Bounds and Exact Mean Node Degree and Node Isolation Probability in Interference-Limited Wireless Ad Hoc Networks With General Fading

We investigate the mean degree and the isolation probability of a network node sustaining intrasystem interference and intersystem interference from multiple coexisting wireless ad hoc networks. Under general fading of the desired signal and interfering signals, a closed-form upper bound on the mean node degree and a lower bound on the node isolation probability are obtained by thoroughly considering dominating interferers and second-order interferers. A closed-form lower bound on the mean node degree is further computed. The ratio between the upper bound and lower bound is bounded, and they are asymptotically tight as the path-loss exponent approaches infinity. Moreover, a nearly closed-form expression for the mean node degree is derived in terms of inverse Laplace transform of the fading distribution of the desired signal. Our derived local network quantities could find application in the approximate study of a number of metrics related to connectivity and delay of information propagation in wireless ad hoc networks.