Content uploaded by Asma Bagheri
Author content
All content in this area was uploaded by Asma Bagheri on Nov 14, 2020
Content may be subject to copyright.
1
Abstract-This paper deals with the issue of reducing energy
consumption and evaluating the network lifetime in a wireless
cognitive sensor network (WCSN) composed of randomly-
distributed sensors to perform multi-channel cooperative
spectrum sensing (MCCSS). More precisely, the paper presents a
probabilistic approach for analyzing the WCSN lifetime whereas
the detection quality is also considered. To this end, it is assumed
that both the number of sensors and primary users in the area
follow two-dimensional Poisson distributions, and accordingly,
the detection probability and false alarm probability for the
sensors are calculated, statistically. Next, the number of required
sensors for MCCSS is minimized under the global probability of
detection (GDP) and the global probability of false alarm
constraints. Then, the tail probability of the lifetime by individual
sensors is found based on the average sensors' energy
consumption. After that, a tail probability for the network
lifetime is calculated through statistical analysis, and it is used to
obtain an analytical expression for the complementary
cumulative density function (CCDF) of the network lifetime.
Using the CCDF, one can find the probability that the network
lifetime extends until a given time if the minimum number of
sensors is used for satisfying the detection quality and the sensors
are distributed randomly. Finally, computer simulations using
the Monte-Carlo method are used to verify the achieved results.
Keywords—Cooperative spectrum sensing, Lifetime, Multi-
channel sensing, Wireless cognitive sensor network.
I. INTRODUCTION
ireless sensor network is a fast-growing technology, and
the growing interest is attributed to the new and wide
range of applications enabled by these networks. A
considerable application is using the sensor network to
monitor the spectral activities of some primary users (PUs) [1]
[2], i.e. Wireless Cognitive Sensor Network (WCSN). It is
composed of tiny sensor devices with the capability to sense
the underutilized spectrum bands, to detect the spectral
activities of the PUs [2]. This technology expands the
spectrum utilization by allowing some secondary users (they
might be the sensors or the other users in a secondary network
using the sensing results, e.g. coexistence of WCSN with
another secondary network in ISM band [3]) to access the
spectrum opportunities without affecting the PUs
transmissions [1].
*Corresponding author
Since WCSN relies on the spectrum sensing to detect the
spectral activities of some PUs, the following two metrics are
mainly used to evaluate the sensing quality: i) detection
probability (DP), i.e. the probability of detecting the PU's
signal if the PU is active actually [4]., and ii) false alarm
probability (FP), i.e. the probability of detecting a signal when
no PU is transmitting on the spectrum [4]. DP is compromised
if only one sensor senses a PU (e.g., the received signal from
the PU experiences high path-loss) [4]. To improve the DP,
cooperative spectrum sensing (CSS) is an effective method. In
a centralized CSS method [4], a fusion center (FC) combines
the detection results from multiple sensors to sense the PUs. It
has been shown that increasing the number of cooperative
sensors increases DP, although it increases the FP, too [5].
However, CSS causes more energy consumption due to
using multiple sensors for sensing a PU [6]. Since the sensors
are usually battery-driven with limited energy due to their
battery size and weight limitations [6] a trade-off exists
between the energy consumption and the detection quality in
CSS scenarios. Therefore, the lifetime of the WCSN,
performing CSS, is a considerable issue. In [7], the design
factors and challenges of spectrum sensing by the cognitive-
radio-based Internet of Thing (CR-based IoT), as an
application example of WCSN, are discussed. This survey
demonstrates that since the ultimate goal is to design light-
weight CR-based IoT devices with a compact size and limited
power, improving the energy efficiency of the devices is a
vital research direction in this area since most of IoT devices
are battery power terminal with a limited lifetime. Also, in [8],
an overview of the recent researches is presented that
addresses the energy efficiency of CSS methods in cognitive
radio networks. Since recharging or replacing batteries are not
possible in a majority of applications, a reduction in the
number of sensors has been proposed as a solution in several
works on WCSNs. One of the most regarded ways to trade off
the detection quality for a long lifetime is to select or to
distribute the sensors based on the signal-to-noise ratio (SNR),
in the PUs-to-sensors links [6]. However, it depends on the
full knowledge about PUs-to-sensors distances, and also, the
radio propagation conditions to estimate the SNR. In some
applications, such as military uses or emergency applications,
it is not possible to know the information. [9] thoroughly
describes spectrum sensing approaches that require no prior
knowledge of the PUs' signal characteristics, in cognitive
Statistical Analysis of Lifetime in Wireless
Cognitive Sensor Network for Multi-channel
Cooperative Spectrum Sensing
Asma Bagheri1,*, Ataollah Ebrahimzadeh2
1,2Department of Electrical & Computer Engineering, Babol University of Technology, Babol, Iran
(e-mail: 1bagheri.asma84@yahoo.com, 2abrahamzadeh@gmail.com ).
