Alpha-stable models of multiuser interference

We present a model for the interference generated by a collection of geographically-distributed, bursty transmitters. Transmitters begin transmission at random times and locations, determined by a Poisson process in space and time. As each transmitted signal propagates to the receiver, it is attenuated by a power-law path loss and shifted in phase by a random angle. We show that the combined interference of all transmitters can be represented as a moving average of Levy motions-impulsive, α-stable random processes which are analogous to filtered white noise. Further, these results can be adapted to include the effects of fading, delay spread, Doppler, and different modulation schemes. The tools developed here may be useful for modeling other impulsive phenomena, such as automobile ignition noise, atmospheric noise, and radar clutter