LU et al.: TRUSTED DEVICE-TO-DEVICE BASED HETEROGENEOUS CELLULAR NETWORKS 11221
powerful mobile devices. Differently, in this paper, we optimize
D2D based HCNs from the perspective of connectivity.
B. Connectivity of CRNs
Recently, extensive research efforts related to connectivity
have focused on spectrum sharing, i.e., Cognitive Radio Net-
work (CRNs) [23]. The connectivity of CRNs is affected not
only by the characteristics of the network itself, but also by
the activity of the coexisted primary network. Many researchers
have studied the connectivity of CRNs using percolation and
random graph theory [24]–[30]. The pioneer work reported
in [24] studies the i mpact on connectivity caused by the trans-
mission power and varying spectrum opportunities. Techniques
and theories of continuum percolation have been used to study
the scaling behavior of the latency of information dissemina-
tion [25]–[27]. In [28], Ao et al. investigate the connectivity
of cooperative secondary networks, in which multiple ad hoc
networks sharing the same spectrum cooperate with each other.
These works, however, consider only the network with a single
channel and do not account for the impact of frequency diversity
which is a key characteristic of CRNs. Sun et al. [29] explore
the tempo-spatial limits of the connectivity in CRNs with mul-
tiple channels. They show that opportunistic access apparently
depends on the spatial density of the coexisting licensed users
and the number of channels accessible by cognitive users. How-
ever, they consider a static density configuration, which cannot
reflect the dynamic nature of the activities of licensed users.
In [30], the authors construct a cognitive radio graph model
to capture the dynamic characteristics of the spectrum that ac-
counts for the impact of the number of channels and the activities
of licensed users. However, this model assumes that all cognitive
users have the same transmission rate configuration, which is
inappropriate to D2D based HCNs. For the UEs in a D2D based
HCN, the spectrum access scenario is similar to that in a CRN,
which is also constrained by the primary network, e.g., the cel-
lular system. However, the existing work on connectivity cannot
be directly extended to D2D based HCNs for t he following two
reasons. First, most of the studies on CRNs assume that trans-
mission occurs in only one femtocell and thus fails to account
for the distribution of the surrounding femtocells and frequency.
By contrast, in D2D based HCNs, the extreme deployment of
femtocells necessitates further exploration of both the spatial
and frequency diversities. Therefore, the activities of licensed
users and the number of channels should be investigated thor-
oughly. Second, D2D based HCNs typically employ a variety
of radio access technologies and the transmission rates of the
channels are also varied. Thus, i t is necessary to develop new
models for the connectivity optimization of D2D based HCNs to
enable the joint consideration of the varying transmission rates
and the number of channels as well as the activities of CUs.
In this paper, we investigate these factors comprehensively and
model opportunistic access as a birth-death process. The pro-
posed model can be seamlessly integrated into our TD-HCN
framework.
C. Connectivity of D2D Based HCNs
In D2D based HCNs, interference management [31] and re-
source allocation [32] have been extensively studied; however,
Fig. 1. D2D-based HCNs with fixed FemtoBSs.
connectivity optimization remains an open question. Li et al.
[10] propose a hybrid access mechanism to optimize the net-
work connectivity. This mechanism allows certain selected UEs
to communicate with other UEs instead of MacroBSs or Femto-
BSs. However, this mechanism lacks accurate consideration of
the spectrum dynamics, which is a key factor affecting the con-
nectivity of D2D networks. Using mixed overlay-underlay spec-
trum sharing, Khoshkholgh et al. [7] investigate CR-assisted
D2D communications in a cellular network. Yao et al. [11]
show that the connectivity of underlay ad hoc D2D networks is
closely related to certain features of the UEs such as their den-
sity and transmit power. In [12], the authors study the distance
of message dissemination and the hitting time, which are two
fundamental issues in the intermittently connected D2D com-
munication networks. However, in all of the work mentioned
above, the D2D network is modeled as a symmetric graph, with-
out considering the trust r elationships among the nodes. Thus,
the proposed approaches are difficult to apply in practical appli-
cations due to their lack of guaranteed security and privacy for
users. Currently, the trust relationships in D2D networks [33]
and the Internet of Things [34] have also been studied. However,
these works mainly focus on the building and management of
trustworthiness. Differently, we construct a trust-based directed
graph model by formulating trust relationships as a renewal pro-
cess to analyze their impact on the connectivity of D2D based
HCNs.
III. F
RAMEWORK FOR TRUSTED D2D-BASED HCNS
We propose a new framework called the TD-HCN framework
with the aim of optimizing the connectivity of D2D HCNs.
To characterize the three uncertain real-life factors mentioned
above, we divide the framework into three components, the
DFEA, the TDGM and the DSGM. The details can be found in
the following subsections.
A. Dynamic FemtoBS Employment Architecture
1) Scheduling of the DFEA: In HCNs, the transmit power
of the FemtoBSs and their distances from the UEs are critical
factors affecting the network connectivity. In traditional D2D
HCNs, the FemtoBSs are all deployed in fixed locations. In the
scenario shown in Fig. 1, UE
1
and UE
2
can offload traffic from
the fixed FemtoBS. When the topology changes, e.g., UE
1
and
UE
2
move out of the coverage range of the fixed FemtoBS,