Assignment:
In GSM cellular phone newtworks, the cells covering wide open environments are approximately circular with a maximum radius of 35 km. Assume the propagation speed of the waves in air to be c = 3 · 108 m/s. Consider a terminal randomly placed within such a cell, so that with x and y the spatial coordinates of the terminal with respect to the base station, the PDF of the rve x = [x, y] is constant within a circle centered at the origin and having a radius of 35 km, and zero outside.
a) Write the expression of px (a1, a2).
b) Find the PDF of the distance r between terminal and base station.
c) With τ the propagation delay over the distance r, find mτ, σ2τ and P[τ > mτ].