Probability Density of the Received Power in Mobile Networks

Probability density of the received power is well analyzed for wireless networks with static nodes. However, most of the present days networks are mobile and not much exploration has been done on statistical analysis of the received power for mobile networks in particular, for the network with random moving patterns. In this paper, we derive probability density of the received power for mobile networks with random mobility models. We consider the power received at an access point from a particular mobile node. Two mobility models are considered: Random Direction (RD) model and Random way-point (RWP) model. Wireless channel is assumed to have a small scale fading of Rayleigh distribution and path loss exponent of 4. 3D, 2D and 1D deployment of nodes are considered. Our findings show that the probability density of the received power for RD mobility models for all the three deployment topologies are weighted confluent hypergeometric functions. In case of RWP mobility models, the received power probability density for all the three deployment topologies are linear combinations of confluent hypergeometric functions. The analytical results are validated through NS2 simulations and a reasonably good match is found between analytical and simulation results.