Volterra series

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

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

Simplified Volterra Series Nonlinear Equalizer for Polarization-Multiplexed Coherent Optical Systems

Abstract: Starting from a previously proposed frequency-domain Volterra series nonlinear equalizer (VSNE), whose complexity evolves as O(N3), with N being the frequency-domain block length, we derive a symmetric VSNE filter array formulation for polarization-multiplexed (PM) signals, whose full VSNE equivalent is up to 3 × more computationally efficient, with zero performance penalty. By gradually reconstructing the third-order kernel from its column/diagonal components, the full VSNE can be reduced to a restrict set of Nk frequency-domain filters, leading to O(Nk N2) complexity, associated with negligible performance loss. Finally, a simplified VSNE approach with invariant Kernel coefficients is proposed, delivering O(Nk N) complexity at the expense of controlled performance penalty. The proposed array of symmetric VSNE filters significantly increases the scalability of the previous matrix-based VSNE, providing a more flexible balance between performance and complexity, which can be freely adjusted to match the available computational resources. Performing a direct comparison between the simplified VSNE and the widely used split-step Fourier method in a long-haul 224 Gb/s PM-16QAM transmission system, we demonstrate a reduction of over 60% in terms of computational effort and 90% in terms of equalization latency.

Volterra models and three-layer perceptrons

Abstract: This paper proposes the use of a class of feedforward artificial neural networks with polynomial activation functions (distinct for each hidden unit) for practical modeling of high-order Volterra systems. Discrete-time Volterra models (DVMs) are often used in the study of nonlinear physical and physiological systems using stimulus-response data. However, their practical use has been hindered by computational limitations that confine them to low-order nonlinearities (i.e., only estimation of low-order kernels is practically feasible). Since three-layer perceptrons (TLPs) can be used to represent input-output nonlinear mappings of arbitrary order, this paper explores the basic relations between DVMs and TLPs with tapped-delay inputs in the context of nonlinear system modeling. A variant of TLP with polynomial activation functions-termed "separable Volterra networks" (SVNs)-is found particularly useful in deriving explicit relations with DVM and in obtaining practicable models of highly nonlinear systems from stimulus-response data. The conditions under which the two approaches yield equivalent representations of the input-output relation are explored, and the feasibility of DVM estimation via equivalent SVN training using backpropagation is demonstrated by computer-simulated examples and compared with results from the Laguerre expansion technique (LET). The use of SVN models allows practicable modeling of high-order nonlinear systems, thus removing the main practical limitation of the DVM approach.

Multipoint Volterra Series Interpolation and $\mathcal{H}_2$ Optimal Model Reduction of Bilinear Systems

Abstract: In this paper, we focus on model reduction of large-scale bilinear systems. The main contributions are threefold. First, we introduce a new framework for interpolatory model reduction of bilinear systems. In contrast to the existing methods where interpolation is forced on some of the leading subsystem transfer functions, the new framework shows how to enforce multipoint interpolation of the underlying Volterra series. Then, we show that the first-order conditions for optimal $\mathcal{H}_2$ model reduction of bilinear systems require multivariate Hermite interpolation in terms of the new Volterra series interpolation framework; thus we extend the interpolation-based first-order necessary conditions for $\mathcal{H}_2$ optimality of LTI systems to the bilinear case. Finally, we show that multipoint interpolation on the truncated Volterra series representation of a bilinear system leads to an asymptotically optimal approach to $\mathcal{H}_2$ optimal model reduction, leading to an efficient model reduction...