In this paper, we consider three ground-aircraft communication issues, namely, ground-centric connectivity, aircraft-centric connectivity, and link capacity analysis. Particularly, we propose the continuous connection probability over at least τ seconds, termed as τ-connectivity, for the ground-centric link and aircraft-centric link respectively, which are derived in the expression of several key parameters such as the aircraft/ground station density, the aircraft velocity, and the connectable elevation angle threshold. Theoretical tradeoff between ergodic outage capacity and the number of connected aircraft is analyzed for low and high transmit power regimes. The hypotheses in the ground-centric τ-connectivity model are tested, and we observe a good match between the theoretic probability and the real world data-based probability although some real world aircraft statistic characters do not match the ideal assumption perfectly. Next, the aircraft-centric τ-connectivity is analyzed theoretically. Approximate yet practically accurate closed form aircraft-centric connection probabilities are derived and verified with Monte Carlo simulations. Furthermore, considering atmospheric gas and cloud attenuation, we compare the link budget and capacity between the ground-centric ground-to-aircraft link and the ground-to-satellite link under the τ-connectivity and demonstrate the advantage of ground-aircraft communication.
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