72 research outputs found
Grant-free Radio Access IoT Networks: Scalability Analysis in Coexistence Scenarios
IoT networks with grant-free radio access, like SigFox and LoRa, offer
low-cost durable communications over unlicensed band. These networks are
becoming more and more popular due to the ever-increasing need for ultra
durable, in terms of battery lifetime, IoT networks. Most studies evaluate the
system performance assuming single radio access technology deployment. In this
paper, we study the impact of coexisting competing radio access technologies on
the system performance. Considering \mathpzc K technologies, defined by time
and frequency activity factors, bandwidth, and power, which share a set of
radio resources, we derive closed-form expressions for the successful
transmission probability, expected battery lifetime, and experienced delay as a
function of distance to the serving access point. Our analytical model, which
is validated by simulation results, provides a tool to evaluate the coexistence
scenarios and analyze how introduction of a new coexisting technology may
degrade the system performance in terms of success probability and battery
lifetime. We further investigate solutions in which this destructive effect
could be compensated, e.g., by densifying the network to a certain extent and
utilizing joint reception
Hyperanalytic denoising
A new threshold rule for the estimation of a deterministic image immersed in noise is proposed. The full estimation procedure is based on a separable wavelet decomposition of the observed image, and the estimation is improved by introducing the new threshold to estimate the decomposition coefficients. The observed wavelet coefficients are thresholded, using the magnitudes of wavelet transforms of a small number of "replicates" of the image. The "replicates" are calculated by extending the image into a vector-valued hyperanalytic signal. More than one hyperanalytic signal may be chosen, and either the hypercomplex or Riesz transforms are used, to calculate this object. The deterministic and stochastic properties of the observed wavelet coefficients of the hyperanalytic signal, at a fixed scale and position index, are determined. A "universal" threshold is calculated for the proposed procedure. An expression for the risk of an individual coefficient is derived. The risk is calculated explicitly when the "universal" threshold is used and is shown to be less than the risk of "universal" hard thresholding, under certain conditions. The proposed method is implemented and the derived theoretical risk reductions substantiated
Time-frequency transforms of white noises and Gaussian analytic functions
A family of Gaussian analytic functions (GAFs) has recently been linked to
the Gabor transform of white Gaussian noise [Bardenet et al., 2017]. This
answered pioneering work by Flandrin [2015], who observed that the zeros of the
Gabor transform of white noise had a very regular distribution and proposed
filtering algorithms based on the zeros of a spectrogram. The mathematical link
with GAFs provides a wealth of probabilistic results to inform the design of
such signal processing procedures. In this paper, we study in a systematic way
the link between GAFs and a class of time-frequency transforms of Gaussian
white noises on Hilbert spaces of signals. Our main observation is a conceptual
correspondence between pairs (transform, GAF) and generating functions for
classical orthogonal polynomials. This correspondence covers some classical
time-frequency transforms, such as the Gabor transform and the Daubechies-Paul
analytic wavelet transform. It also unveils new windowed discrete Fourier
transforms, which map white noises to fundamental GAFs. All these transforms
may thus be of interest to the research program `filtering with zeros'. We also
identify the GAF whose zeros are the extrema of the Gabor transform of the
white noise and derive their first intensity. Moreover, we discuss important
subtleties in defining a white noise and its transform on infinite dimensional
Hilbert spaces. Finally, we provide quantitative estimates concerning the
finite-dimensional approximations of these white noises, which is of practical
interest when it comes to implementing signal processing algorithms based on
GAFs.Comment: to appear in Applied and Computational Harmonic Analysi
Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms
We propose a novel method for constructing Hilbert transform (HT) pairs of
wavelet bases based on a fundamental approximation-theoretic characterization
of scaling functions--the B-spline factorization theorem. In particular,
starting from well-localized scaling functions, we construct HT pairs of
biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet
filters via a discrete form of the continuous HT filter. As a concrete
application of this methodology, we identify HT pairs of spline wavelets of a
specific flavor, which are then combined to realize a family of complex
wavelets that resemble the optimally-localized Gabor function for sufficiently
large orders.
Analytic wavelets, derived from the complexification of HT wavelet pairs,
exhibit a one-sided spectrum. Based on the tensor-product of such analytic
wavelets, and, in effect, by appropriately combining four separable
biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for
constructing 2D directional-selective complex wavelets. In particular,
analogous to the HT correspondence between the components of the 1D
counterpart, we relate the real and imaginary components of these complex
wavelets using a multi-dimensional extension of the HT--the directional HT.
Next, we construct a family of complex spline wavelets that resemble the
directional Gabor functions proposed by Daugman. Finally, we present an
efficient FFT-based filterbank algorithm for implementing the associated
complex wavelet transform.Comment: 36 pages, 8 figure
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