Optimal Power Allocation for Relay Assisted Cognitive Radio Networks

Conference Paper (PDF Available)inVehicular Technology Conference, 1988, IEEE 38th · September 2010with19 Reads
DOI: 10.1109/VETECF.2010.5594529 · Source: DBLP
Conference: Proceedings of the 72nd IEEE Vehicular Technology Conference, VTC Fall 2010, 6-9 September 2010, Ottawa, Canada
Abstract
In this paper, we study the optimal power allocation of wireless relay nodes which are used in the secondary user (SU) communication of a cognitive radio (CR) network. We consider the behavior of transmitting powers of SUs where those powers are limited to the tolerable interference as seen by the primary user (PU) communication. To improve the performance of the secondary communication based on minimizing the outage probability, we re-formulate the power allocation problem with a new set of constraints. These are obtained by considering the co-channel interference generated by the SU communication to the PU communication. The power allocation problem is solved for both regenerative and non regenerative relay models under Rayleigh fading conditions. SU communication with N number of relays is discussed and compared. The outage probability of SU communication is limited by the interference power threshold (IPT) constraints of PUs and is affected significantly by the IPT levels of PUs.
Optimal Power Allocation for Relay Assisted
Cognitive Radio Networks
L.K. Saliya Jayasinghe
, Nandana Rajatheva
Telecommunications Field of Study, School of Engineering and Technology,
Asian Institute of Technology, Klong Luang, Pathumthani 12120, Thailand
keeth.saliya@yahoo.com
, rajath@ait.ac.th
Abstract—In this paper, we study the optimal power allocation
of wireless relay nodes which are used in the secondary user
(SU) communication of a cognitive radio (CR) network. We
consider the behavior of transmitting powers of SUs where those
powers are limited to the tolerable interference as seen by the
primary user (PU) communication. To improve the performance
of the secondary communication based on minimizing the outage
probability, we re-formulate the power allocation problem with
a new set of constraints. These are obtained by considering the
co-channel interference generated by the SU communication to
the PU communication. The power allocation problem is solved
for both regenerative and non regenerative relay models under
Rayleigh fading conditions. SU communication with N number
of relays is discussed and compared. The outage probability of
SU communication is limited by the interference power threshold
(IPT) constraints of PUs and is affected significantly by the IPT
levels of PUs.
I. INTRODUCTION
Cognitive radio (CR) is a promising technology that enables
solutions for complicated problems in wireless communication
which are believed to be infeasible in the past. Demand for
data rates gradually increase due to the rapid development
of services needed which makes the efficient use of available
spectrum, a sine qua non, in wireless system implementations.
Recent surveys from the Federal Communications Commis-
sion (FCC) indicate that in about 90 percent of the time, many
licensed frequency bands remain idle [1]. The concept of CR
introduced as a method to improve the spectrum utilization
by allowing a secondary user (SU) to utilize a licensed band
when the primary user (PU) is absent.
SU transmission is possible with the same spectrum via
different types of strategies. A common approach is to dynam-
ically sense a frequency hole vacated by a PU and use that
frequency slot for communication [2]. Additionally, interesting
techniques are introduced to use the same frequency band by
controlling the power levels of the SU transmissions to limit
the interferences to PU communication [3].
In some cases PUs utilize different licensed spectrum bands
in multiple geographic areas and hence the SU communication
between those geographical areas [3] is made possible by
maintaining a certain level of interference to the PUs. How-
ever, the required SU transmitting power can be much higher
in direct communication and thus causing severe interference
to the PUs. The circumstances where the SUs limit their power
and use the same spectrum as the PUs simultaneously are
discussed in [3] where the use of a cooperative relay scheme
between the SUs to reduce SU transmitting power is proven
to be an effective way of ensuring lower interference to the
PUs [4]. The relay based transmission is introduced to the sec-
ondary communication in [4] and the positive improvements
of that method also are discussed in their research work.
It is found that cooperative relay communication enhances
the system performance, reduces unwanted interference and
saves power at the source [5]. The performance of cooperative
relay networks is discussed with different parameters and
channel environments in [6, 7] where improvements in the
overall transmission rate and the diversity are obtained. The
power allocation schemes for relays to achieve better perfor-
mance are discussed for the regenerative, non regenerative, etc.
cases in [8–10].