W
2
radio networks. The tutorial provides a thorough background,
major implementations, and limitations of the spectrum
sensing approaches using an energy detector. However, this
work focuses on the detection quality and throughput and it
does not cover the energy limitations and lifetime issues. In a
WCSN, the transmission of all approximation SNR results to
the FC consumes much of the spectral and energy resources.
Furthermore, it is not always possible to estimate SNR
accurately. Also, the FC has to select sensors and order the
selected nodes to perform sensing, in each sensing time.
Hence, it causes additional processing and messaging cost that
may reduce the network lifetime. Therefore, a possible
solution is determining the least number of sensors for sensing
the PUs, based on the statistical distribution of nodes and the
network conditions. In these cases, the network lifetime is a
random variable; hence, determining its distribution can be
useful for analyzing the WCSN lifetime.
Motivated by the above discussion, the major contributions
of this paper are summarized as follows:
This paper assumes a WCSN performing multi-channel
CSS (MCCSS) in which the required number of sensors is
determined as a function of the PUs number. We find a
closed-form expression for the minimum number of
sensors under the detection quality constraints. Moreover,
we assume that there is no information about the position
of PUs, the PUs-to-sensors distances, the radio propagation
conditions, and the SNR in the PUs-to-sensors links. The
assumed model is a complicated problem that has not been
considered in the previous works, to the best of our
knowledge. To this end, we model the number of sensors
and PUs as two-dimensional Poisson distributions and
compute the minimum number of nodes according to both
the sensors’ average detection probability and the sensors’
average false alarm probability.
Then, in order to the reduction in energy consumption and
cost, a WCSN is assumed with the least required number
of sensors. We find a closed-form expression for the tail
probability of the lifetime by individual sensors. Finally,
for the first time, we calculate a complementary
cumulative density function (CCDF) for the WCSN
lifetime.
Computer simulations using the Monte-Carlo method are
conducted to evaluate the obtained results.
The rest of the paper is organized as follows. Section II
reviews the related works. Section III expresses the system
model. Section IV discusses the model of sensors' energy
consumption. Section V presents the statistical analysis for
determining the minimum number of sensors needed for
performing MCCSS under detection quality constraints.
Section VI obtains a closed-form distribution for the WCSN
lifetime. The simulation results are conducted in Section VII
and finally, the conclusions are presented in section VIII.
II. RELATED WORKS
There have been extensive works focused on reducing the
energy consumption of CSS and extending the lifetime of
WCSNs. Regardless of sensing only one PU or multi-channel
scenario, one of the main approaches is reducing the number
of sensing nodes [6], [8]. The number of cooperative sensors
may be determined in many ways. These ways may be
classified into three main approaches:
In the first approach, known as sensor selection, only a
subset of sensors is selected for sensing. The other sensors are
not allowed to sense the spectrum, and they turn to the sleep
mode to save energy [10]-[14]. In [10], sensors are selected
based on the DP and FP to use the lowest number of sensors to
extend the network lifetime. [11] presents an energy-efficient
heuristic algorithm for sensor selection based on the sensors'
energy and detection qualities. Also, [12] and [13] propose
lifetime maximization algorithms for CSS in a WCSN, for
sensing one channel and MCCSS scenarios, respectively. In
these works, the sensor selection is done based on the known
PUs-to-sensors distances and radio propagation conditions.
In the second approach, known as censoring, all nodes
make local sensing observations but some of them cannot
report this information. In this technique, it is possible to
censor nodes during the sensing process, i.e., based on the up-
to-date local sensing results [14]. Naturally, this approach
needs to know information about PUs-to-sensors distances and
radio propagation conditions for better performances.
