UtilityRegionsforDFRelayinOFDMA‐Based
SecureCommunicationwithUntrustedUsers
Ravikant Saini, Deepak Mishra and Swades De
The self-archived postprint version of this journal article is available at Linköping
University Institutional Repository (DiVA):
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-155746
N.B.: When citing this work, cite the original publication.
Saini, R., Mishra, D., De, S., (2017), Utility Regions for DF Relay in OFDMA-Based Secure
Communication with Untrusted Users, IEEE Communications Letters, 21(11), 2512-2515.
https://doi.org/10.1109/LCOMM.2017.2730186
Original publication available at:
https://doi.org/10.1109/LCOMM.2017.2730186
Copyright: Institute of Electrical and Electronics Engineers (IEEE)
http://www.ieee.org/index.html
©2017 IEEE. Personal use of this material is permitted. However, permission to
reprint/republish this material for advertising or promotional purposes or for
creating new collective works for resale or redistribution to servers or lists, or to reuse
any copyrighted component of this work in other works must be obtained from the
IEEE.
1
Utility Regions for DF Relay in OFDMA-based
Secure Communication with Untrusted Users
Ravikant Saini, Member, IEEE, Deepak Mishra, Student Member, IEEE, and Swades De, Senior Member, IEEE
Abstract—This paper investigates the utility of a trusted
decode-and-forward relay in OFDMA-based secure communica-
tion system with untrusted users. For deciding whether to use the
relay or not, we first present optimal subcarrier allocation policies
for direct communication (DC) and relayed communication (RC).
Next we identify exclusive RC mode, exclusive DC mode, and
mixed (RDC) mode subcarriers which can support both the
modes. For RDC mode we present optimal mode selection policy
and a suboptimal strategy independent of power allocation which
is asymptotically optimal at both low and high SNRs. Finally, via
numerical results we present insights on relay utility regions.
Index Terms—Physical layer security, DF relay, maximum ratio
combining, secure OFDMA, subcarrier allocation, mode selection
I. INTRODUCTION
With growing number of users, utilization of friendly relays
for providing secure communication to cell-edge users is
becoming very popular [1]. Also due to its relative difficulty
as compared to source based broadcast, because of the possi-
bility of information interception in both the hops, significant
research attention is being paid in this regard recently [2].
The authors in [3] proposed several cooperation strategies
for secrecy enhancement in single carrier communication sys-
tems. While considering four single antenna half duplex nodes,
[4] investigated the role to be played by the relay to maximize
ergodic secrecy rate. For a similar setting, [5] considered the
outage constrained secrecy throughput maximization problem.
In an amplify and forward (AF) relay assisted system
without availability of direct source-destination link, a time
division based protocol was proposed in [6] using one of the
users as the helper node for secure communication to untrusted
users. In another related work [7], time division based relay
and user selection scheme was studied to improve secrecy of a
cooperative AF relay network, assuming availability of direct
link. With multi-antenna nodes, [8] investigated multiuser
resource allocation for decode and forward (DF) relay assisted
system without direct link, in the presence of single eavesdrop-
per. The authors in [9] considered resource allocation problem
for a DF relay assisted orthogonal frequency division multiple
access (OFDMA) system with multiple untrusted users.
Manuscript received June 24, 2017; accepted July 16, 2017. This work has
been supported by the Department of Science and Technology under Grant
no. SB/S3/EECE/0248/2014. The associate editor coordinating the review of
this paper and approving it for publication was K. Tourki.
R. Saini is with the Department of Electrical Engineering, Shiv Nadar
University, Uttar Pradesh 201314, India (email: ravikant.saini@snu.edu.in).
D. Mishra and S. De are with the Department of Electrical Engineering and
Bharti School of Telecommunication, Indian Institute of Technology Delhi,
New Delhi 110016, India (e-mail: {deepak.mishra, swadesd}@ee.iitd.ac.in).
Digital Object Identifier xxxxxxxxxxxxxxxxx
Assuming the availability of direct link, the optimal power
allocation and transmission mode selection for DF relay-
assisted secure communication was considered in [10]. Obser-
ving that strategies for a single source-destination pair with
joint transmit power budget for source and relay cannot be
extended for an untrusted users’ model with individual power
budgets, we intend to investigate whether utilizing a relay is
always useful in multiuser secure OFDMA system.