In cognitive radio with the relay based secondary communi-
cation, it is essential to improve the performance of secondary
system subject to pre-determined interference levels to PUs.We
should consider optimum power allocation to achieve this
objective.
To the best of authors knowledge the power allocations
problem where a relay is used in the secondary transmission is
not previously considered in the open literature. Therefore, we
study this issue in Rayleigh fading channels. To improve the
secondary communication, the power has to be distributed in
an optimal way among the source and relay nodes to minimize
the outage probability while maintaining a reliable primary
link. We formulate an optimization problem for power allo-
cation in the relays which are used in the SU communication
where we also introduce additional IPT constraints for the
SU which guarantee predetermined interference levels at the
PUs. Both regenerative and non regenerative relay models are
considered.
The rest of the paper is organized as follows. In section II,
we describe the system and the channel model. In addition to
that, the basic formulation of optimization problem is given
there. In section III, we study the case of a single relay
node for both regenerative and non regenerative cases. N relay
nodes scheme for the secondary communication is discussed in
section IV and the Numerical results are presented in section
V. Finally, conclusions are given in section VI.
978-1-4244-3574-6/10/$25.00 ©2010 IEEE
II. SYSTEM MODEL AND PROBLEM
FORMULATION
In the problem formulation, we consider a communication
system with N relay nodes and it is shown in Fig.1.
.
...
.
.
U
a
U
b
s
d
a
b
m n
r
N
r
2
r
1
Secondary transmission using Cooperative scheme
r
3
Intereferences for PUs
I
a-b
I
b-a
I
b-a
I
a-b
Fig. 1. N relay nodes used in secondary communication. Source node and
relay nodes are transmit signal with different frequency sets.
U
a
and U
b
are PUs and their coverage areas are shown as
a and b. s and d are two SUs which use relays r
1
to r
N
for
their communication. Frequency sets are selected as shown in
Fig.1 to satisfy the condition that s or d does not interfere
with their nearest PU.
I
a
: Available spectrum for s
I
b
: Available spectrum for d
I
ab
= I
a
- I
b
: Idle channel set in a, but busy in b
s to r
1
transmission uses I
ab
frequency set and r
1
to r
2
,..,
r
N1
to r
N
, r
N
to d transmissions use I
ba
frequency set.
In addition to this, we assume that the SUs can sense the
spectrum and distribute their channel state information (CSI)
to each other. SU source and destination nodes have the
capability to sense and locate the most affected PUs in their
PU coverage areas.
m and n are primary users of U
a
and U
b
. n is the most
affected user at U
b
due to the transmission of source s and m
be the most affected user in U
a
. IPT level is the highest that
can be tolerated by a PU. The transmit power of source s is
denoted as p
s
and that of relay node r
n
by p
n
. The link gain
between node i and node j is h
ij
. The IPT levels on m and n
are T
a
and T
b
. Total power allocated for source and relays is
denoted as P
T
.
Interferences from nodes which are used in the secondary
communication should fulfill the following requirements to
have stable PU communication.
p
s
h
sn
T
b
(1)
N
n=1
p
n
h
r
n
m
T
a
(2)
The signal envelopes of the links are assumed to have Rayleigh
distributions. Therefore, the Signal-to-noise ratio (SNR) of the
channel is exponentially distributed. In general, the average
SNR of the links
γ
n
can be written as γ
n
= G
n
p
n
. G
n
contains parameters such as the antenna gains, path loss,
shadowing, noise power, and similar parameters [11], and p
n
is the transmitted power of the n
th
relay.
we select the outage probability of secondary communica-
tion as our objective function and formulate an optimization
problem by considering total power constraint and IPT con-
straints.
min P
out
subject to
p
s
+
N
n=1
p
n
= P
T
p
n
P
max
: n =1, 2, ..., N
p
s
P
max
p
s
h
sn
T
b
N
n=1
p
n
h
r
n
m
T
a
Outage probabilities that we obtain for this are convex
functions and our constraints are linear. The convexity of the
feasibility set also satisfied due to linearity. Therefore, we
can solve this as a convex optimization problem and obtain
a unique solution.
III. SINGLE RELAY TRANSMISSION
Here, we consider the power allocation of the source and
the r elay node for both regenerative and non regenerative relay
systems.
