On the distribution of cumulated interference power in Rayleigh fading channels

This paper deals with the distribution of cumulated instantaneous interference power in a Rayleigh fading channel for an infinite number of interfering stations, where each station transmits with a certain probability, independently of all others. If all distances are known, a necessary and sufficient condition is given for the corresponding distribution to be nondefectire. Explicit formulae of density and distribution functions are obtained in the interesting special case that interfering stations are located on a linear grid. Moreover, the Laplace transform of cumulated power is investigated when the positions of stations follow a oneor two-dimensional Poisson process. It turns out that the corresponding distribution is defective for the two-dimensional models.