This collection of MATLAB scripts were used to study the large deviations of the signal-to-inference ratio (SIR) of stationary users (in the uplink) in a single-cell phone network, where the results were published in the SpaSWiN 2018 conference paper[1]. All files were run on a standard desktop machine. 

This work is purely simulation based, but it is motivated by the theoretical results in the probability paper[2]. This paper examines the large deviations of the proportion of disconnected users (based on their SIR values) in wireless networks. This setting is much more genera, with multiple base stations, user mobility and (single-hop) relays, but that not is simulated or examined in any of these files or in [1].

For an introduction, run the files PlatzPoisson.m or PlatzStatisticsSIR.m.

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**MATLAB script files**

(See invidual files for more details.)

PlatzPoisson.m -- This MATLAB script file produces Figures 1 and 2 in the paper[1]. Takes a several seconds to run on a standard computer.

PlatzStatisticsSIR.m -- This MATLAB script file produces configurations (statistically) equivalent to those illustrated in Figures 1 and 2 in the paper[1]. Takes less than minute to run on a standard computer. The bulk of this script became the MATLAB function file funPlatzLDPSim.m.

VaryLambdaLDPStatistics.m -- This MATLAB script file varies lambda (ie the user density, which increases *exponentially*), and for each lambda value, runs stochastic simulations in oder to estimate the probability of a proportion of disconnected users being above some threshold b. It then plots the log of this probability rescaled by lambda (giving an estimate of equation (11) in paper [1]). This estimates the rate function of the large deviations principle for the random proportion (or fraction) of disconnected users in a single-cell phone network; see Figures 3 to 6 in [1]. 

If there is a single lambda value, then this MATLAB file also estimates a heatmap of the density of user configurations that give a unlikely (high) number of disconencted users; Figure 7 in [1]. 

HeatmapUnlikelyConfigurations.m -- This MATLAB script file create a heat map of unlikely configurations, similarly to that in Figure 7 in thepaper[1], but it takes a couple hours on a standard machine. simConstant=10^5 to create results (statistically) equivalent to those in Figure 7 in [1]. WARNING: To create the heatmap, a low user density BUT a LARGE number of simulations is required (for example, it took a couple of hours to produce Figure 7 in [1]). 

funPlatzLDPSim.m -- This MATLAB script file can produce results (statistically) equivalent to those illustrated in Figures 3 to 6 in the paper[1]. With current parameters, it takes a few seconds to run, but can take minutes or hours, if, for example, the number of simulations (ie simNumb) is increased. 

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**Data files**

hvp0_area_1M_edited.txt -- An ASCII text file with a matrix of path loss values. Every row/colum corresponds to y/x value in a rectangular region (surrounding Hausvogteiplatz in Berlin) with dimensions 311 metres by 274 metres. The path loss values were estimated from ray-launching simulations carried out in RaLaNS; see [1] for details

hvp_outdoor_1m.cfg -- An ASCII text file that has three columns of numbers. The first two columns are x/y values of points where buildings exist. The third column is not relevant (it's connected to antenna heights in the ray-launching simulation work).


WIAS_klein_2D.pbm -- a PBM file showing the buildings in a rectangular region surrounding  Hausvogteiplatz in Berlin. This file is NOT used for any simulations or results. 

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If you use this code in your research, please cite the published work [1]. If you cite the results on large deviations, please cite both [1] and [2].

Author: H. Paul Keeler, 2018. keeler@wias-berlin.de or 

References:
[1] H.P. Keeler, B. Jahnel, O. Maye, D. Aschenbach, M. Brzozowski, "Disruptive events in high-density cellular networks", 2018, SpaSWiN 2018
[2] C. Hirsch, B. Jahnel, P. Keeler, and R.I.A. Patterrson, "Large deviations in relay-augmented wireless networks", 2018, Queueing Systms