  This paper studies the impact of the base station (BS) idle mode capability
(IMC) on the network performance of multi-tier and dense heterogeneous cellular
networks (HCNs). Different from most existing works that investigated network
scenarios with an infinite number of user equipments (UEs), we consider a more
practical setup with a finite number of UEs in our analysis. More specifically,
we derive the probability of which BS tier a typical UE should associate to and
the expression of the activated BS density in each tier. Based on such results,
analytical expressions for the coverage probability and the area spectral
efficiency (ASE) in each tier are also obtained. The impact of the IMC on the
performance of all BS tiers is shown to be significant. In particular, there
will be a surplus of BSs when the BS density in each tier exceeds the UE
density, and the overall coverage probability as well as the ASE continuously
increase when the BS IMC is applied. Such finding is distinctively different
from that in existing work. Thus, our result sheds new light on the design and
deployment of the future 5G HCNs.
