Joint statistics of interference in a wireless communications link resulted from a poisson field of interferers

We consider a multi-user wireless communication scenario, where signal reception is often corrupted by interference from co-channel users. Under the assumptions that the path loss between the source and destination increases with distance in a power-law fashion, and that during each symbol interval the interferers form a Poisson point processes in space, which are independent between different symbols, it has been shown in the past that interference samples, obtained at symbol rate, constitute an i.i.d, α-stable process. The latter independence assumption, however, is unrealistic as it implies that the session life of each interferer is one symbol interval long only. In this paper we let the session life of each interferer be a random variable. We show that the resulting interference is non i.i.d. and derive its joint statistics. As a special case, a heavy-tail distributed session life results in long-range dependent interference. We validate our claims via simulations, and demonstrate the importance of taking into account the dependence of the interference when performing signal detection.