Heterogeneous cellular network performance analysis under open and closed access

We study the downlink signal-to-interference ratio (SIR) in a multi-tier heterogeneous cellular network under the open and closed access schemes. Each tier is characterized by a base-station (BS) arrangement according to a homogeneous Poisson point process with certain density, constant transmission power and random shadow fading factors with arbitrary distribution. The mobile-station (MS) communicates with the BS that has the maximum instantaneous received power among those to which it is allowed access. The chosen BS provides coverage to the MS if the SIR is above a certain threshold determined by the BS´s tier. The coverage probability and average rate expressions are derived for the open access scheme for any arbitrary SIR threshold assigned for each tier, and for the closed access scheme when the SIR thresholds are greater than one.