The key contributions of this letter are four fold. Firstly,
we present a generalized secure rate definition for DF relay
assisted secure OFDMA system with the availability of direct
link, while considering the possibility of tapping in both
the hops. Secondly, observing that each subcarrier can be
utilized in direct communication (DC) mode, we identify the
conditions for using a subcarrier in relayed communication
(RC) mode, and obtain optimal subcarrier allocation policies
for both modes. Thirdly, noting that a set of subcarriers can
be used in both the modes, we find optimal mode selection
strategy resulting in higher secure rate over such subcarriers.
Finally, asymptotically optimal and suboptimal mode selection
schemes, that are independent of power allocation, are derived.
To the best of our knowledge, it is the first work studying utility
of a DF relay in secure OFDMA system with untrusted users.
II. SYSTEM MODEL
Downlink of a trusted DF relay R assisted secure OFDMA
system, with source S, and M untrusted users is considered.
Untrusted users is a hostile scenario, where each user behaves
as a potential eavesdropper for others. For each U
m
there are
effectively M −1 eavesdroppers, and the one having maximum
signal-to-noise ratio (SNR) is called equivalent eavesdropper.
Apart from the direct (S − U
m
) link, there exists a two hop
(S − R) and (R − U
m
) link for information transfer to U
m
.
Assumptions: All nodes are equipped with single antenna,
and R operates in two hop half duplex DF mode [8], [10].
All subcarriers on S − R, S − U
m
, R − U
m
links are assumed
to follow quasi-static Rayleigh fading. Perfect channel state
information over all links is available at S [8], [10], [11]. Users
are capable of utilizing maximum ratio combining (MRC)[10].
III. PROPOSED SECURE RATE DEFINITION
Before introducing secure rate definition in an untrusted user
scenario with two tapping, we first discuss rate definitions in
classical co-operative communication. Let us denote the rate
achieved by user U
m
over subcarrier n in DC and RC mode as
R
m
n
|
DC
and R
m
n
|
RC
, respectively. With S utilizing optimum
transmission mode for achieving maximum secure rate, the
effective rate R
m
n
is given by R
m
n
= max {R
m
n
|
DC
, R
m
n
|
RC
}.
2
A. Rate Definitions in Classical Co-operative Communication
Let R
sm
n
, R
sr
n
, and R
srm
n
, respectively, denote the rates of
U
m
for S − U
m
, S − R, and S − R− U
m
links over subcarrier
n. Here R
srm
n
denotes the rate of U
m
due to MRC of signals
from S and R. The rates of U
m
in DC and RC modes are:
R
m
n
|
DC
= R
sm
n
; R
m
n
|
RC
= (1/2) min {R
sr
n
, R
srm
n
} . (1)
The factor
1
2
in R
m
n
|
RC
arises due to the half duplex protocol.
Thus, R
m
n
=
1
2
max {2R
sm
n
, min {R
sr
n
, R
srm
n
}}.
Let P
s
n
and P
r
n
, respectively, denote source and relay power
over subcarrier n. The channel gain of i–j link over subcarrier
n is denoted by γ
ij
n
where i ∈ {s, r} and j ∈ {r, 1, 2, · · · M}.
The rates of S −U
m
, S −R, and S −R−U
m
links are respecti-
vely given by R
sm
n
= log
2
1 + P
s
n
γ
sm
n
/σ
2
, R
sr
n
= log
2
1+
P
s
n
γ
sr
n
σ
2
, and R
srm
n
= log
2
1 +
P
s
n
γ
sm
n
+P
r
n
γ
rm
n
σ
2
. After some
simplifications the rate R
m
n
can be restated as
R
m
n
=
1
2
R
sr
n
if 2R
sm
n
≤ R
sr
n
< R
srm
n
R
srm
n
if 2R
sm
n
≤ R
srm
n
≤ R
sr
n
2R
sm
n
otherwise.
