An analysis of the temporal correlation of interference in extended wireless networks

We consider an extended wireless network, in which nodes arrive in the network according to a joint spatio-temporal (possibly non-homogenous) Poisson process. We assume that each node remains active for a random duration of time with a certain distribution, independent of the arrival process. During the activity period, each node transmits a signal from a Gaussian alphabet at a fixed power (variance) level. We derive the autocovariance function of the interference experienced by a node located at any given point in the network. We show that, the spatial and the temporal components of the autocovariance function are separable and they take effect in the form of a product. Also, somewhat surprisingly, the “shape” of the autocovariance function is dictated by the service distribution of a single node. Hence, the bandwidth of the cumulative interference is identical to that, caused by a single node. Finally, if duration of the activity period is heavy tailed, then the interference process becomes long range dependent.