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In heterogeneous cellular networks (HCNs), the interference received at a user is correlated over time slots since it comes from the same set of randomly located base stations (BSs). This results in the correlations of link successes, thus affecting network performance. Under the assumptions of a K-tier Poisson network, strongest long-term averaged biased-received- power based BS association, and independent Rayleigh fading, we first quantify the correlation coefficients of interference. We observe that the interference correlation is independent of the number of tiers, BS density, signal-to-interference-ratio (SIR) threshold, and transmit power. Then, we study the correlations of link successes in terms of the joint success probability over multiple time slots.We show that analysis without considering the temporal interference correlation underestimates the joint success probability. Moreover, we explore the effects of BS density, transmit power and user association bias on the joint success probability. In particular, BS density and transmit power affect the joint success probability of the overall network by influencing the association probability of each tier. We also reveal that the unbiased cell association outperforms the biased cell association in terms of the joint success probability. Finally, we conduct simulations to validate our analysis.

Correlations of Interference and Link Successes in Heterogeneous Cellular Networks