Volterra series

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

A Linearization Strategy for Undersampling Analog-to-Digital Converters

Abstract: The ability of high performance Radar and Broadband Systems to detect weak targets in presence of strong interferers or clutter is given by their Spurious Free Dynamic Range (SFDR). Although the Signal-to- Noise-Ratio (SNR) necessary for detection may be improved by well-known system processing gains, the dynamic range is ultimately limited by distortion terms caused by nonlinear behaviour of receiver components. The Software Defined Radio (SDR) paradigm assigns the Analog-to-Digital Converter a key role in receiver design. For systems using IF- Subsampling, linearity requirements place a heavy burden on the ADC, as SFDR signifcantly degrades with increasing input frequency. As a consequence, the ADC can only be used at input frequencies fairly below its intrinsic full power bandwidth, restricting the systems IF placement. This contribution discusses the possibility of processing ADC output data in the digital domain to achieve improved linearity. The Volterra series approach of nonlinear systems and its constrained variants are discussed. We will show in detail that for higher input frequencies, dynamic errors cause the harmonic terms to loose their in-phase ability; in higher Nyquist zones a frequency-dependend dynamic phase error has to be considered. Assumptions are backed by an evaluation of coherent data from the LTC2208 (16 Bit, 120 MSPS). A specific correction algorithm incorporating the dynamic phase error will be presented, which yielded 25 dB SFDR improvement in the 7th Nyquist Zone (360-420 MHz). The reproducibility of correction results is considered in some detail.

A novel support vector machine robust model based electrical equaliser for coherent optical orthogonal frequency division multiplexing systems

Abstract: Classifiers, such as artificial neural networks non-linear equaliser (ANN-NLE), Wiener–Hammerstein non-linear equaliser, Volterra non-linear equaliser (Volterra-NLE) and support vector machine non-linear equaliser (SVM-NLE), can play a significant role in compensating non-linear imperfections in the optical communications context. Using classifiers to mitigate the non-linear effects in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems is an interesting idea to be investigated. In this study, a novel support vector machine robust version, specifically adapted to a 100 Gb/s CO-OFDM data structure for long haul distance, is proposed. Firstly, the authors demonstrate that SVM-NLE upgrades the system performance by about 10−1 in terms of bit-error rate compared to Volterra-NLE at optical signal-to-noise ratio equal to 14 dB. Then, they show that it can double the transmission distance up to 1600 km over single mode fibre channel. Furthermore, a performance comparison is performed using 16 quadrature amplitude modulation and 40 Gb/s bit rate for SVM-NLE, ANN-NLE and inverse Volterra series transfer function non-linear equaliser, respectively.

Baseband volterra filters with even-order terms: Theoretical foundation and practical implications

Abstract: The baseband Volterra series is a general approach to model nonlinear passband systems like radio frequency power amplifiers in equivalent baseband. In the present paper, we review the derivation of the baseband Volterra series using a compact vector notation and show that it only includes odd-order terms. After that, we present a new derivation which shows that by assuming modified basis functionals in the passband, one obtains a baseband Volterra series which also includes even-order terms. By simulations, we demonstrate that the inclusion of the proposed even-order basis functionals improves the performance of behavioral modeling and digital predistortion and decreases the condition number of the regression matrix.

Volterra – lax-wendroff algorithm for modelling sea surface flow pattern from jason-1 satellite altimeter data

Abstract: This paper introduces a modified formula for geostrophic current. The method is based on utilization of the Volterra series expansion in the geostrophic current equation. The purpose of this method is to transform the time series JASON-1 satellite altimeter data into a real ocean surface current. Then, the Volterra kernel inversion used to acquire the sea surface current velocity. In doing so, the finite element model of Lax-Wendorff scheme used to determine the spatial variation of current flow. The results show that the new formula of geostrophic current is able to avoid the impact of Coriolis and geoid parameters. The second-order Volterra kernel illustrates an error standard deviation of 0.03, thus performing a better estimation of flow pattern as compared to first-order Volterra kernel. We conclude that modeling of sea surface current by using JASON-1 satellite altimeter data can be operationalized by using the new formula for geostrophic current.