(2)
2R
sm
n
≤ R
sr
n
can be simplified as γ
sr
n
≥ γ
sm
n
a
m
n
where
a
m
n
=
2 +
P
s
n
γ
sm
n
σ
2
, which upper bounds P
s
n
as P
s
n
≤
P
sm
n
u
,
(γ
sr
n
−2γ
sm
n
)σ
2
(γ
sm
n
)
2
. 2R
sm
n
≤ R
srm
n
leads to P
r
n
≥ P
rm
n
l
,
P
s
n
γ
sm
n
γ
rm
n
1 +
P
s
n
γ
sm
n
σ
2
. Thus, if P
s
n
is below a certain threshold,
and P
r
n
is above a certain threshold, RC mode can be used,
otherwise DC mode is a better option. R
sr
n
< R
srm
n
leads to
P
r
n
P
s
n
>
γ
sr
n
−γ
sm
n
γ
rm
n
, ∆
m
n
, where ∆
m
n
is referred as relay versus
source power (RSP) ratio. Thus, R
m
n
(2) can be simplified as
R
m
n
=
1
2
R
sr
n
ifγ
sr
n
≥ γ
sm
n
a
m
n
, P
r
n
≥ max{P
rm
n
l
, P
s
n
∆
m
n
}
1
2
R
srm
n
if γ
sr
n
≥ γ
sm
n
a
m
n
, P
s
n
∆
m
n
≥ P
r
n
≥ P
rm
n
l
R
sm
n
otherwise.
(3)
Remark 1: From (3), we note that, if P
r
n
≤ P
s
n
∆
m
n
, MRC
link S − R − U
m
is the bottleneck compared to S − R link,
and the rate is R
srm
n
. As γ
sr
n
≥ γ
sm
n
, MRC link remains as the
bottleneck even for increased P
s
n
. This rate in RC mode can
be improved by increasing P
r
n
till R
sr
n
= R
srm
n
, after which
S − R link becomes the bottleneck. Thus, maximum rate in
RC mode is achieved when R
sr
n
= R
srm
n
, i.e., P
r
n
= P
s
n
∆
m
n
.
B. Incompleteness of Classical Rate Definition
The rate definition of R
m
n
|
RC
in RC mode is based on an
implicit assumption that P
r
n
> 0. When P
r
n
= 0, R
srm
n
=
R
sm
n
, and R
m
n
|
RC
=
1
2
min {R
sr
n
, R
sm
n
} which is positive for
P
s
n
> 0. But this has no physical significance as the decoded
information at R is not forwarded to U
m
. Ideally, P
r
n
= 0
should indicate that R
m
n
|
RC
= 0, such that R
m
n
= R
m
n
|
DC
.
The proposed rate definition is complete as it takes care of
this gap. With P
r
n
= 0 and R
srm
n
= R
sm
n
, the definition gets
simplified to R
m
n
=
1
2
max {2R
sm
n
, min {R
sr
n
, R
sm
n
}}. Thus,
with P
r
n
= 0, when either R
sr
n
< R
sm
n
or R
sr
n
≥ R
sm
n
, rate
R
m
n
= 2R
sm
n
= R
m
n
|
DC
, i.e., subcarrier is used in DC mode.
C. Secure Rate Definition
The secure rate R
m
s
n
of U
m
over a subcarrier n is the
difference of rate R
m
n
of U
m
and rate R
e
n
of the equivalent
eavesdropper U
e
[11]. Mathematically, R
m
s
n
is given by
R
m
s
n
= [R
m
n
− R
e
n
]
+
=
h
R
m
n
− max
o∈{1,2,···M}\m
R
o
n
i
+
(4)
where x
+
= max{0, x}. The definition in (4) considers
tapping in both slots. Further, in contrast to the secure rate
definition used in [5] and [8], which did not consider direct
link availability, the proposed definition is a generalized one.