A. Regenerative Relay scheme
Outage probability is given by the following equation [12],
[13],
P
out
=1 e
γ
th
(
1
G
1
p
1
+
1
G
2
p
2
)
(3)
where p
1
and p
2
are source and relay node transmit powers.
Minimizing P
out
in this case is equivalent to minimizing
γ
th
(
1
G
1
p
1
+
1
G
2
p
2
) term. Therefore the problem reduces to,
min γ
th
(
1
G
1
p
1
+
1
G
2
p
2
)
subject to
2
n=1
p
n
= P
T
p
n
P
max
: n =1, 2
p
1
h
sn
T
b
p
2
h
rm
T
a
Since this is a convex problem, Lagrangian function given as
Λ(p
1
,p
2
)=γ
th
(
1
G
1
p
1
+
1
G
2
p
2
)+μ(p
1
+ p
2
P
T
)+λ
1
(p
1
T
b
h
sn
)+λ
2
(p
2
T
a
h
rm
)+λ
3
(p
1
p
max
)+λ
4
(p
2
p
max
).
(4)
By using Karush-Kuhn-Tucker (KKT) conditions, we obtain
the solutions as follows.
Neglecting all inequality constraints,we have the following
optimal solution.
p
1
= P
T
[1 +
G1
G2
]
1
and p
2
= P
T
[1 +
G2
G1
]
1
(5)
The inequality constraints are relevant at higher P
T
values, for
lower values there is no use of those to obtain the solution.
In general we can assume both
T
b
h
sn
and
T
a
h
rm
are always less
than p
max
. Therefore we neglect p
max
and by considering the
IPT constraints, we get
p
1
=
P
T
[1 +
G1
G2
]
1
: P
T
<min[
T
b
h
sn
(1 +
G
1
G
2
),
T
a
h
rm
(1 +
G
2
G
1
)])
T
b
h
sn
: if
T
b
h
sn
(1 +
G
1
G
2
)=min[
T
b
h
sn
(1 +
G
1
G
2
),
T
a
h
rm
(1 +
G
2
G
1
)] and
T
b
h
sn
(1 +
G
1
G
2
) <P
T
<
T
a
h
rm
+
T
b
h
sn
P
T
T
a
h
rm
: if
T
a
h
rm
(1 +
G
2
G
1
)=min[
T
b
h
sn
(1 +
G
1
G
2
),
T
a
h
rm
(1 +
G
2
G
1
)] and
T
a
h
rm
(1 +
G
2
G
1
) <P
T
<
T
a
h
rm
+
T
b
h
sn
T
b
h
sn
: P
T
T
a
h
rm
+
T
b
h
sn
We can clearly see that with different P
T
values, the optimal
power allocation has different solutions. Outage probability
variation with P
T
is considered in the numerical results
section.
B. Non regenerative Relay scheme
Non regenerative relay receives the signal from source s
and amplifies and forwards it to the destination d. Outage
probability for a dual hop systems i s given by [13],
P
out
=1
2C
G
1
p
1
G
2
p
2
K
1
(
2C
G
1
p
1
G
2
p
2
)e
γ
th
(
1
G
1
p
1
+
1
G
2
p
2
)
(6)
K
1
is first order modified Bessel function and C = γ
th
or
C =
γ
th
2
+ γ
th
. Therefore the problem formulation for
non-regenerative relay is given by,
min 1
2C
G
1
p
1
G
2
p
2
K
1
(
2C
G
1
p
1
G
2
p
2
)e
γ
th
(
1
G
1
p
1
+
1
G
2
p
2
)
subject to
2
n=1
p
n
= P
T
p
n
P
max
: n =1, 2
p
1
h
sn
T
b
p
2
h
rm
T
a
We have use the following expression [14] of Bessel functions
to solve this using KKT conditions.
z
d
dz
K
v
(z)+vK
v
(z)=zK
v1
(z) (7)
We assume both
T
b
h
sn
and
T
a
h
rm
are always less than p
max
.
