  Handover rate is one of the most import metrics to instruct mobility
management and resource management in wireless cellular networks. In the
literature, the mathematical expression of handover rate has been derived for
homogeneous cellular network by both regular hexagon coverage model and
stochastic geometry model, but there has not been any reliable result for
heterogeneous cellular networks (HCNs). Recently, stochastic geometry modeling
has been shown to model well the real deployment of HCNs and has been
extensively used to analyze HCNs. In this paper, we give an effective handover
analysis for HCNs by stochastic geometry modeling, derive the mathematical
expression of handover rate by employing an infinitesimal method for a
generalized multi-tier scenario, discuss the result by deriving some meaningful
corollaries, and validate the analysis by computer simulation with multiple
walking models. By our analysis, we find that in HCNs the handover rate is
related to many factors like the base stations' densities and transmitting
powers, user's velocity distribution, bias factor, pass loss factor and etc.
Although our analysis focuses on the scenario of multi-tier HCNs, the
analytical framework can be easily extended for more complex scenarios, and may
shed some light for future study.
