A Traffic Model for Machine-Type Communications Using Spatial Point Processes

A source traffic model for machine-to-machine communications is presented in this paper. We consider a model in which devices operate in a regular mode until they are triggered into an alarm mode by an alarm event. The positions of devices and events are modeled by means of Poisson point processes, where the generated traffic by a given device depends on its position and event positions. We first consider the case where devices and events are static and devices generate traffic according to a Bernoulli process, where we derive the total rate from the devices at the base station. We then extend the model by defining a two-state Markov chain for each device, which allows for devices to stay in alarm mode for a geometrically distributed holding time. The temporal characteristics of this model are analyzed via the autocovariance function, where the effect of event density and mean holding time are shown.Comment: Accepted at the 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC) - Workshop WS-07 on "The Internet of Things (IoT), the Road Ahead: Applications, Challenges, and Solutions

Variational Bayesian Inference of Line Spectra

In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are continuous-valued, i.e., not restricted to a grid; and the coefficients are governed by a Bernoulli-Gaussian prior model turning model order selection into binary sequence detection. Unlike earlier works which retain only point estimates of the frequencies, we undertake a more complete Bayesian treatment by estimating the posterior probability density functions (pdfs) of the frequencies and computing expectations over them. Thus, we additionally capture and operate with the uncertainty of the frequency estimates. Aiming to maximize the model evidence, variational optimization provides analytic approximations of the posterior pdfs and also gives estimates of the additional parameters. We propose an accurate representation of the pdfs of the frequencies by mixtures of von Mises pdfs, which yields closed-form expectations. We define the algorithm VALSE in which the estimates of the pdfs and parameters are iteratively updated. VALSE is a gridless, convergent method, does not require parameter tuning, can easily include prior knowledge about the frequencies and provides approximate posterior pdfs based on which the uncertainty in line spectral estimation can be quantified. Simulation results show that accounting for the uncertainty of frequency estimates, rather than computing just point estimates, significantly improves the performance. The performance of VALSE is superior to that of state-of-the-art methods and closely approaches the Cram\'er-Rao bound computed for the true model order.Comment: 15 pages, 8 figures, accepted for publication in IEEE Transactions on Signal Processin

Superfast Line Spectral Estimation

A number of recent works have proposed to solve the line spectral estimation problem by applying off-the-grid extensions of sparse estimation techniques. These methods are preferable over classical line spectral estimation algorithms because they inherently estimate the model order. However, they all have computation times which grow at least cubically in the problem size, thus limiting their practical applicability in cases with large dimensions. To alleviate this issue, we propose a low-complexity method for line spectral estimation, which also draws on ideas from sparse estimation. Our method is based on a Bayesian view of the problem. The signal covariance matrix is shown to have Toeplitz structure, allowing superfast Toeplitz inversion to be used. We demonstrate that our method achieves estimation accuracy at least as good as current methods and that it does so while being orders of magnitudes faster.Comment: 16 pages, 7 figures, accepted for IEEE Transactions on Signal Processin