Approximations for distributions of aggregate interference in spectrum sharing systems

In spectrum sharing systems interference to the primary system from unlicensed devices (UDs) can be controlled by defining UD exclusive regions (protection regions) around the primary system. Most previous studies model UDs to be distributed in a Poisson point process outside the protection regions. However, for such systems the distribution of aggregate interference at the primary system cannot be determined and therefore, approximate distributions have been used. Previous studies however, do not analyse whether these approximations lead to underestimation or overestimation of the required size of the protection regions, which in turn causes uncertainty in the safety of the primary system. In this paper, we use lognormal and shifted-lognormal approximations for the distribution of interference, and obtain approximate sizes of the protection regions required to limit the probability of outage of the primary system to specified values. We obtain the exact protection region sizes from Monte Carlo simulations, and compare them with the approximated values, analysing their accuracy and their ability to overestimate protection regions, rather than underestimating. A single one of the two approximations is not suitable to use over the entire range of system parameters considered in this paper. We develop a novel practical approach that uses both the approximations to always generate overestimated protection regions and therefore always keeps the primary system safe.