Approximate SIR Analysis in General Heterogeneous Cellular Networks

Abstract

The current cellular networks have evolved to be more randomly, irregularly, and heterogeneously deployed to meet the exponential growth of mobile data traffic and the demand for seamless coverage, making the signal-to-interference ratio (SIR) distribution more challenging to analyze. Therefore, in this paper, we propose two simple approximative approaches to the SIR distribution of general heterogeneous cellular networks (HCNs) based on the ASAPPP method, which stands for “approximate SIR analysis based on the Poisson point process” and the MISR (mean interference-to-signal ratio)-based gain for each individual tier of the HCNs. Specifically, we first establish a per-tier ASAPPP approximation to general HCNs and then present an effective gain ASAPPP method as a further simplification when the path loss exponents are the same for all the tiers, that is, we give an explicit expression for the effective gain $G_{\rm{ eff}}$ of general HCNs such that the SIR distribution is obtained by scaling the SIR threshold $\theta$ to $\theta/G_{\rm{ eff}} $ . The asymptotic behavior for the tail of the SIR distribution is also given. Furthermore, to highlight the simplicity and effectiveness of the approximative approaches, we derive the exact distribution of the SIR in the two-tier HCNs modeled by $\beta$ -Ginibre and Poisson point processes and compare it with the approximate results. The results demonstrate that the proposed approaches give a simple yet excellent approximation for the SIR distribution.