IV. SUBCARRIER ALLOCATION POLICY
Now, we discuss the conditions for achieving positive secure
rate by U
m
over a subcarrier n. From (3), a subcarrier can be
utilized in either DC or RC mode. In DC mode, the required
condition is R
sm
n
> R
se
n
which can be simplified as γ
sm
n
>
γ
se
n
. With π
m
n
DC
denoting the subcarrier allocation variable in
DC mode, the subcarrier allocation policy can be stated as
π
m
n
DC
=
1 if m = arg max
o∈{1,2,···M}
γ
so
n
0 otherwise.
(5)
Positive secure rate conditions for RC mode are given below.
Proposition 1: U
m
can use a subcarrier n in RC mode if: (i)
γ
sr
n
> max{γ
so
n
a
o
n
}, (ii) P
r
n
> max{P
ro
n
l
} (iii) P
r
n
≤ P
s
n
∆
m
n
,
and (iv) ∆
m
n
= min{∆
o
n
} ∀o ∈ {1, 2, · · · M}.
Proof: The conditions for activating RC mode over
subcarrier n are γ
sr
n
≥ γ
sm
n
a
m
n
and P
r
n
≥ P
rm
n
l
(cf. (3)). Its ge-
neralization for M users leads to the first and the second con-
ditions: γ
sr
n
≥ max
o∈{1,2,···M}
γ
so
n
a
o
n
and P
r
n
≥ max
o∈{1,2,···M}
P
ro
n
l
.
Let ∆
e
n
denote RSP ratio (cf. (3)) for U
e
over subcarrier n.
If P
r
n
> P
s
n
∆
m
n
, rate of U
m
is R
sr
n
. The rate of U
e
is either
R
sr
n
when P
r
n
> P
s
n
∆
e
n
, or R
sre
n
otherwise. In the first case
the secure rate is zero, while in the second case R
m
s
n
= R
sr
n
−
R
sre
n
=
1
2
n
log
2
σ
2
+P
s
n
γ
sr
n
σ
2
+P
s
n
γ
se
n
+P
r
n
γ
re
n
o
, which is a decreasing
function of P
r
n
, enforcing P
r
n
= 0, i.e., DC mode (cf. Section
III-B). Thus, for RC mode P
r
n
≤ P
s
n
∆
m
n
which is second
condition. Lastly, we prove the third condition ∆
e
n
> ∆
m
n
by
contradiction that if ∆
e
n
≤ ∆
m
n
then positive secure rate cannot
be achieved. The condition ∆
e
n
≤ ∆
m
n
can be restated as
γ
sr
n
−γ
se
n
γ
re
n
≤
γ
sr
n
−γ
sm
n
γ
rm
n
. (6)
Simplifying γ
sr
n
from the definition of ∆
e
n
, we get γ
sr
n
=
γ
se
n
+ ∆
e
n
γ
re
n
. Substituting ∆
e
n
in (6), we obtain γ
sr
n
≥ γ
sm
n
+
∆
e
n
γ
rm
n
. Substituting γ
sr
n
results in γ
se
n
+ ∆
e
n
γ
re
n
≥ γ
sm
n
+
∆
e
n
γ
rm
n
. Multiplying both the sides with P
s
n
, and substituting
P
s
n
∆
e
n
as P
r
n
, we get P
s
n
γ
se
n
+ P
r
n
γ
re
n
≥ P
s
n
γ
sm
n
+ P
r
n
γ
rm
n
,
which will lead to zero secure rate as R
e
n
≥ R
m
n
. Thus, to
achieve positive secure rate ∆
e
n
> ∆
m
n
. Under this condition,
the rates of U
m
and U
e
are given as R
srm
n
and R
sre
n
, respecti-
vely, and the secure rate definition in (4) gets simplified to
R
m
s
n
=
1
2
log
2
σ
2
+P
s
n
γ
sm
n
+P
r
n
γ
rm
n
σ
2
+P
s
n
γ
se
n
+P
r
n
γ
re
n
. (7)
The condition ∆
e
n
> ∆
m
n
must be satisfied for all possible
U
e
. Thus U
m
has to be chosen for having minimum ratio
3
∆
o
n
∀o ∈ {1, 2, · · · M}. With π
m
n
RC
as subcarrier allocation
variable in RC mode, optimal subcarrier allocation policy is
π
m
n
RC
=
1 if m = arg min
o∈{1,2,.M}
∆
o
n
,
γ
sr
n
−γ
so
n
γ
ro
n
0 otherwise.
(8)
After sorting RSP ratios (∆
o
n
) over a subcarrier in ascending
order, the user having the minimum value is U
m
, and the one
having just next better value is the corresponding U
e
.
Physical Interpretation of (8): From (3), RSP ratio ∆
o
n
=
γ
sr
n
−γ
so
n
γ
ro
n
is the factor by which P
r
n
should be provided for a
fixed P
s
n
to achieve the same SNR over S −R and S −R−U
m
links. So a user having a lower ratio will require lower P
r
n
to achieve maximum secure rate. Thus, once a user is chosen
with minimum value of the ratio as the main user U
m
, then
for any other user U
e
having higher value of RSP ratio, its
R − U
e
link becomes the bottleneck link (as it requires higher
P
r
n
to become equal to the S − R link) and its rate will be
lower than that of the main user. Thus, allocation in (8) always
leads to positive secure rate over a subcarrier in RC mode.
Remark 2: Due to the possibility of tapping in the first slot,
the condition γ
sm
n
> γ
se
n
(cf. (5)) must be satisfied in RC mode
as well. So, the main user in RC mode (cf. (8)) also satisfies
positive secure rate requirement for DC mode (cf. (5)) .
Remark 3: In case the same user is selected as main user
through the policies (5) and (8), that subcarrier satisfies
positive secure rate requirement for both DC and RC modes.
However, corresponding eavesdroppers in the two modes can
be different. With U
e
and U
e
0
respectively denoting eavesdrop-
pers in RC and DC modes over n, from (5): γ
se
0
n
≥ γ
se
n
.
V. UTILITY OF RELAY: RC VERSUS DC MODE SELECTION
To highlight the utility of relay, here we present the condi-
tions for enhanced performance of RC mode over DC mode.
Thus, we intend to derive conditions for R
m
s
n
|
RC
> R
m
s
n
|
DC
.
Consider the general case where the eavesdroppers of user U
m
are different in RC mode (U
e
) and DC mode (U
e
0
). The condi-
tion can be simply stated as (R
m
n
−R
e
n
)|
RC
> (R
m
n
−R
e
0
n
)|
DC
.
1
2
log
2
σ
2
+P
s
n
γ
sm
n
+P
r
n
γ
rm
n
σ
2
+P
s
n
γ
se
n
+P
r
n
γ
re
n
> log
2
σ
2
+P
s
n
γ
sm
n
σ
2
+P
s
n
γ
se
0
n
. (9)
Using energy efficient solution P
r
n
= P
s
n
∆
m
n
[9], the resulting
condition gets simplified as:
γ
rm
n
γ
re
n
> ρ ,
(γ
sr
n
−γ
sm
n
)(σ
2
+P
s
n
γ
sm
n
)
2
ρ
den
. (10)
where ρ
den
= γ
sr
n
(σ
2
+ P
s
n
γ
se
0
n
)
2
− γ
se
n
(σ
2
+ P
s
n
γ
sm
n
)
2
−
σ
2
{(σ
2
+ P
s
n
γ
se
0
n
) + (σ
2
+ P
s
n
γ
sm
n
)}(γ
sm
n
− γ
se
0
n
). ρ < 0
indicates exclusive DC mode. Next, we discuss mode selection
under asymptotic conditions, and with and without known P
s
n
.
