Abstract-There is emerging interest in more detailed models for wireless shadowing, which may include nonconstant shadowing variance, non-lognormal shadowing, and, most importantly, correlation between paths; we focus on this last aspect. This paper offers a structured synthesis of the existing literature on autocorrelation and cross-correlation in wireless shadowing and attempts to fill existing gaps in the analysis of correlation models. We make a survey of these models and argue, as has previously been observed, that certain models are not mathematically feasible, which may lead to problems in simulations or analysis. We then state some theorems that test whether the models are positive semidefinite, which is the central necessary condition for feasibility, and evaluate the existing models accordingly. Additionally, we evaluate the models according to their physical plausibility, which leads us to choose one model among many as arguably the best one in existence so far. This paper should be useful as a guide on how to implement shadowing correlation in one's work, how to choose an appropriate correlation model, and how to modify existing models or create new models so that they fulfill mathematical feasibility.

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Abstract-Finding the distribution of the sum of lognormal random variables is an important mathematical problem in wireless communications, as well as in many other fields. While several methods exist to approximate this distribution, their performance tends to deteriorate in both tail areas. Finding a good overall fit remains an open problem. Other disadvantages of these methods are their complexity and, in some cases, their limitation to particular scenarios.In this paper we examine the sum of independent lognormal random variables with arbitrary parameters. We define the concept of best lognormal fit to a tail and show what it means in terms of convergence. We restate a known result about asymptotes to the higher tail of the distribution. To our knowledge, the lower tail has not yet been studied. We give a simple closed-form expression for an asymptote to the lower tail.We also show that known methods for finding the sum of lognormals use distribution functions that do not have this asymptotic behaviour in the tails. Our results are complementary to the existing knowledge, which together can combine to solve the problem of the sum of lognormals simply and exactly. We support our results by simulations.Index Terms-interference statistics, sum of lognormals, tail distribution.

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Abstract-We prove that the distribution of the sum of identically distributed jointly lognormal random variables, where all pairs have the same strictly positive correlation coefficient, converges to a lognormal with known parameters as becomes large. We confirm our theorem by simulations and give an application of the theorem.Index Terms-Sum of lognormals, interference analysis.

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