PLS_CooperativeJamming

Python scripts to run PLS (Physical Layer Security) simulations using Cooperative Jamming techniques in V2X networks.

Script descriptions

Bertrand_Model2.py

Produces a graphical representation of the Bertrand Paradox Model 2 to generate uniformly distributed straight lines in a circular area. In V2X networks, this is one of the techniques to produce streets in a given randomly generated region.

A realization of the script

In it, a midpoint (red dot) is generated with angle θ and a radius P obtained from independent uniform distributions. The line is then generated by tracing a segment perpendicular to P that crosses the midpoint, terminating when it reaches the extremities of the circular area. The final points (X1,Y1) and (X2,Y2) are calculated through simple trigonometry given that the distance between each of them and the midpoint is denoted by Q. It can be pointed out that these points are uniformly alongside the perimeter of the circunference of radius r. The printing of the trigonometric measurements (r and Q) on the figure can be toggled through the variable plot_markers.

When plot_markers = True, the result is:

Same realization of the script, but with the aforementioned trigonometric measurements

Spatial_Sim.py

Produce vehicular and planar nodes inspired in a C-V2X network presented in:

"Physical Layer Security Enhancement Using Artificial Noise in Cellular Vehicle-to-Everything (C-V2X) Networks" by Wang et. al, available in: https://doi.org/10.48550/arXiv.2009.14500.

The amount of each element is obtained from a Poisson distribution, in which the parameter is given by the Lebesgue Measurement (that in euclidian spaces of n=[1,2,3] corresponds to the length, area and voume, respectively) times the process intensity.

• The streets are generated by a Poisson Linear Process (PLP) based on the Model 2 of the Bertrand Paradox. The Lebesgue Measurement is the perimeter of the circular area.

• The planar nodes (pedestrians and infrastructure) are generated by Poisson Point Processes (PPPs) and the Lebesgue Measurement in this case is the area of the circle. The positions of each node is determined randomly by an uniform distribution of its polar coordinates.

• The vehicular nodes are obtained through Poisson Linear Cox Processes (PLCPs) in which each street obtained by the PLP is then populated with a 1-D PPP alongside its length (Lebesgue Measurement). The position of each node is given by a uniform distribution U(-1,1) that sweeps the whole segment between (X1,Y1) and (X2,Y2).