Therefore, we neglect the effect of p
max
constraints and the
optimal solution is given by,
p
1
=
[
G1
G2
1
(P
T
p
1
)
2
+
C
γ
th
G1
G1
K
0
(
2C
G
1
p
1
G
2
p
2
)
K
1
(
2C
G
1
p
1
G
2
p
2
)
×
(
1
p
1
(P
T
p
1
)
3
1
p
1
3
(P
T
p
1
)
)]
1/2
T
b
h
sn
P
T
T
a
h
rm
K
0
(.) is the zeroth-order modified Bessel function of the
second kind and the first expression for p
1
is obtained when
all the constraints are relaxed. The first solution is a transcen-
dental function of p
1
and therefore numerical techniques have
to be used to solve it. Techniques such as Newton algorithm
can be considered.
Additionally, the closed form solution that we have for the
regenerative model can be approximated to the non regenera-
tive case. These details are discussed in the numerical results
section.
IV. N R
ELAY TRANSMISSION
Outage probability for regenerative relay scheme
in Rayleigh faded case is given as P
out
=
1 e
γ
th
G
s
p
s
N
n=1
e
γ
th
G
n
p
n
.
Minimizing the outage probability is similar to maxi-
mizing e
γ
th
G
s
p
s
N
n=1
e
γ
th
G
n
p
n
and it reduces to minimizing
N
n=1
γ
th
G
n
p
n
+
γ
th
G
s
p
s
. P
max
constraint can be neglected without
causing much damage to original problem. This is possible,
since node powers are limited by the IPT values. Lagrangian
function is given as,
Λ(p
s
,p
n
)=
N
n=1
γ
th
G
n
p
n
+
γ
th
G
s
p
s
+ μ(p
s
+
N
n=1
p
n
P
T
)+λ
s
(p
s
T
b
h
sn
)+λ
0
(
N
n=1
p
n
h
r
n
m
T
a
)
(8)
Problem is solved using KKT conditions and the optimal
solutions have different expressions depending on P
T
and gain
parameters.
1) Case where P
T
has a lower value, both interference
inequalities do not have a contribution to the optimal so-
lution. Optimal solution given as(λ
s
=0and λ
0
=0),
p
n
= P
T
[1+
G
n
N
k=1,k=n
1
G
k
+
G
n
G
s
]
1
: n =1, 2, ..., N
(9)
p
s
= p
n
G
n
G
s
(10)
The following two inequalities are needed to be satisfied
by other parameters to obtain above optimal solution.
P
T
[1 +
G
n
N
k=1,k=n
1
G
k
+
G
n
G
s
]
1
G
n
G
s
<
T
b
h
sn
(11)
N
n=1
h
r
n
m
P
T
[1+
G
n
N
k=1,k=n
1
G
k
+
G
n
G
s
]
1
<T
a
(12)
2) Case where the p
s
is limited by the IPT threshold. Then
the source power reaches its maximum power
T
b
h
sn
and
node powers are given by (λ
s
=0and λ
0
=0),
p
n
=(P
T
T
b
h
sn
)[1 +
G
n
N
k=1,k=n
1
G
k
]
1
(13)
p
s
=
T
b
h
sn
(14)
3) Both m and n users sense maximum interference from
the source and relay nodes, when both IPT constraints
are satisfied with equality (λ
s
=0and λ
0
=0). P
T
has no effect in the optimal solution.
p
s
=
T
b
h
sn
(15)
p
n
= T
a
[h
r
n
m
+
G
n
N
k=1,k=n
h
r
n
m
h
r
k
m
1
G
k
]
1
(16)
4) Most probable case in a real environment is where all
relay nodes get power levels to interfere primary user m.
The p
s
does not reach its maximum. In other words, this
simply means λ
s
=0and λ
0
=0. The closed form
expressions are not available for this and the following
equations are obtained by simplifying KKT conditions.
p
n
= p
1
[
G
n
G
1
h
r
n
m
h
r
1
m
+
G
n
G
s
p
2
1
p
2
s
(1
h
r
n
m
h
r
1
m
)]
1/2
(17)
The above can be simplified into p
n
= K
n
p
1
and K
n
is a function of p
1
and p
s
. Then the following two
equations are dependent only on p
1
and p
s
. Therefore
the optimal solutions can be obtained by carrying out a
numerical technique.
p
1
[h
r
1
m
+
N
i=2
h
r
i
m
K
i
]=T
a
(18)
p
1
[1 +
N
i=2
K
i
]+P
s
= P
T
(19)
V. NUMERICAL RESULTS
Numerical results are obtained for three different instances.
