Volterra series

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

Consideration of Volterra Series With Excitation and/or Impulse Responses in the Form of Dirac Impulses

Abstract: In this brief, the possible extensions of the Volterra series and also incorporating Dirac impulses in it are discussed. It is shown that two of them are valid, but the third one, in the usual sense, is not. These extensions form associated models, which are very helpful in the simplification of some calculations in the nonlinear analysis of systems described by the Volterra series.

Nonlinear Dynamic Compensation of Sensors Using Inverse-Model-Based Neural Network

Abstract: Many sensors (such as low-cost sensors), in essence, display strongly nonlinear dynamic behavior that cannot be calibrated by well-developed linear dynamic compensation methods. So far, no general nonlinear dynamic compensation (NLDC) method exists, although there are some approaches based on nonlinear models (including Volterra series expansion, Wiener kernels, the Hammerstein model, and finite impulse response) that were developed to compensate some special kinds of nonlinear sensors. In this paper, we suggest a general framework for NLDC, in which removal of the influence of disturbance by using an auxiliary sensor is significantly studied and presented. The inverse model and differential-estimation-filter arrays are embedded in this general framework, where a neural network is applied to approximate the inverse mapping, and differential-filter arrays are used to estimate signal differentials up to a certain order. We also discuss the existence conditions of the general framework. The detailed design procedure of this general method is given as well. Simulation and experiments are presented to illustrate the proposed general NLDC method.

Adaptive Nonlinear Equalization Combining Sparse Bayesian Learning and Kalman Filtering for Visible Light Communications

Abstract: Nonlinear post equalization (NPE) based on Volterra series (VS) is considered as an effective way to mitigate the severe light emitting diode (LED) nonlinearity and multipath effect in a visible light communication (VLC) system. However, it is restricted by kernel complexity in practical applications. In this paper, we formulate the kernel extraction of VS-based NPE to be a sparse recovery problem, and propose an efficient sparsity-aware approach, using combined sparse Bayesian learning (SBL) and Kalman filtering (KF) to extract the active VS kernels and thus to reduce the redundancy of NPE. First, from the view of probability, a Bayesian strategy is applied to select the dominant regressors from the original measurement matrices by exploiting the learning of hyperparameters, which encourages the sparseness of VS kernels with an imposed prior. Then, based on the specified regression matrix, the improved KF iteration is used in the estimation of the kernel coefficients to overcome the system instability in a dynamic noise environment. With this methodology, the active VS kernels can be effectively extracted and the corresponding kernel quantity is significantly reduced at least by 65%. Moreover, the system can still work effectively in the case of a lower size of training samples. The simulation results show that the proposed scheme is beneficial to both the nonlinearity compensation and multipath interference mitigation, and exhibits better overall performance than some existing methods, which demonstrates the potential and validity of kernel extraction in VS-based NPE.

Frequency domain non-linear adaptive filter

Abstract: A new non-linear adaptive filter is presented. The algorithm is based on the Volterra series implemented in the frequency domain. For a finite memory of length N, the algorithm converges to the equivalent time domain non-linear adaptive filter as proposed by Roy and Sherman [1]. The frequency domain implementation offers a significant reduction in computation. For the second order Volterra series, the proposed algorithm requires O(N2) multiply-adds for N output points as opposed to an O(N3) for the time domain algorithm. For a large number of taps (≥ 32), the linear version of the proposed algorithm also offers a significant reduction in computation. Another advantage is its fast convergence to the Wiener solution due to the "pseudo-orthogonality" obtained by adapting in the frequency domain.

Increase in Capacity of an IM/DD OFDM-PON Using Super-Nyquist Image-Induced Aliasing and Simplified Nonlinear Equalization

Abstract: For long reach passive optical networks, double-sideband intensity modulation and direct detection can offer the advantages of low cost and low complexity. In this paper, we investigate a joint chromatic dispersion (CD) and nonlinearity compensation technique using super-Nyquist image-induced aliasing and a Volterra series-based simplified nonlinear equalizer (SNE) in a decision feedback manner. The SNE employed in our experiments offers signal-to-noise ratio (SNR) performance comparable to the conventional nonlinear equalizers (NE), but with much fewer coefficients. The distribution of the nonlinear coefficients and the memory length of the SNE/NE are also investigated. Experimental results show that with the proposed aliasing-based CD compensation technique combined with SNE used in each down-sampled signal before per-subcarrier maximum ratio combining, the SNR can be significantly improved. The data rate of the 10-GHz optical OFDM signals is increased by 45%, 52%, and 51% after 48.8, 79.2, and 99.6 km of standard single mode fiber transmission, respectively, compared with those without CD/nonlinearity compensation.