Hee-Seok Oh

A Survey of Measurement-Based Spectrum Occupancy Modeling for Cognitive Radios

Spectrum occupancy models are very useful in cognitive radio designs. They can be used to increase spectrum sensing accuracy for more reliable operation, to remove spectrum sensing for higher resource usage efficiency, or to select channels for better opportunistic access, among other applications. In this survey, various spectrum occupancy models from measurement campaigns taken around the world are investigated. These models extract different statistical properties of the spectrum occupancy from the measured data. In addition to these models, spectrum occupancy prediction is also discussed, where autoregressive and/or moving-average models are used to predict the channel status at future time instants. After comparing these different methods and models, several challenges are also summarized based on this survey.

Multi-resolution time series analysis applied to solar irradiance and climate reconstructions

A better understanding of natural climate variability is crucial for global climate change studies and the evaluation of the sensitivity of the climate system to imposed perturbations. External forcing factors might contribute substantially to both high and low frequency variations in climate but a clear separation of their impact from internally generated fluctuations is difficult. We employ wavelet decomposition to identify common characteristics in forcing and climatic time series of the last four centuries. Here, we focus on solar irradiance variations by applying this statistical method to a selection of widely used proxy-based reconstructions. Major variability components are isolated through time-scale decomposition. Two classical solar modes (85 and 11 years) are not only identified within the limited time period covered by the solar datasets, but their relative influences on climate as represented by hemispheric surface temperature reconstructions are also estimated. While the low-frequency component shows close ties between solar variations and surface climate, a relationship between the 11-year sunspot cycle and temperature reconstructions is more difficult to attribute. However, the statistical multi-resolution analysis appears to be an ideal tool to uncover relationships and their changes at different temporal scales normally hidden by the strong background noise in the climate system.

Fast Nonparametric Quantile Regression With Arbitrary Smoothing Methods

The calculation of nonparametric quantile regression curve estimates is often computationally intensive, as typically an expensive nonlinear optimization problem is involved. This article proposes a fast and easy-to-implement method for computing such estimates. The main idea is to approximate the costly nonlinear optimization by a sequence of well-studied penalized least squares-type nonparametric mean regression estimation problems. The new method can be paired with different nonparametric smoothing methods and can also be applied to higher dimensional settings. Therefore, it provides a unified framework for computing different types of nonparametric quantile regression estimates, and it also greatly broadens the scope of the applicability of quantile regression methodology. This wide applicability and the practical performance of the proposed method are illustrated with smoothing spline and wavelet curve estimators, for both uni- and bivariate settings. Results from numerical experiments suggest that estimates obtained from the proposed method are superior to many competitors. This article has supplementary material online.

Extending the scope of empirical mode decomposition by smoothing

This article considers extending the scope of the empirical mode decomposition (EMD) method. The extension is aimed at noisy data and irregularly spaced data, which is necessary for widespread applicability of EMD. The proposed algorithm, called statistical EMD (SEMD), uses a smoothing technique instead of an interpolation when constructing upper and lower envelopes. Using SEMD, we discuss how to identify non-informative fluctuations such as noise, outliers, and ultra-high frequency components from the signal, and to decompose irregularly spaced data into several components without distortions.

A new sparse variable selection via random-effect model

We study a new approach to simultaneous variable selection and estimation via random-effect models. Introducing random effects as the solution of a regularization problem is a flexible paradigm and accommodates likelihood interpretation for variable selection. This approach leads to a new type of penalty, unbounded at the origin and provides an oracle estimator without requiring a stringent condition. The unbounded penalty greatly enhances the performance of variable selections, enabling highly accurate estimations, especially in sparse cases. Maximum likelihood estimation is effective in enabling sparse variable selection. We also study an adaptive penalty selection method to maintain a good prediction performance in cases where the variable selection is ineffective.

Bidimensional Statistical Empirical Mode Decomposition

This letter proposes a new algorithm, termed bidimensional statistical empirical mode decomposition (BSEMD) that adopts a smoothing procedure instead of an interpolation when constructing 2-D upper and lower envelopes. For this purpose, we investigate the sifting process effect of conventional bidimensional empirical mode decomposition (BEMD) on the decomposition results, and propose a modified BEMD via the smoothing sifting process coupling with a new identification method of 2-D local extrema. Furthermore, theoretical rationale for smoothing sifting is investigated.

Wavelet spectrum and its characterization property for random processes

The wavelet spectrum of a random process comprises the variances of the wavelet coefficients of the process computed within each scale. This paper investigates the possibility of using the wavelet spectrum, obtained from a continuous wavelet transform (CWT), to uniquely represent the second-order statistical properties of random processes-particularly, stationary processes and long-memory nonstationary processes. As is well known, the Fourier spectrum of a stationary process is mathematically equivalent to the autocovariance function (ACF) and thus uniquely determines the second-order statistics of the process. This characterization property is shown to be possessed also by the wavelet spectrum under very mild regularity conditions that are easily satisfied by many widely used wavelets. It is also shown that under suitable regularity conditions, the characterization property remains valid for processes with stationary increments including 1/f noise.

An Automatic Statistical Methodology to Extract Pulse-Like Forcing Factors in Climatic Time Series: Application to Volcanic Events

To understand the full range of natural climate variability, it is important to attribute past climate variations to particular forcing factors. In this paper, our main focus is to introduce an automatic procedure to estimate the impact of strong but short-lived perturbations from large explosive volcanic eruptions on climate. An extraction method to simultaneously model the slowly changing background climate component and the superposed volcanic pulse-like events is presented and applied to a variety of data sets (tree-ring data and a multi-proxy temperature reconstruction over the last 4 centuries and output from a coupled ocean-atmosphere general circulation model). This approach based on a statistical multi-state space model provides an accurate estimator of the timing and duration of the climate response to an eruption. It not only allows for a more objective estimation of its associated peak amplitude and the subsequent time evolution of the signal, but at the same time it provides a measure of confidence through the posterior probability for each cooling event. Because the background noise changes in time, this technique uses the local characteristics of the volcanic signal to associate a probability that is not necessarily linked to the absolute intensity of the event. This flexibility is not included in direct thresholding techniques.

Hierarchical-likelihood-based wavelet method for denoising signals with missing data

This letter proposes a wavelet denoising method in the presence of missing data. This approach is based on a coupling of wavelet shrinkage and hierarchical (or h)-likelihood method. The h-likelihood provides an effective imputation methodology of missing data to give wavelet estimators for signals and motivates a fast and simple algorithm. The method can be easily extended to other settings, such as image denoising. Simulation studies demonstrate empirical properties of the proposed method.

Hybrid local polynomial wavelet shrinkage: wavelet regression with automatic boundary adjustment

An usual assumption underlying the use of wavelet shrinkage is that the regression function is assumed to be either periodic or symmetric. However, such an assumption is not always realistic. This paper proposes an effective method for correcting the boundary bias introduced by the inappropriateness of such periodic or symmetric assumption. The idea is to combine wavelet shrinkage with local polynomial regression, where the latter regression technique is known to possess excellent boundary properties. Simulation results from both the univariate and bivariate settings provide strong evidence that the proposed method is extremely effective in terms of correcting boundary bias.