Critical Sensing Radius to Cover the Surface of a Unit Sphere by N Sensors
Bhupendra Gupta
In this article, we address the issue of maintaining sensing coverage of surface of a unit sphere. Here we assumed ‘N’ sensors, uniformly distributed over the surface of a unit sphere. The sensing radius of these ‘N’ sensors draw spherical caps of area 4πp(N) on the surface of unit sphere. Here ‘p(N)’ be the probability that any point (on the surface of unit sphere) to be covered by a specified spherical cap of angular distance (angular radius) ‘a’. Author has derived the strong threshold function for the size of random caps to cover the surface of a unit sphere. If Np(N)/log N > 1/2 the surface of sphere is completely covered by the N caps almost surely, and if Np(N)/log N ≤ 1/2 a partition of the surface of sphere is remains uncovered by the N caps almost surely.
Keywords: Coverage Problem, Random Caps, Threshold Function, Wireless LAN, Wired LAN.