Grid-Based Exclusive Region Design for 3D UAV Networks: A Stochastic Geometry Approach

This paper presents a stochastic geometry analysis of radio interference and a grid-based design of a primary exclusive region (PER) for spectrum sharing in the 3D unmanned aerial vehicle (UAV) networks. When a UAV network shares frequency bands with a primary system (e.g., a weather radar system), the UAVs must avoid harmful interference with the primary system. To facilitate the design of a complex-shaped PER according to a primary user's antenna pattern, spatial grid models, namely cylindrical and cubic grid models, are introduced. In the cylindrical grid model, to approximate the distribution of the interference at the radar, the cumulants of the interference are expressed by expressions with simple integrals or even closed-form expressions based on the assumption that the distributions of the UAVs in each grid cell follow an inhomogeneous 3D Poisson point process (PPP). In the cubic grid model, the shape of the grid cell is approximated by the cylindrical grid cell to derive the cumulants of the interference because they cannot be calculated in the same manner as in the cylindrical grid model. Using the derived interference cumulants to determine a PER to satisfy the radar's outage probability target, an optimization problem that minimizes the number of the UAVs forbidden from transmitting signals is formulated. The numerical results confirm that the approximated interference distribution using cumulants is in acceptable agreement with the simulation results and the PER obtained from the proposed optimization problem improves the number of the transmitting UAVs by reducing the volume of grid cells

A Comparison between Orthogonal and Non-Orthogonal Multiple Access in Cooperative Relaying Power Line Communication Systems

Most, if not all, existing studies on power line communication (PLC) systems as well as industrial PLC standards are based on orthogonal multiple access schemes such as orthogonal frequency-division multiplexing and code-division multiple access. In this paper, we propose non-orthogonal multiple access (NOMA) for decode-and-forward cooperative relaying PLC systems to achieve higher throughput and improve user fairness. To quantitatively characterize the proposed system performance, we also study conventional cooperative relaying (CCR) PLC systems. We evaluate the performance of the two systems in terms of the average capacity. In this respect, accurate analytical expressions for the average capacity are derived and validated with Monte Carlo simulations. The impact of several system parameters such as the branching, impulsive noise probability, cable lengths, the power allocation coefficients and input signal-to-noise ratio are investigated. The results reveal that the performance of the proposed NOMA-PLC scheme is superior compared to that of the CCR-PLC system. It is also shown that NOMA-PLC can be more effective in reducing electromagnetic compatibility associated with PLC and that increasing the network branches can considerably degrade performance. Moreover, optimizing the power allocation coefficients is found to be of utmost importance to maximize the performance of the proposed system

Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications

The monograph investigates the misapplication of conventional statistical techniques to fat tailed distributions and looks for remedies, when possible. Switching from thin tailed to fat tailed distributions requires more than "changing the color of the dress". Traditional asymptotics deal mainly with either n=1 or $n=\infty$, and the real world is in between, under of the "laws of the medium numbers" --which vary widely across specific distributions. Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence. A few examples: + The sample mean is rarely in line with the population mean, with effect on "naive empiricism", but can be sometimes be estimated via parametric methods. + The "empirical distribution" is rarely empirical. + Parameter uncertainty has compounding effects on statistical metrics. + Dimension reduction (principal components) fails. + Inequality estimators (GINI or quantile contributions) are not additive and produce wrong results. + Many "biases" found in psychology become entirely rational under more sophisticated probability distributions + Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions. This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles