  This paper studies the carrier-to-interference ratio (CIR) and
carrier-to-interference-plus-noise ratio (CINR) performance at the mobile
station (MS) within a multi-tier network composed of M tiers of wireless
networks, with each tier modeled as the homogeneous n-dimensional (n-D, n=1,2,
and 3) shotgun cellular system, where the base station (BS) distribution is
given by the homogeneous Poisson point process in n-D. The CIR and CINR at the
MS in a single tier network are thoroughly analyzed to simplify the analysis of
the multi-tier network. For the multi-tier network with given system
parameters, the following are the main results of this paper: (1)
semi-analytical expressions for the tail probabilities of CIR and CINR; (2) a
closed form expression for the tail probability of CIR in the range
[1,Infinity); (3) a closed form expression for the tail probability of an
approximation to CIR in the entire range [0,Infinity); (4) a lookup table based
approach for obtaining the tail probability of CINR, and (5) the study of the
effect of shadow fading and BSs with ideal sectorized antennas on the CIR and
CINR. Based on these results, it is shown that, in a practical cellular system,
the installation of additional wireless networks (microcells, picocells and
femtocells) with low power BSs over the already existing macrocell network will
always improve the CINR performance at the MS.
