A Tractable Framework for Spectrum Coexistence Between Satellite Receivers and Terrestrial Networks

We study the interference resulting from transmissions from terrestrial cellular networks on passive satellite receivers. This has important implications for the future allocation and terrestrial use of spectrum on a shared basis with satellite systems, in particular above 100 GHz. We develop an extensive, general model for the interference received at a typical passive satellite. Utilizing a stochastic geometry framework, we precisely characterize the outage probability for a set of satellites - which is the distribution of the interference with respect to spatial and temporal randomness inherent in the aforementioned interference model. We obtain upper and lower bounds on the outage probability using a new analytical method based on a matrix function generalization of the Laplace transform of the interference model. This analytical method allows for the distribution of the interference to be tightly bounded while affording a similar level of tractability to that encountered in the more typical coverage probability analysis of wireless networks using stochastic geometry. Using the analytical characterizations for outage probability, we investigate design choices and constraints such as the antenna gain and positioning at the passive satellite receiver and terrestrial nodes, out-of-band rejection, terrestrial network density, and the scan pattern of the passive receiver. Our analysis indicates that spectrum coexistence is feasible with minimal spectral separation, and that in-band coexistence may even be possible with low, but non-negligible, outage probability. A key insight from our analysis is that outage events are largely driven by spatial events corresponding to the presence of large clusters of transmitters as opposed to temporal fluctuations in interference power. The impact of these spatial events on EESS sensors may be mitigated by varying the boresight direction of the receive beam over the measurement duration.