Volterra series

About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.

Identification of linear systems in the presence of nonlinear distortions

Abstract: A method is presented to measure and identify a linear system in the presence of nonlinear distortions. The method is based on a two-step approach. In the first step the influence of nonlinear systems up to degree 4 is eliminated. In the second step the remaining linear system is identified using a weighted least squares method. The kernel of the proposed technique is the excitation of the system with a pure sinusoid. Special attention is paid to the elimination of higher harmonics in the excitation signal which are due to the nonlinear load of the generator.

Behavioral modeling of narrowband microwave power amplifiers with applications in simulating spectral regrowth

Abstract: A new behavioral model for narrowband microwave power amplifiers is proposed. Analytic expressions for the gain compression (AM-AM) and amplitude dependent phase distortion (AM-PM) of a nonlinear amplifier are derived from a third-order Volterra series model. The cases of a single-tone and of a two-tone signal are explored. We show that the gain compression characteristics of nonlinear amplifiers depend on the amplitude modulation characteristics of the signal. Furthermore, we show that the time-averaged phase deviation is independent of the modulation envelope. This justifies the new model proposed for obtaining the envelope transfer characteristics by applying the Bessel-Fourier technique only to the AM-AM characteristic. This model is verified by comparing spectral regrowth simulations of digitally-modulated signals to those measured in a 1.9 GHz GaAs FET power amplifier.

Memory fading Volterra series model for high power infrastructure amplifiers

Abstract: This paper presents a novel technique of adapting the generalized Volterra series behavioral model to describe, with improved accuracy, power amplifiers targeting cellular infrastructure applications. The generalized Volterra series is reformulated with respect to the discrete time domain to allow impendent specification of memory depth for each kernel. A memory fading concept is then adopted to align memory depth to increasing kernel order. The number of Volterra coefficients needed to represent a strong PA non-linearity are significantly reduced (to a manageable level), while retaining certain high order kernels essential for realizing exceptional model fidelity. Results show model residuals better than -60 dBc for single- and two-carrier WCDMA signals when applied to a 350W LDMOS Doherty power amplifier circuit.

Multiwavelet Constructions and Volterra Kernel Identification

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.

Performance of Multilevel Baseband Digital Systems in a Nonlinear Environment

Abstract: 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.