Volterra Series Truncation and Kernel Estimation of Nonlinear Systems in the Frequency Domain

The Volterra series model is a direct generalisation of the linear convolution integral and is capable of displaying the intrinsic features of a nonlinear system in a simple and easy to apply way. Nonlinear system analysis using Volterra series is normally based on the analysis of its frequency-domain kernels and a truncated description. But the estimation of Volterra kernels and the truncation of Volterra series are coupled with each other. In this paper, a novel complex-valued orthogonal least squares algorithm is developed. The new algorithm provides a powerful tool to determine which terms should be included in the Volterra series expansion and to estimate the kernels and thus solves the two problems all together. The estimated results are compared with those determined using the analytical expressions of the kernels to validate the method. To further evaluate the effectiveness of the method, the physical parameters of the system are also extracted from the measured kernels. Simulation studies demonstrates that the new approach not only can truncate the Volterra series expansion and estimate the kernels of a weakly nonlinear system, but also can indicate the applicability of the Volterra series analysis in a severely nonlinear system case

EVM and Achievable Data Rate Analysis of Clipped OFDM Signals in Visible Light Communication

Orthogonal frequency division multiplexing (OFDM) has been considered for visible light communication (VLC) thanks to its ability to boost data rates as well as its robustness against frequency-selective fading channels. A major disadvantage of OFDM is the large dynamic range of its time-domain waveforms, making OFDM vulnerable to nonlinearity of light emitting diodes (LEDs). DC biased optical OFDM (DCO-OFDM) and asymmetrically clipped optical OFDM (ACO-OFDM) are two popular OFDM techniques developed for the VLC. In this paper, we will analyze the performance of the DCO-OFDM and ACO-OFDM signals in terms of error vector magnitude (EVM), signal-to-distortion ratio (SDR), and achievable data rates under both average optical power and dynamic optical power constraints. EVM is a commonly used metric to characterize distortions. We will describe an approach to numerically calculate the EVM for DCO-OFDM and ACO-OFDM. We will derive the optimum biasing ratio in the sense of minimizing EVM for DCO-OFDM. Additionally, we will formulate the EVM minimization problem as a convex linear optimization problem and obtain an EVM lower bound against which to compare the DCO-OFDM and ACO-OFDM techniques. We will prove that the ACO-OFDM can achieve the lower bound. Average optical power and dynamic optical power are two main constraints in VLC. We will derive the achievable data rates under these two constraints for both additive white Gaussian noise (AWGN) channel and frequency-selective channel. We will compare the performance of DCO-OFDM and ACO-OFDM under different power constraint scenarios

Communication Research

Contains reports on five research projects.Rand Corporatio

Estimating Receptive Fields from Responses to Natural Stimuli with Asymmetric Intensity Distributions

The reasons for using natural stimuli to study sensory function are quickly mounting, as recent studies have revealed important differences in neural responses to natural and artificial stimuli. However, natural stimuli typically contain strong correlations and are spherically asymmetric (i.e. stimulus intensities are not symmetrically distributed around the mean), and these statistical complexities can bias receptive field (RF) estimates when standard techniques such as spike-triggered averaging or reverse correlation are used. While a number of approaches have been developed to explicitly correct the bias due to stimulus correlations, there is no complementary technique to correct the bias due to stimulus asymmetries. Here, we develop a method for RF estimation that corrects reverse correlation RF estimates for the spherical asymmetries present in natural stimuli. Using simulated neural responses, we demonstrate how stimulus asymmetries can bias reverse-correlation RF estimates (even for uncorrelated stimuli) and illustrate how this bias can be removed by explicit correction. We demonstrate the utility of the asymmetry correction method under experimental conditions by estimating RFs from the responses of retinal ganglion cells to natural stimuli and using these RFs to predict responses to novel stimuli

Receptive Field Inference with Localized Priors

The linear receptive field describes a mapping from sensory stimuli to a one-dimensional variable governing a neuron's spike response. However, traditional receptive field estimators such as the spike-triggered average converge slowly and often require large amounts of data. Bayesian methods seek to overcome this problem by biasing estimates towards solutions that are more likely a priori, typically those with small, smooth, or sparse coefficients. Here we introduce a novel Bayesian receptive field estimator designed to incorporate locality, a powerful form of prior information about receptive field structure. The key to our approach is a hierarchical receptive field model that flexibly adapts to localized structure in both spacetime and spatiotemporal frequency, using an inference method known as empirical Bayes. We refer to our method as automatic locality determination (ALD), and show that it can accurately recover various types of smooth, sparse, and localized receptive fields. We apply ALD to neural data from retinal ganglion cells and V1 simple cells, and find it achieves error rates several times lower than standard estimators. Thus, estimates of comparable accuracy can be achieved with substantially less data. Finally, we introduce a computationally efficient Markov Chain Monte Carlo (MCMC) algorithm for fully Bayesian inference under the ALD prior, yielding accurate Bayesian confidence intervals for small or noisy datasets

Models of Neuronal Stimulus-Response Functions: Elaboration, Estimation, and Evaluation

Rich, dynamic, and dense sensory stimuli are encoded within the nervous system by the time-varying activity of many individual neurons. A fundamental approach to understanding the nature of the encoded representation is to characterize the function that relates the moment-by-moment firing of a neuron to the recent history of a complex sensory input. This review provides a unifying and critical survey of the techniques that have been brought to bear on this effort thus far—ranging from the classical linear receptive field model to modern approaches incorporating normalization and other nonlinearities. We address separately the structure of the models; the criteria and algorithms used to identify the model parameters; and the role of regularizing terms or “priors.” In each case we consider benefits or drawbacks of various proposals, providing examples for when these methods work and when they may fail. Emphasis is placed on key concepts rather than mathematical details, so as to make the discussion accessible to readers from outside the field. Finally, we review ways in which the agreement between an assumed model and the neuron's response may be quantified. Re-implemented and unified code for many of the methods are made freely available

Identification of Nonlinear Systems- A Survey

A survey of nonlinear system identification algorithms and related topics is presented by extracting significant results from the literature and presenting these in an organised and systematic way. Algorithms based on the functional expansions of Weiner and Volterra, the identification of block oriented and bilinear systems, the selection of input signals, structure detection, parameter estimation and recent results from catastrophe theory are included. The limitations, relationships and applicability of the methods are discussed throughout