Clustering is the third approach to decrease the energy
consumption in WCSNs, especially by selecting some nodes
as cluster heads (CHs) by the goal of energy efficiency and
lifetime maximization. For instance, LEACH is one of the
famous clustering protocols to extend a WCSN lifetime [3]. In
LEACH, the CH is elected in a probabilistic manner and tries
to balance the energy consumption at each sensor on a rotation
basis. However, it does not consider the distribution of sensors
and their remaining energy. LEACH-C is another protocol to
elect the CH by using the location information of each sensor
in a controller center [3]. However, it increases the network
overhead since all the sensors are required to send their
location information to the center, and also, it leads to more
energy consumption. In [15], a clustering method is used for
energy efficiency. The goal is achieved by activating only one
subset of the cluster for CSS while putting the rest of the
subsets into sleep mode. However, the active sensors are
chosen considering their respective time durations for sensing
based on their received signal-to-noise ratio (SNR). [16], [17],
and [18] are other examples of using the clustering approach
to extend the network lifetime. All the mentioned latter works
have used the information about either PUs-to-sensors
distances or radio propagation conditions.
Some other works have focused on optimizing the other
parameters for CSS, rather than the sensor selection or
clustering, to lifetime maximization, such as [19] proposes a
joint optimization of the sensing time, the detection threshold
and the length of symbol sequence to maximize the energy
efficiency of WCSNs. However, they assumed a completely
different system model using a soft fusion rule, and also, the
proposed solution based on the known information about PUs-
to-sensors distances and radio propagation conditions.
More works related to lifetime maximization or energy-
efficiency in CSS for WCSNs can be found in a survey by K.
3
Cicho´n et al. [6]. Reducing the number of sensors or
determining the proper nodes is convenient for lifetime
extending in WCSNs providing the SNR, in the PUs-to-
sensors links, is known. These methods need to know the PUs-
to-sensors distances and radio propagation conditions.
In cases that there is no information about PUs-to-sensors
distances and radio propagation conditions, the number of
sensing nodes can be chosen through statistical analysis.
Therefore, the network lifetime is a random variable, and the
energy reduction or lifetime extending solutions proposed in
previous works cannot be used. In [20], to maximize the
energy efficiency of CSS, the minimum number of sensors
needed for spectrum sensing is calculated to guarantee the
desired accuracy of sensing results. However, the main goal of
the paper is a security enhancement, and they analyze the
trade-off between energy efficiency and security. In [21], the
minimum number of sensors required for satisfying the
desired detection probability is studied, assuming only one PU
in a known position.
To the best of our knowledge, there is a gap study to
provide a closed-form expression for the minimum number of
sensors as a solution for energy reduction if there is no
information about the position of sensors and PUs. Also, a
statistical analysis of a WCSN lifetime with the described
model has not been investigated. There are the following
differences between the paper and other related works:
First, this paper assumes a MCCSS scenario, i.e. there is
more than one PU under sense. Also, this paper assumes
the sensors just can sense one channel at the same time, but
a sensor can sense different channels in different sensing
times. This assumption is due to the hardware (energy and
cost) limitations of sensors in sensing more than one
channel [22]. Hence, the system model in this paper is
completely different from [20] and [21].
Second, this paper considers scenarios that there is no
information about the SNR in the PUs-to-sensors links.
Therefore, the energy reduction or lifetime extending
solutions proposed in the mentioned related works ([10]-
[19]) cannot be used in these cases.
Third, however, in [20], a minimum number of sensors is
calculated for CSS but there are main differences between
this paper and [20]. This paper uses the OR rule for
combining the detection results of sensors, but [20] uses
the ''K out of N''. The main goal of [20] is security
enhancement against attacks from some nodes that send
false sensing results to mislead the CSS. Unlike [20], this
paper considers both the detection probability and false
alarm probability for the desired detection quality; hence,
the problem formulation in this paper is completely
different from [20]. Also, in this paper, the problem is
statistically analyzed and a closed-form expression for the
minimum number of sensors needed for sensing is
determined but [20] finds the solution by exhaustive
searching, and it does not calculate a specific expression
for the number of required sensors.
