Average connectivity properties of wireless ad hoc networks

We consider the average radio coverage area size of a connected cluster Omega (alpha, r) in a uniformly randomly deployed wireless network over a D-dimensional infinite field (D greater than or equal to 1), where r is the radio distance, and alpha the nodal deployment density. We show Chat Omega(N)(y)(=)(Delta)alphaOmega(alpha,r) isafunction of y(=)(Delta)alphaPhi (r) only, where (l (r) denotes the volume of a sphere with radius r. We provide an explicit form of Omega(N)(y) for arbitrary D as the sum of three terms, dominated by one that exhibits exponential behavior. For D = 1, we show that Omega(N)(y) = exp (y/2) + y/2 -1. Our simulations validate our 1-d solution, and show that e exponent for 2-d deployment is smaller than y.