Coverage analysis for 2D/3D millimeter wave peer-to-peer networks

This paper presents a theoretical analysis for estimating the coverage probability in two-dimensional (2D) and three-dimensional (3D) peer-to-peer (P2P) millimeter-wave (mmWave) wireless networks. The analysis is carried out adopting suitable link state models and realistic propagation conditions, involving path-loss attenuation, angular dispersion, mid- and small-scale fading, which comply with recent channel measurements. The presented framework accounts in detail for the actual shape of the transmitting/receiving antenna patterns and for the spatial statistic that describes the node location, by considering the widely adopted Poisson point process, the uniform distribution, and the random waypoint mobility model. Analytical expressions for the statistic of the received power and simple integral formulas for the coverage probability in the presence of interference and noise are derived. The accuracy of the obtained estimations and of the introduced approximations is checked by independent Monte Carlo validations. As possible applications in the 3D mmWave context, the conceived mathematical theory is used to discuss the impact of the interference model on the reliability of the noise-limited approximation, and to estimate the average link capacity of an interfered P2P communication

The Intensity Matching Approach: A Tractable Stochastic Geometry Approximation to System-Level Analysis of Cellular Networks

The intensity matching approach for tractable performance evaluation and optimization of cellular networks is introduced. It assumes that the base stations are modeled as points of a Poisson point process and leverages stochastic geometry for system-level analysis. Its rationale relies on observing that system-level performance is determined by the intensity measure of transformations of the underlaying spatial Poisson point process. By approximating the original system model with a simplified one, whose performance is determined by a mathematically convenient intensity measure, tractable yet accurate integral expressions for computing area spectral efficiency and potential throughput are provided. The considered system model accounts for many practical aspects that, for tractability, are typically neglected, e.g., line-of-sight and non-line-of-sight propagation, antenna radiation patterns, traffic load, practical cell associations, general fading channels. The proposed approach, more importantly, is conveniently formulated for unveiling the impact of several system parameters, e.g., the density of base stations and blockages. The effectiveness of this novel and general methodology is validated with the aid of empirical data for the locations of base stations and for the footprints of buildings in dense urban environments.Comment: Submitted for Journal Publicatio

On asymptotic validity of naive inference with an approximate likelihood

Many statistical models have likelihoods which are intractable: it is impossible or too expensive to compute the likelihood exactly. In such settings, a common approach is to replace the likelihood with an approximation, and proceed with inference as if the approximate likelihood were the exact likelihood. In this paper, we describe conditions on the approximate likelihood which guarantee that this naive inference with an approximate likelihood has the same first-order asymptotic properties as inference with the exact likelihood. We investigate the implications of these results for inference using a Laplace approximation to the likelihood in a simple two-level latent variable model, and using reduced dependence approximations to the likelihood in an Ising model on a lattice.Comment: Updated to add an additional example (inference for an Ising model on a lattice using reduced dependence approximations to the likelihood

Ab initio statistical mechanics of surface adsorption and desorption: II. Nuclear quantum effects

We show how the path-integral formulation of quantum statistical mechanics can be used to construct practical {\em ab initio} techniques for computing the chemical potential of molecules adsorbed on surfaces, with full inclusion of quantum nuclear effects. The techniques we describe are based on the computation of the potential of mean force on a chosen molecule, and generalise the techniques developed recently for classical nuclei. We present practical calculations based on density functional theory with a generalised-gradient exchange-correlation functional for the case of H$_2$O on the MgO~(001) surface at low coverage. We note that the very high vibrational frequencies of the H$_2$O molecule would normally require very large numbers of time slices (beads) in path-integral calculations, but we show that this requirement can be dramatically reduced by employing the idea of thermodynamic integration with respect to the number of beads. The validity and correctness of our path-integral calculations on the H$_2$O/MgO~(001) system are demonstrated by supporting calculations on a set of simple model systems for which quantum contributions to the free energy are known exactly from analytic arguments.Comment: 11 pages, including 2 figure