Characterization of aggregate interference in arbitrarily-shaped underlay cognitive networks

This paper characterizes the aggregate interference at the primary user (PU) due to M secondary users (SUs) in an underlay cognitive network, where appropriate SU activity protocols are employed in order to limit the interference generated by the SUs. Different from prior works, we assume that the PU can be located anywhere inside an arbitrarily-shaped convex network region. Using the moment generating function (MGF) of the interference from a random SU, we derive general expressions for the n-th moment and the n-th cumulant of the aggregate interference for guard zone and multiple-threshold SU activity protocols. Using the cumulants, we study the convergence of the distribution of the aggregate interference to a Gaussian distribution. In addition, we compare the well-known closed-form distributions in the literature to approximate the complementary cumulative distribution function (CCDF) of the aggregate interference. Our results show that care must be undertaken in approximating the aggregate interference as a Gaussian distribution, even for a large number of SUs, since the convergence is not monotonie in general. In addition, the shifted lognormal distribution provides the overall best CCDF approximation, especially in the distribution tail region, for arbitrarily-shaped network regions.