A. Asymptotically Optimal Mode Selection Policy
At low SNR regime, (9) can be simplified using approxi-
mation log(1 + x) ≈ x, ∀x 1, and P
r
n
= P
s
n
∆
m
n
, as:
γ
rm
n
γ
re
n
> ρ
l
,
γ
sr
n
−γ
sm
n
γ
sr
n
−2(γ
sm
n
−γ
se
0
n
)−γ
se
n
. (11)
Under high SNR scenario, using the approximation log(1 +
x) ≈ log(x), ∀x 1, the condition in (9) gets simplified to:
γ
rm
n
γ
re
n
> ρ
h
,
(γ
sr
n
−γ
sm
n
)(γ
sm
n
)
2
γ
sr
n
(γ
se
0
n
)
2
−γ
se
n
(γ
sm
n
)
2
(12)
B. Optimal Mode Selection for given Power Allocation
First, we show that ρ
l
< ρ. Thus, if
γ
rm
n
γ
re
n
< ρ
l
, the subcarrier
has to be used exclusively in DC mode. Referring (10) and
(11), condition ρ
l
< ρ can be stated as: γ
sr
n
−2(γ
sm
n
−γ
se
0
n
)−
γ
se
n
>
ρ
den
(σ
2
+P
s
n
γ
sm
n
)
2
. Substituting ρ
den
, this gets simplified as:
γ
sr
n
− 2(γ
sm
n
− γ
se
0
n
) − γ
se
n
> γ
sr
n
σ
2
+P
s
n
γ
se
0
n
σ
2
+P
s
n
γ
sm
n
2
− σ
2
(σ
2
+P
s
n
γ
sm
n
)+(σ
2
+P
s
n
γ
se
0
n
)
(σ
2
+P
s
n
γ
sm
n
)
2
− γ
se
n
. (13)
After arranging terms and some simplification steps, we obtain
(γ
sm
n
− γ
se
0
n
)
(2σ
2
+P
s
n
(γ
sm
n
+γ
se
0
n
))(σ
2
+P
s
n
γ
sr
n
)
(σ
2
+P
s
n
γ
sm
n
)
2
− 2
> 0. With
P
s
n
> 0 and (γ
sm
n
− γ
se
0
n
) > 0, it gets reduced to (γ
sr
n
−
2γ
sm
n
)(2σ
2
+ P
s
n
γ
sm
n
) + σ
2
(γ
sm
n
+ γ
se
0
n
) + P
s
n
γ
sr
n
γ
se
0
n
> 0.
Observing that γ
sr
n
> 2γ
sm
n
, the above condition always holds.
Similarly, we prove that ρ
h
> ρ, such that if
γ
rm
n
γ
re
n
> ρ
h
, the
subcarrier should be in RC mode exclusively. The equivalent
condition for ρ
h
> ρ can be stated as (cf. (10) and (12)):
γ
se
0
n
γ
sm
n
2
<
σ
2
+P
s
n
γ
se
0
n
σ
2
+P
s
n
γ
sm
n
2
−
σ
2
γ
sr
n
(σ
2
+P
s
n
γ
sm
n
)+(σ
2
+P
s
n
γ
se
0
n
)
(σ
2
+P
s
n
γ
sm
n
)
2
(14)
After arranging the terms, this condition gets simplified
as σ
2
(γ
sm
n
− γ
se
0
n
)γ
sr
n
h
σ
2
(γ
sm
n
+ γ
se
0
n
) + 2P
s
n
γ
sm
n
γ
se
0
n
i
>
σ
2
(γ
sm
n
− γ
se
0
n
)(γ
sm
n
)
2
h
2σ
2
+ P
s
n
(γ
sm
n
+ γ
se
0
n
)
i
. With γ
sm
n
>
γ
se
0
n
, and rearranging the terms, the condition gets re-
duced to σ
2
γ
sm
n
γ
sr
n
− 2γ
sm
n
−
P
s
n
(γ
sm
n
)
2
σ
2
+ σ
2
γ
sr
n
γ
se
0
n
+
P
s
n
γ
sm
n
γ
se
0
n
(2γ
sr
n
− γ
sm
n
) > 0, which is always true as
P
s
n
< P
sm
n
u
and γ
sr
n
> γ
sm
n
. The complete mode selection
policy with known power allocation can be summarized as:
γ
rm
n
γ
re
n
> ρ
h
R
m
s
n
|
RC
> R
m
s
n
|
DC
Exclusive RC
∈ [ρ
l
, ρ
h
] RDC
(
P
s
n
< P
s
n
th
RC
P
s
n
≥ P
s
n
th
DC
< ρ
l
R
m
s
n
|
RC
< R
m
s
n
|
DC
Exclusive DC
(15)
where P
s
n
th
is positive root of quadratic obtained from (10).
