  In this paper, we consider the downlink signal-to-interference-plus-noise
ratio (SINR) analysis in a heterogeneous cellular network with K tiers. Each
tier is characterized by a base-station (BS) arrangement according to a
homogeneous Poisson point process with certain BS density, transmission power,
random shadow fading factors with arbitrary distribution, arbitrary path-loss
exponent and a certain bias towards admitting the mobile-station (MS). The MS
associates with the BS that has the maximum SINR under the open access cell
association scheme. For such a general setting, we provide an analytical
characterization of the coverage probability at the MS.
