Spatio-Temporal Interference Correlation and Joint Coverage in Cellular Networks

This paper provides an analytical framework with foundations in stochastic geometry to characterize the spatio-temporal interference correlation as well as the joint coverage probability at two spatial locations in a cellular network. In particular, modeling the locations of cellular base stations (BSs) as a Poisson point process, we study interference correlation at two spatial locations <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math></inline-formula> separated by a distance <inline-formula> <tex-math notation="LaTeX">$v$ </tex-math></inline-formula>, when the user follows the <italic>closest BS association policy</italic> at both spatial locations and moves from <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math></inline-formula>. With this user displacement, two scenarios can occur: i) the user is handed off to a new serving BS at <inline-formula> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math></inline-formula>, or ii) no handoff occurs and the user is served by the same BS at both locations. After providing intermediate results, such as probability of handoff and distance distributions of the serving BS at the two user locations, we use them to derive exact expressions for spatio-temporal interference correlation coefficient and joint coverage probability for any distance separation <inline-formula> <tex-math notation="LaTeX">$v$ </tex-math></inline-formula>. We also study two different handoff strategies: i) <italic>handoff skipping</italic>, and ii) <italic>conventional handoffs</italic>, and derive the expressions of joint coverage probability for both strategies. The exact analysis is not straightforward and involves a careful treatment of the neighborhood of the two spatial locations and the resulting handoff scenarios. To provide analytical insights, we also provide easy-to-use expressions for two special cases: i) static user (<inline-formula> <tex-math notation="LaTeX">$v =0$ </tex-math></inline-formula>) and ii) highly mobile user (<inline-formula> <tex-math notation="LaTeX">$v \rightarrow \infty )$ </tex-math></inline-formula>. As expected, our analysis shows that the interference correlation and joint coverage probability decrease with increasing <inline-formula> <tex-math notation="LaTeX">$v$ </tex-math></inline-formula>, with <inline-formula> <tex-math notation="LaTeX">$v \rightarrow \infty $ </tex-math></inline-formula> corresponding to a completely uncorrelated scenario. Further design insights are also provided by studying the effect of few network/channel parameters, such as BS density and path loss on the interference correlation.