasis has been put on memory-effects since they can have a determinant impact on the performance of the model. If too short a memory length is considered, it is not possible to fully characterize the PA, whereas using an excessively long memory length results in a slower, less efficient model. Therefore, it is vital to find the optimum memory length during model extraction. In this paper we present a novel approach to estimating the optimum memory length required for accurate behavioral modeling of RF power amplifiers. For example, using this method, we can directly find the optimum memory length needed in a time delay neural network or a Volterra series based model from the measured input and output signals of the PA in the time domain. Experimental examples are presented here for the case of discrete Volterra series based models.