Power allocation with and without IPT constraints and uniform
allocation are considered. Optimal outage probabilities for
these cases are plotted with total power P
T
.
In addition to that, numerical results are obtained for both
non regenerative and regenerative cases by assuming certain
parameters. We take γ
th
=3, G
1
=1, G
2
=10, T
b
=10,
h
sn
=0.2 , T
a
=20and h
rm
=0.2. Also in the equal
power allocation case, powers are equally divided between the
source and the relay node. Fig.2. shows the outage variation
with the total power f or regenerative relay based secondary
communication. The case without IPT constraints is also
plotted in t he same graph. Fig.3 describes the outage variation
of regenerative and non regenerative models.
0 5 10 15 20 25
10
−2
10
−1
10
0
Total power,[dB]
Outage Probability
Optimal − With IPT
Optimal − Without IPT
Equal power − Without IPT
Fig. 2. Single regenerative relay based secondary communication outage
probability behavior
0 5 10 15 20 25
10
−2
10
−1
10
0
Total power,[dB]
Outage Probability
Non Regenerative,no IPTs
Regenerative,no IPTs
Non Regenerative,IPTs
Regenerative,IPTs
Fig. 3. Outage probability comparison between non regenerative and
regenerative relay cases
0 5 10 15 20 25 30 35
10
−3
10
−2
10
−1
P
total
dB
Bit Error Rate
With IPT constraints
Without IPT constraints
Fig. 4. Average BER of a regenerative relay system with BPSK modulation.
With and without IPT constraints cases are considered.
Outage probability reduces with the total power P
T
in each
case that we consider here. Interestingly, in the cognitive case,
the outage probability does not reduce below a certain level
with P
T
. This happens due to the IPT constraints that we
introduce into the optimization problem. When the secondary
communication reaches its minimum outage probability, PUs
experience the highest interference from the secondary trans-
mission. Therefore, there is a limit in the outage probability
that the s econdary transmission can achieve. Also by referring
to Fig.3, we can see that the regenerative model can be
approximated to the non regenerative case. Plots obtained for
both are very much related.
Fig. 4 compares the average bit-error rate (BER) for the
regenerative relay with the binary phase shift keying (BPSK)
modulation. Here we have consider the optimal power allo-
cation cases with and without IPT constraints. It is clear that
have BER also behaves similar to the outage probability as
seen in Fig.4.
Fig. 5 shows the multi-hop transmission comparison up
0 5 10 15 20 25
10
−2
10
−1
10
0
Total power,[dB]
Outage Probability
Four relays
Three relays
Two relays
Single relay
Fig. 5. Outage probability comparison between N realy model with 1,2,3
and 4 relays
0 5 10 15 20 25
10
0
Total power,[dB]
Outage Probability
Optimal power allocation
Equal power allocation
Optimal power allocation − no IPTs
Fig. 6. Outage probability of comparison with 3 series relays. Optimal
power allocation with IPT constraints, equal power allocation and optimal
power allocation without considering IPT constraints compared
to four relays. Relays are in series and the regenerative
relay model with Rayleigh fading channel environment is
selected for the comparison. When the number of relays are
increased, outage probability becomes higher. Fig. 6 compares
the outage behavior in the three relay nodes model. Optimal
power allocation s hows much better outage performance when
compared to equal power allocation and the IPT constraints
effect is visible as in the previous case.
VI. CONCLUSIONS
In this paper, we consider the optimum power allocation
for relay based secondary transmission schemes. Cooperative
relay network cases are reformulated by introducing additional
interference power threshold constraints. These are convex
optimization problems and we consider the outage probability
of the secondary communication as the objective function.
Then the problem is solved for the single relay model. Both
regenerative and non regenerative cases are considered where
they behave in a similar manner even though the objective
function has different expressions.
It is observed from the numerical results that the outage
probability cannot be reduced after a certain level, even
though there is sufficient total power. Optimal solutions for
the general case with N relay nodes are obtained. They have
different expressions depending on the other parameters like
channels gains and total power of relay nodes. Performance
of the secondary user communication improves with the stable
primary user transmission at the same time.
Finally, by considering results that we have, the optimal
power allocation guarantees that the primary user will not be
affected due to the secondary transmission while the secondary
user achieves its maximum possible performance under some
limitations.
