Abstract
This paper presents the stochastic-geometry analysis and designs a primary exclusive region (PER) for a spatial grid-based spectrum database system. The purpose of the spatial grid is to utilize information, such as the primary receiver (PR) antenna pattern, and the secondary transmitter (ST) density and transmission power, in each divided region. This paper introduces polar and square grids. For these spatial grids, the cumulants of the aggregate interference at a PR, from the STs, are derived, where the probability generating functional for the Poisson point process (PPP) is used on the assumption that the distribution of the STs in each divided region follows an inhomogeneous PPP. In addition, by introducing the allowable transmission probability of STs in each divided region, the PER optimization problem can be formulated as a continuous optimization problem. Numerical results demonstrate that a PER, corresponding to the information, is successfully designed and that more detailed information, due to a reduction in the area of each divided region, leads to a smaller and complex-shaped PER.
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