Physical Interpretation of (15): Secure rate improvement
with P
r
n
depends on relative gain
γ
rm
n
γ
re
n
. In low SNR case, all
RDC mode subcarriers are in RC mode as P
s
n
< P
s
n
th
. Thus,
if
γ
rm
n
γ
re
n
< ρ
l
, the subcarrier is in DC mode, otherwise it can
be in RC mode. In high SNR case, with P
s
n
> P
s
n
th
, all RDC
mode subcarriers switch to DC mode. Only those subcarriers
which have
γ
rm
n
γ
re
n
> ρ
h
are in RC mode, rest are in DC mode.
C. Sub-optimal Mode Selection Policy
We now propose a suboptimal mode selection strategy that
does not require explicit knowledge of P
s
n
. Let us introduce a
term ‘satisfaction level’ α which is considered as the minimum
acceptable SNR level over a subcarrier, i.e.,
P
s
n
γ
sm
n
σ
2
> α ∀n.
As higher value of α requires higher source power on each
subcarrier, it can be considered as an abstraction parameter
mapping minimum supported SNR to source power budget.
Remark 4: As γ
sr
n
> γ
sm
n
and P
s
n
γ
sm
n
+ P
r
n
γ
rm
n
> P
s
n
γ
sm
n
,
P
s
n
γ
sm
n
σ
2
> α is enough to ensure successful communication.
4
To have a higher secure rate in RC mode than in DC
mode P
s
n
th
> P
s
n
>
σ
2
α
γ
sm
n
. Substituting P
s
n
, we have:
γ
rm
n
γ
re
n
> ρ
α
,
α
num
α
den
, where α
num
= (γ
sr
n
− γ
sm
n
)(1 + α)
2
, and
α
den
= γ
sr
n
(1 + α
γ
se
0
n
γ
sm
n
)
2
− γ
se
n
(1 + α)
2
− (γ
sm
n
− γ
se
0
n
){(1 +
α) + (1 + α
γ
se
0
n
γ
sm
n
)}. For the limiting cases α → 0 and α → ∞,
ρ
α
respectively tends to the low and high SNR bounds ρ
l
and
ρ
u
on
γ
rm
n
γ
re
n
discussed in Section V-A. This corroborates our
reasoning behind α being a measure of source power budget.
VI. NUMERICAL RESULTS
The downlink of an OFDMA system is considered with
N = 64 subcarriers which are assumed to experience quasi-
static Rayleigh fading with path loss exponent = 3. We study
performance variation with relay position, secure rate impro-
vement due to optimal mode selection and utility regions.
Fig. 1(a) presents the effect of relay placement on its utility
in improving the secure rate. Considering DC mode as a
benchmark, improvement in system performance is presented
by plotting the percentage of subcarriers that have higher rate
in RC mode. Assuming S to be located at (0, 0) and M = 8
users randomly distributed inside a unit square centered at
(2, 0), position of R is varied along a horizontal line (x
r
, 0)
with 0.1 ≤ x
r
≤ 1.5. Note that, R should placed closer to
S, to have γ
sr
n
≥ γ
sm
n
a
m
n
and stand against DC mode. Source
power budget variation is captured by varying α. Even though
optimal relay location x
∗
r
increases with α, it is still in the left
half, i.e., x
∗
r
< 0.5, for the considered system. Note that with
increased α percentage of RC mode subcarriers reduces as
more and more RDC mode subcarrier switches to DC mode.
0.5 1 1.5
Relay Location (Horizontal)
0
5
10
15
20
% RC mode subcarriers
(a)
α → 0
α = −6 dB
α = 0 dB
α = 6 dB
α = 12 dB
α → ∞
0 10 20 30
Source power P
S
(dB)
-10
0
10
20
30
40
% Secure rate improvement
(b)
Opt mode
Low SNR based
High SNR based
Fig. 1: (a) Performance with horizontal variation in relay position,
(b) Secure rate improvement through mode selection.