Forth, however, in [21], the minimum number of sensors is
calculated for satisfying the desired detection probability
for sensing only one channel with one PU in a known
position, but the problem is complicated and a numerical
method is used for solving the problem. Unlike [21], this
paper assumes a MCCSS scenario in which the positions
of PUs are not known, which makes the problem more
complicated. However, this paper does not use
approximation or numerical methods to compute the
results and determines a closed-form expression for the
minimum number of sensors. Furthermore, this paper
analyzes the CCDF of lifetime in a WCSN which has not
been investigated in the previous works.
III. SYSTEM MODEL
We consider a WCSN with an FC located in origin, and the
sensors and PUs are distributed randomly in a circular region
with radius R. It is assumed that each PU uses one of the equal
bandwidth licensed channels for transmitting, and the PUs
transmit signals with the same modulation and power. The
number of sensors and PUs in every selected part of the region
are random variables modeled by two-dimensional Poisson
distributions with parameter and , respectively [23].
Table 1 List of notations and their definitions
N
Total number of sensors
M
Number of channels/PUs
The average number of sensors per unit area
The average number of PUs per unit area
The signal energy in channel m measured by sensor n
The received signal from the channel m that is observed by the sensor n
K
The number of samples
Γ
The predefined threshold of the energy detector
Nyquist sampling
Sensing time
The hypothesis that the PU is not transmitting
The hypothesis that the PU is transmitting
PU signal power
PU signal with variance over channel m
PU-sensor channel gains
The noise of PU- sensor channel
The distance between the n-th sensor and the FC
d
The random variable denoting the distance between each pair of the sensor-PU
The network lifetime random variable
Energy for the electronic circuits
Consumed energy for sensor n
/
Sensing / Transmission energy for sensor n
Amplifying coefficient
/
GDP/GFP for the m-th channel
The PU signals wavelength
/
DP/FP of n-th sensor about m-th PU
The lower bound for acceptable GDP
The decision bit of the sensor n about the channel m
The upper bound for acceptable GFP
The random variable denoting the lifetime of a sensor n
The initial energy of sensors
The distance of the first nearest sensor to a PU
The number of sensors in a circle with the radius
The number of performing CSS for a sensor between the times of MCCSS
A minimum distance that if a sensor is located in around the PU, it can detect the PU signal with probability higher than
The threshold level that if a sensor to the FC distance is lower than it, the sensor lifetime is greater than with probability upper than
4
In [24] and [25], it has been shown that if the total number of
nodes in an area is given and these nodes are uniformly
distributed over the area, then the number of nodes in every
selected part of the area is a Poisson random variable. A list of
notations used throughout the paper is provided in Table 1. It
is assumed that the sensors have an energy detector (ED), and
denotes the detector threshold. In this scheme, the signal
energy in a channel m is measured by a sensor n as:
, in which denotes the k-th sample
of the received signal from the channel observed by the
sensor. The number of samples is denoted by K and is
calculated as the product of the sensing time and the sampling
rate of the energy detector (ED). Then, the signal energy is
compared with , to generate one decision bit, i.e. . It
shows the detected status of the PU by the sensor, as follows:
(1)
If the decision bit is one, it states that the PU is transmitting on
the channel, and if it is zero, it means that the PU is not
transmitting. Two hypotheses are defined for the absence and
the presence of the PU signals. The first, i.e. , says that the
PU is transmitting, and the second, i.e. , says that the PU is
not transmitting. Hence, the is written as:
(2)
where denotes the k-th sample of the PU signal. It is
assumed that is an i.i.d random Gaussian process with
zero mean and variance . Also, the additive white Gaussian
noise with zero-mean and variance is denoted by . It
is assumed that and are independent. The channel
gain between the m-th PU and the n-th sensor is denoted by a
random variable . It describes the channel path loss [12].
Therefore, if the signal wavelength and transmission power of
the PUs are denoted by and , and is a random variable
denoting the distance between each pair of the sensor-PU, the
sensor received SNR from the PU is obtained as [13]:
(3)
There are two metrics for the sensing quality of a sensor:
the false alarm probability (FP) and the detection probability
(DP). The FP is the probability that a sensor detects a signal if
the channel is free actually. It is calculated as [13]:
(4)
where denotes the complementary distribution function.
