### Characterizing The SINR in Poisson Network Using Factorial Moment

#### Abstract

Usually, cellular networks are modeled by placing

each tier (e.g macro, pico and relay nodes) deterministically

on a grid. When calculating the metric performances such

as coverage probability, these networks are idealized for not

considering the interference. Overcoming such limitation by

realistic models is much appreciated. This paper considered two-

tier two-hop cellular network, each tier is consisting of two-hop

relay transmission, relay nodes are relaying the message to the

users that are in the cell edge. In addition, the locations of the

relays, base stations (BSs), and users nodes are modeled as a point

process on the plane to study the two hop downlink performance.

Then, we obtain a tractable model for the k-coverage probability

for the heterogeneous network consisting of the two-tier network.

Stochastic geometry and point process theory have deployed to

investigate the proposed two-hop scheme. The obtained results

demonstrate the effectiveness and analytical tractability to study

the heterogeneous performance.

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