8074 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 9, SEPTEMBER 2017
Finally, the performance of the proposed scheme in different
scenarios is investigated via simulations.
The paper is organized as follows. System model is described
in Section II. Limited rate f eedback schemes are proposed in
Section III. The limited rate feedback resource allocation prob-
lem is formulated and solved in Section IV. In Section V,
practical considerations, i.e., noisy feedback channel and CDI
estimation error, are investigated. Simulation and numerical re-
sults are provided in Section VI and finally conclusions are
drawn in Section VII.
II. S
YSTEM MODEL
We consider a D2D communication scenario underlaying an
existing cellular network. It is assumed the downlink transmis-
sion in the cellular network where the BS transmits information
to a cellular user while at the same time; the existing D2D pair
performs its own transmission on the same channel. Such a
scenario can be interpreted as there are many cellular users in
the network each of which is assigned to a channel over which
the BS sends information to them. Assuming this assignment is
performed based on some network parameters and is fixed, two
cellular users exploit one of the available cellular channels to
perform their information transmission directly. In this paper,
we assume that this assignment is predefined. In addition to cel-
lular user and D2D pair, we assume that there exists a malicious
user which wants to eavesdrop on the information transmission
of cellular network, i.e., from the BS to the CU. However, the
malicious user does not eavesdrop on the D2D pair. Such as-
sumption can be justified when the malicious user is not aware
of the existence of D2D pair as such sharing can be performed
opportunistically (i.e., D2D pair may or may not exist at any
time) when the malicious user is not interested in D2D pair in-
formation, or when the D2D pair applies upper layer security
measures, e.g., cryptography. In such case, the malicious user
treats the signals from D2D pair as noise.
Let h
BC
, h
BD
, h
DD
, h
DC
, h
BE
, and h
DE
denote, respectively,
the noise normalized channel power gain of the channel from
BS to CU, from BS to the receiver of D2D pair (RD2D), from
the transmitter of D2D pair (TD2D) to RD2D, from TD2D to
CU, from BS to the eavesdropper, and from the TD2D to the
eavesdropper. We assume that all channels undergo independent
block fading with Rayleigh distribution meaning that the chan-
nel power gains, i.e., h
BC
, h
BD
, h
DD
, h
DC
, h
BE
, and h
DE
,are
exponentially distributed with the mean of
¯
h
BC
,
¯
h
BD
,
¯
h
DD
,
¯
h
DC
,
¯
h
BE
, and
¯
h
DE
, respectively.
In this paper, we assume that the eavesdropper has complete
knowledge about the instantaneous channel power gains and
the CDI of the channels from BS to CU and from BS to it-
self. We further assume that the legitimate receivers, i.e., the
cellular user and the RD2D, know the CDI of all channels and
only the instantaneous channel power gains of their respective
channels. We assume that, the legitimate transmitters do not
have perfect values of channel power gains and the knowledge
of legitimate transmitters about their respective direct channel
power gains is obtained via their respective limited rate feed-
back channels. In this case, the space of h
BC
is divided into a
finite number of M regions, i.e., [0,
h
BC
(1)), [
h
BC
(1),
h
BC
(2)),
···, [
h
BC
(M − 1),
h
BC
(M)) where
h
BC
(M)=∞. Similarly,
for D2D pair, the space of h
DD
is divided into a finite num-
ber of N regions, i.e., [0,
h
DD
(1)), [
h
DD
(1),
h
DD
(2)), ···,
[
h
DD
(N − 1),
h
DD
(N)) where
h
DD
(N)=∞. The receiver, i.e.,
CU, measures the channel power gain h
BC
and feedbacks the in-
dex m if h
BC
lies in the region [
h
BC
(m),
h
BC
(m + 1)). Similarly,
RD2D measures the channel power gain h
DD
and feedbacks the
index n if h
DD
lies in the region [
h
DD
(n),
h
DD
(n + 1)).Inthis
paper, we assume that the feedback links are confidential. This
means that, the feedbacked index of the cellular network could
not be overheard by D2D pair and that of D2D pair could not be
overheard by the cellular network. In this case, the power-rate
tuples will depend only on the corresponding feedbacked index,
i.e., we have (p
BC
(m),r
BC
(m),r
BC
S
(m)) for cellular communi-
cation which are the transmit power, the transmission rate and
the secrecy rate at which BS transmits information to CU, re-
spectively. Moreover, we consider (p
DD
(n),r
DD
(n)) for D2D
communications which are the transmit power and the trans-
mission rate at which TD2D transmits information to RD2D,
respectively.
In fact, the proposed schemes operate in two phases. In the
first phase (off-line phase), several parameters that are later
used for resource allocation are computed. It is done before
the communication established and based on the CDIs of the
network’s links the optimum boundary regions and code-books
are designed by the base station. At the end of this phase, all
code-words are informed to users by BS. However, the channel
partitioning structure is kept at the CU. In the second phase
(on-line phase) that is employed during communication, the
transmitters use the parameters obtained in off-line phase. In
fact, in the on-line phase, the CU and D2D receiver measure the
related CSIs and based on them find the related channel partition
and boundary region. Then, they transmit back the index to the
base station and D2D transmitter in order to select the corre-
sponding code-word from the obtained code-book. Note that the
code-book, which contains a set of code-words, is designed off-
line and known by each node. The computational burden takes
place during the initialization (off-line) phase and requires a
negligible burden during the transmission (online) phase and
it is certainly desirable from an implementation perspective
[30]–[32]. In this paper, we consider that there is a central pro-
cessing unit and some assignments are performed in this step.
Then, the network uses the information prepared in the central
processing [33]–[35].
For the resource allocation, two approaches could be adopted.
One is to consider the problem of pairing the D2D and cellular
links as well as the designing limited feedback scheme jointly.
In this way, the outcome of the resource allocation problem is
which D2D link is paired with which cellular link as well as
code-books (power allocation and boundary regions). However,
this approach is much complex and would be computationally
prohibitive. Another approach which could lower the complex-
ity of the scheme is to consider the pairing problem and limited
rate feedback design separately. In this case, one first solves
the problem of pairing D2D and cellular link. Then, given this