It is observed that the FP only depends on the noise power if
the detector threshold and the number of samples are fixed.
The DP states the probability that a sensor detects the PU
signal if the PU is transmitting actually. Under the assumed
model, if a PU is transmitting on a channel, a sensor detects
the PU signal if the received SNR is higher than , i.e.:
(5)
Now, we define a sensor DP about the status of channel m as:
(6)
Due to the noise and attenuation effects, we assume a CSS
scheme [4], in which the sensors send their decisions to the
centrally located FC. The FC fuses the decision bits to make
the final decision about the busy or idle status of the channels.
Because of hardware limitations of sensors in sensing more
than one channel [22], in each of the sensing durations, all the
nodes should be classified into disjoint groups and every
group of sensors sense only one channel. In this paper, the
cooperative sensors for sensing every channel m are already
specified and inserted in a set
1
. The sets are non-
overlapping. We assume the FC uses the logic OR rule to fuse
the sensors' decision bits (For a comparison on the fusion rules
see [26]). Thus, the global detection probability (GDP) and the
global false alarm probability (GFP) for a channel m are
calculated, respectively.
, (7)
, (8)
where shows the number of sensors in the set .
Therefore, using OR fusion rule, if the number of cooperative
nodes increases, both the GDP and GFP increase. The higher
GDP is more satisfying, but the higher GFP is not, because it
leads to a lower ability to detect empty channels which
negatively reflects the throughput of the network
2
. Therefore,
we prefer the least number of sensors for CSS; meanwhile, it
leads to lower energy consumption and longer lifetime [4].
IV. ENERGY MODEL
In the WCSN, the sensor energy consumption mainly
depends on two factors: the sensing energy, and the
transmission energy. Therefore, the energy consumption of a
sensor n is calculated as [13]:
(9)
The sensing energy, i.e. , is the amount of energy that a
sensor consumes to sense a channel and to make its decision
about the status of the channel. It is assumed that is
constant, and it is the same for all sensors (It is assumed that
all sensors pick samples with a similar sampling rate in a fixed
sensing duration, although the results can be extended to the
different assumptions such as different sensing times or
different bandwidth for different channels). The denotes
the consumption energy to send the sensor's decision bit to the
FC reliably, and it is calculated as [13]:
, (10)
where , , and denote the used energy for the
electronic circuits of a sensor transmitter, the amplifying
coefficient, and the n-th sensor to FC distance, respectively.
V. THE PROBLEM OF LEAST NUMBER OF SENSORS
First, this paper calculates the minimum number of sensors
1
This assumption can be extended to the other scenarios whether the
sensors can select the under monitor channel or the sensors can sense more
than one channel in a sensing time, easily [5]. However, the paper assumes the
more practical scenario.
2
Since using OR fusion rule increases the GFP which negatively reflects
the throughput of the network, finding a solution for fusing the decision bits
can be considered as a future work.
5
for the MCCSS. It should satisfy constraints on the GDP and
GFP about the PUs (which are distributed uniformly over the
network). However, if the PUs' positions are not known,
determining the GDP, and therefore, the minimum required
number of sensors is complicated [21]. This paper presents a
novel and easy-to-solve solution for the problem. First, we
calculate the least number of sensors for sensing only one
channel such that if a PU is located at each point of the area,
the GDP and GFP satisfy some constraints. Then, we extend
the results to calculate the least number of sensors for the
MCCSS. We present a statistical analysis for the detection
quality of sensors and also, the network lifetime. To this end,
we model the number of sensors and PUs as two-dimensional
Poisson distribution and the required number of sensors is
calculated from the direct definition of DP with respect to the
sensors' distances from the PUs, which are random variables,
in (6).
A. The least number of sensors for sensing one channel
In this section, the least number of sensors for sensing only
one channel is determined, such that if a PU is located in each
point of the area, the GDP is greater than a predefined
threshold ; meanwhile, the GFP is lower than a predefined
threshold . The problem is formulated as follows:
Problem 1:
subject to;
1. (11-1)
2.
