White noise

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

Pilot-Aided Carrier Recovery in the Presence of Phase Noise

Abstract: The paper deals with carrier recovery based on pilot symbols in single-carrier systems. The system model considered in the paper includes the channel additive white noise and the phase noise that affects the local oscillators used for up/down-conversion. Wiener's method is used to determine the optimal filter in estimation of phase noise assuming that a sequence of equally spaced pilot symbols is available. Our analysis allows to capture the cyclostationary performance of the estimate, a phenomenon that is not considered in the previous literature. In the paper, closed-form formulas for the transfer function of the optimal filter and for the mean-square phase error are derived for the case where the phase noise is modelled as random phase walk. For this case, a suboptimal filter is proposed. Numerical results are presented to substantiate the analysis.

Batch nonlinear continuous-time trajectory estimation as exactly sparse Gaussian process regression

Abstract: In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent variable. Our continuous-time prior can be defined by any nonlinear, time-varying stochastic differential equation driven by white noise; this allows the possibility of smoothing our trajectory estimates using a variety of vehicle dynamics models (e.g. `constant-velocity'). We show that this class of prior results in an inverse kernel matrix (i.e., covariance matrix between all pairs of measurement times) that is exactly sparse (block-tridiagonal) and that this can be exploited to carry out GP regression (and interpolation) very efficiently. When the prior is based on a linear, time-varying stochastic differential equation and the measurement model is also linear, this GP approach is equivalent to classical, discrete-time smoothing (at the measurement times); when a nonlinearity is present, we iterate over the whole trajectory to maximize accuracy. We test the approach experimentally on a simultaneous trajectory estimation and mapping problem using a mobile robot dataset.

Testing for calibration systematics in the EDGES low-band data using Bayesian model selection

Abstract: Cosmic Dawn, when the first stars and proto-galaxies began to form, is commonly expected to be accompanied by an absorption signature at radio frequencies. This feature arises as Lyman-$\alpha$ photons emitted by these first luminous objects couple the 21 cm excitation temperature of intergalactic hydrogen gas to its kinetic temperature, driving it into absorption relative to the CMB. The detailed properties of this absorption profile encode powerful information about the physics of Cosmic Dawn. Recently, Bowman et al. analysed data from the EDGES low-band radio antenna and found an unexpectedly deep absorption profile centred at 78 MHz, which could be a detection of this signature. Their specific analysis fit their measurements using a polynomial foreground model, a flattened Gaussian absorption profile and a white noise model; we argue that a more accurate model, that includes a detailed noise model and accounting for the effects of plausible calibration errors, is essential for describing the EDGES data set. We perform a Bayesian evidence-based comparison of models of the EDGES low-band data set and find that those incorporating these additional components are decisively preferred. The subset of the best fitting models of the data that include a global signal favour an amplitude consistent with standard cosmological assumptions (A < 209 mK). However, there is not strong evidence to favour models of the data including a global 21 cm signal over those without one. Ultimately, we find that the derivation of robust constraints on astrophysics from the data is limited by the presence of systematics.

Confidence intervals for regression (MEM) spectral estimates

Abstract: The probability density and confidence intervals for the maximum entropy (or regression) method (MEM) of spectral estimation are derived using a Wishart model for the estimated covariance. It is found that the density for the estimated transfer function of the regression filter may be interpreted as a generalization of the student's t distribution. Asymptotic expressions are derived which are the same as those of Akaike. These expressions allow a direct comparison between the performance of the maximum entropy (regression) and maximum likelihood methods under these asymptotic conditions. Confidence intervals are calculated for an example consisting of several closely space tones in a background of white noise. These intervals are compared with those for the maximum likelihood method (MLM). It is demonstrated that, although the MEM has higher peak to background ratios than the MLM, the confidence intervals are correspondingly larger. Generalizations are introduced for frequency wavenumber spectral estimation and for the joint density at different frequencies.