  We give numerically tractable, explicit integral expressions for the
distribution of the signal-to-interference-and-noise-ratio (SINR) experienced
by a typical user in the down-link channel from the k-th strongest base
stations of a cellular network modelled by Poisson point process on the plane.
Our signal propagation-loss model comprises of a power-law path-loss function
with arbitrarily distributed shadowing, independent across all base stations,
with and without Rayleigh fading. Our results are valid in the whole domain of
SINR, in particular for SINR<1, where one observes multiple coverage. In this
latter aspect our paper complements previous studies reported in [Dhillon et
al. JSAC 2012].