Considering equal power allocation, rate improvement
achieved by optimal mode selection compared to static DC
mode is plotted in Fig 1(b). Following the observation from
Fig 1(a), relay is placed at (0.5, 0). Performance of low
and high SNR based policies have been plotted to highlight
efficacy of optimal policy. Rate improvement reduces with
increasing P
S
as all RDC subcarriers move to DC mode. At
higher P
S
, negative improvement is observed in low SNR
based policy because RDC subcarriers which could have
achieved higher rate in DC mode are pushed to RC mode.
Fig 2 presents spatial utility of relay where users’ locations
on a 2-D Euclidean plane are plotted after categorizing them
according to the percentage of RC mode subcarriers. Assuming
users to be located randomly in a 4×4 square centered around
(0, 0), S and R are considered to be located at (0, 0.5) and
-2 -1 0 1 2
-2
-1
0
1
2
>=2%
>=5%
>=8%
>=11%
>=14%
S
R
Fig. 2: Relay utility regions.
(0, −0.5), respectively. Note that the best utility is around
relay where more than 14% subcarriers are benefited by RC
mode. Due to direct link availability, decreasing trend of per-
centage RC mode subcarriers with distance is not symmetric.
VII. CONCLUSION
Considering two slot tapping, this paper presents a generali-
zed secure rate definition. After identifying conditions for RC
mode, optimal subcarrier allocation policies for both RC and
DC modes are obtained. A subcarrier can be used either in
exclusive DC mode, in exclusive RC mode, or in RDC mode.
Identifying that optimal mode selection policy for RDC mode
subcarriers is integrated with power allocation, an α based
suboptimal policy is discussed, which asymptotically matches
with the optimal policy respectively at low and high SNR
regimes. As direct link is available, results indicate that R
should be placed closer to S. Though the user locations around
R are more benefited, relay utility regions are not circular.
REFERENCES
[1] R. Bassily et al., “Cooperative security at the physical layer: A summary
of recent advances,” IEEE Signal Process. Magazine, vol. 30, no. 5, pp.
16–28, Sep. 2013.
[2] A. Mukherjee et al., “Principles of physical layer security in multiuser
wireless networks: A survey,” IEEE Commun. Surveys Tuts., vol. 16,
no. 3, pp. 1550–1573, Aug. 2014.
[3] L. Lai and H. Gamal, “The relay eavesdropper channel: Cooperation for
secrecy,” IEEE Trans. Inf. Theory, vol. 54, no. 9, pp. 4005–4019, Sep.
2008.
[4] H. Deng et al., “Secrecy transmission with a helper: To relay or to jam,”
IEEE Trans. Inf. Forensics Security, vol. 10, no. 2, pp. 293–307, Feb.
2015.
[5] T. X. Zheng et al., “Outage constrained secrecy throughput maximization
for DF relay networks,” IEEE Trans. Commun., vol. 63, no. 5, pp. 1741–
1755, May 2015.
[6] H. Xu et al., “Cooperative privacy preserving scheme for downlink
transmission in multiuser relay networks,” IEEE Trans. Inf. Forensics
Security, vol. 12, no. 4, pp. 825–839, Apr. 2017.
[7] A. Mabrouk et al., “Transmission mode selection scheme for physical
layer security in multi-user multi-relay systems,” in Proc. IEEE PIMRC,
Sep. 2016, pp. 1–6.
[8] D. Ng et al., “Secure resource allocation and scheduling for OFDMA
decode-and-forward relay networks,” IEEE Trans. Wireless Commun.,
vol. 10, no. 10, pp. 3528–3540, Oct. 2011.
[9] R. Saini et al., “OFDMA-based DF secure cooperative communication
with untrusted users,” IEEE Commun. Lett., vol. 20, no. 4, pp. 716–719,
Apr. 2016.
[10] C. Jeong and I.-M. Kim, “Optimal power allocation for secure multi-
carrier relay systems,” IEEE Trans. Signal Process., vol. 59, no. 11, pp.
5428–5442, Nov. 2011.
[11] X. Wang et al., “Power and subcarrier allocation for physical-layer
security in OFDMA-based broadband wireless networks,” IEEE Trans.
Inf. Forensics Security, vol. 6, no. 3, pp. 693–702, Sep. 2011.