—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 pertier 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 Geff of general HCNs such that the SIR distribution is obtained by scal...