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    • "In this study, we address these two issues of interference minimization and SU data rate maximization in an integrated framework. Unlike the popular interference management solutions in CRNs [11][12][13][14], focusing only on transmit power control, we adopt a cross layer approach. The cross layer approaches find their basis in combining the principle of layered design of network functionalities with the idea of designing greater interactions among layers in the network protocol stack. "
    [Show abstract] [Hide abstract] ABSTRACT: An opportunistic routing problem in a cognitive radio ad hoc network is investigated with an aim to minimize the interference to primary users (PUs) and under the constraint of a minimum end-to-end data rate for secondary users (SUs). Both amplify-and-forward (AF) and decode-and-forward (DF) relaying techniques are considered for message forwarding by SU nodes in the network. Unlike popular transmit power control based solutions for interference management in cognitive radio networks, we adopt a cross layer approach. The optimization problem is formulated as a joint power control, channel assignment and route selection problem. Next, closed form expression for transmission power is derived and corresponding channel selection scheme and routing metric are designed based on this solution. The proposed route selection schemes are shown to depend not only on gains of the interference channels between SUs and PUs but also on the values of the spectrum sensing parameters at the SU nodes in the network. Two distributed routing schemes are proposed based on our analysis; (i) optimal_DF and (ii) suboptimal_AF. The routing schemes could be implemented using existing table driven as well as on demand routing protocols. Extensive simulation results are provided to evaluate performance of our proposed schemes in random multihop networks. Results show significant reduction in PUs' average interference experience and impressive performance as opportunistic routing schemes can be achieved by our schemes compared to traditional shortest path based routing schemes. Performance improvement is also reported over prominent recent schemes.
    Full-text · Article · Dec 2015
    • "Joint relay selection and power allocation scheme was proposed in [5] to maximize system throughput with limited interference to primary used in cognitive radio system. The optimal power allocation (OPA) technique was addressed in [6] and [7]. The outage performance of single relay networks was researched in [8]. "
    [Show abstract] [Hide abstract] ABSTRACT: In this paper, we investigate the outage performance of multi-node relay network under equal power allocation (EPA) scheme. Due to the mobility of relay nodes, we proposed to design a method that considers random relay location based on random model. We conduct deep experiments which demonstrate that there exists optimal relay location to minimize the outage probability of multi-node relay networks. Finally, simulation results show that the outage performance of the multi-node relay network is closely related to the relay location.
    Full-text · Article · Aug 2013
    • "In [3], OFDM based hybrid power allocation and in [4] optimal and suboptimal power loading algorithm in different OFDM subcarriers are proposed. Relay in various forms, like maximizing signal to noise ratio (SNR) on its path selection [5], using decode and forward (DF), amplify and forward (AF) in OFDM system with a sum-power constraint [6], power allocation incorporating dynamically changing environment [7] , cooperative relay schemes (CRS) to increase signal-tointerference noise ratio (SINR) at secondary receiver [8] and many others have been explored in CR research. The selection of relay strategy depends upon the channel condition and the performance criterion. "
    [Show abstract] [Hide abstract] ABSTRACT: This paper proposes power allocation algorithm in orthogonal frequency division multiplexing (OFDM) based cognitive radio (CR) system using decode and forward (DF) relay. It is reported in the literature that both classical i.e. uniform power loading scheme and water filling methods that allocate power on OFDM subcarriers based on the channel gain are not effective for cognitive radio network (CRN) as the schemes introduce large interference to primary user (PU). To this aim, the present work proposes a simple, computationally efficient yet effective power loading scheme that maximizes the transmission capacity of CR while keeping the interference introduced to the PU below acceptable limits. To meet the objective, proposed power allocation to subcarriers not only considers channel gains but also the relative distances between CR subcarriers and PU band. This capacity performance is further improved significantly using DF relay, where our research direction focuses on optimal sharing of power between CR and relay using maximal ratio combiner (MRC) at destination receiver. Performance for the proposed power allocation schemes are compared with OFDM based hybrid power allocation as well as joint subcarrier and power adaptation methods reported in the literature. Numerical results show that the relative gain on CR's capacity are 3.7 times and 2.3 times, respectively compared to the optimal and hybrid OFDM power allocation schemes, while for interference introduced to PU is set at 3 times 10-6 (in watt). Finally, a few related research problems are also highlighted as future scope of works.
    Full-text · Article · Dec 2012
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