White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.

A maximum rate loading algorithm for discrete multitone modulation systems

Abstract: A novel approach to loading for discrete multitone modulation (DMT) systems is proposed. This algorithm assigns energy to different subchannels in order to maximize the data rate for a given margin while previous algorithms proposed are aimed mainly at maximizing the margin at a target data rate. Two implementations are suggested, both with finite granularity: the first one leads to the optimal waterfilling solution, and the second results in a suboptimal but slightly less complex flat-energy distribution. The algorithm is extended to the case of a rate adaptive system with both a target guaranteed fixed data rate service and a variable one. Simulation results are presented for a Rayleigh fading channel with additive white Gaussian noise.

Which data residual norm for robust elastic frequency-domain full waveform inversion?

Abstract: Elastic full-waveform inversion is an ill-posed data-fitting procedure that is sensitive to noise, inaccuracies of the starting model,definitionofmultiparameterclasses,andinaccuratemodeling of wavefield amplitudes. We have investigated the performance of different minimization functionals as the least-squares norm 2, the least-absolute-values norm 1, and combinations of both the Huber and so-called hybrid criteria with reference to twonoisyoffshoreValhallmodelandonshoreoverthrustmodel synthetic data sets. The four minimization functionals were implemented in 2D elastic frequency-domain full-waveform inversion FWI, where efficient multiscale strategies were designed by successive inversions of a few increasing frequencies. For the offshore and onshore case studies, the 1-norm provided the most reliable models for P- and S-wave velocities VP and VS, even when strongly decimated data sets that correspond to fewfrequencieswereusedintheinversionandwhenoutlierspolluted the data. The 2-norm can provide reliable results in the presence of uniform white noise for VP and VS if the data redundancyisincreasedbyrefiningthefrequencysamplingintervalin the inversion at the expense of computational efficiency. The 1-norm and the Huber and hybrid criteria, unlike the 2-norm, allowforsuccessfulimagingoftheVSmodelfromnoisydataina soft-seabed environment, where the P-to-S-waves have a small footprint in the data. However, the Huber and hybrid criteria are sensitive to a threshold criterion that controls the transition between the criteria and that requires tedious trial-and-error investigations for reliable estimation. The 1-norm provides a robust alternativetothe2-normforinvertingdecimateddatasetsinthe frameworkofefficientfrequency-domainFWI.

Linear stochastic systems

Abstract: This Report presents an investigation of the behaviour of randomly excited linear-dynamical systems whose parameters are subject to either incremental Brownian or Gaussian, 'physical white noise' variations. The Fokker-Planck equation governing the first probability density of the response is derived, and from it the equations that determine the response moments are obtained. Expressions are found for the correIation functions and spectral densities of the response. Various examples are given to illustrate the methods used, and results from an analog computer simulation are shown to agree c10sely with theoretical results.

The stochastic Burgers equation

Abstract: We study Burgers Equation perturbed by a white noise in space and time. We prove the existence of solutions by showing that the Cole-Hopf transformation is meaningful also in the stochastic case. The problem is thus reduced to the anaylsis of a linear equation with multiplicative half white noise. An explicit solution of the latter is constructed through a generalized Feynman-Kac formula. Typical properties of the trajectories are then discussed. A technical result, concerning the regularizing effect of the convolution with the heat kernel, is proved for stochastic integrals.

The modified Cramer-Rao bound in vector parameter estimation

Abstract: In this paper we extend the scalar modified Cramer-Rao bound (MCRB) to the estimation of a vector of nonrandom parameters in the presence of nuisance parameters. The resulting bound is denoted with the acronym MCRVB, where "V" stands for "vector". As with the scalar bound, the MCRVB is generally looser than the conventional CRVB, but the two bounds are shown to coincide in some situations of practical interest. The MCRVB is applied to the joint estimation of carrier frequency, phase, and symbol epoch of a linearly modulated waveform corrupted by correlated impulsive noise (encompassing white Gaussian noise as a particular case), wherein data symbols and noise power are regarded as nuisance parameters. In this situation, calculation of the conventional CRVB is infeasible, while application of the MCRVB leads to simple useful expressions with moderate analytical effort. When specialized to the case of white Gaussian noise, the MCRVB yields results already available in the literature in fragmentary form and simplified contexts.