(11-2)
From (4) and (8), it is concluded that the does not
depend on the sensors position and their distances from the
PU, the first constraint is easily converted to:
(12)
It describes an upper bound for the number of sensors.
However, the second constraint complicates the problem
because it depends on the sensors' position and their distances
from the PU [21]. Now, we propose a novel approach to find a
solution more easily. To this end, we define an alternative
problem. The problem determines the minimum number of
sensors such that if a PU is located in every point of the area,
there is at least one sensor that its DP about the PU is greater
than . It ensures that the GDP of fusing the sensors' decision
bits in the FC is greater than (using the OR rule in (7)).
Now, a minimum distance, i.e. , for sensors to a PU is
defined such that if a sensor is located in around the
PU, it can detect the PU signal with probability greater than :
(13)
Now, using the properties of the Poisson process [25], if the
nearest sensor to the PU is located in a distance lower than
with probability greater than , at least one sensor detects the
PU signal with DP higher than . Then, we have:
, (14)
where the random variables and denote the distance of
the first nearest sensor to the PU and the number of sensors
located in a circle with the radius around the PU,
respectively. Also, shows the average number of sensors
per unit area and its minimum is calculated as:
(15)
Hence, if a PU is located in each point of the area, the DP of at
least one sensor is greater than , if the minimum number of
sensors over the network is calculated as [24]:
(16)
Therefore, from (12) and (16) a solution is obtained as:
(17)
Therefore, if the number of sensors calculated from the
above equation and these sensors randomly distributed in the
area, the GDP about a randomly located PU is higher than .
B. The least number of sensors for the MCCSS
In this section, the least number of sensors for the MCCSS
is determined, such that if there are M PUs in every desired
point of the area, the GDP about the PUs is greater than ;
meanwhile, the GFP is lower than . Therefore, the problem is
formulated as follows:
Problem 2:
subject to;
1. (18-1)
2. (18-2)
The first constraint does not depend on the number of PUs,
hence it is easily solved such as (12), and it describes an upper
bound for the number of sensors that cooperatively sense a
channel. In practice, the PUs might be anywhere over the area;
hence the positions of PUs are independent. Therefore, for the
second constraint, we use the property of the Poisson process
that if more than one point is selected in an area, the
probability of locating one arrival around all the points is
independent [25]. Therefore, the probability of locating at
least one sensor in a distance lower than around all the
PUs is computed as:
(19)
This probability should be greater than , hence the least
required average number of sensors per area, is calculated as:
, (20)
and the number of cooperative sensors for a WCSN over an
environment with area S is calculated, from (12) and (20), as:
(21)
If the number of sensors, calculated from the above
equation and these sensors randomly distributed over the area,
then the GDP about all the PUs, that may be located in each
point of the environment, is higher than . It is noted that we
6
round up the number of sensors to the nearest number (the
nearest coefficient of M). In practice, the sensors are randomly
divided into M clusters, and every cluster cooperatively sense
one of the PUs. This scheme is used to mitigate the limited
ability of tiny sensors in sensing more than one channel in a
desired sensing time. Therefore, we calculate the minimum
required sensors for sensing every one of the channels as:
(22)
Therefore, the minimum number of sensors for sensing all
the channels is calculated, practically, as follows:
(23)
VI. THE LIFETIME DISTRIBUTION ANALYSIS
In the previous section, a solution for the minimum number
of sensors for the MCCSS was presented, such that the GDP
and GFP satisfy the constraints. In this section, a closed-form
expression for the probability distribution of the network
lifetime is calculated, due to statistical analysis, if the number
of sensors is obtained from (23). The network lifetime is
defined as the number of iterations in which all the sensors are
kept alive (i.e. iterations in which the MCCSS is performed
with the desired GDP and GFP.) multiplied by the duration
between the sensing periods. Here, it is assumed that the
MCCSS is performed continuously and at constant intervals;
hence the network lifetime is plotted as the number of
iterations in which the MCCSS is performed with the desired
GDP and GFP.
First, we calculate the probability distribution of lifetime
for a sensor over the network, and then the network lifetime
distribution is obtained. Due to the random position of sensors
on the area, the consumption energy, and then the lifetime of
sensors is a random variable. The random variable denotes
the lifetime of a sensor n, and the probability that the sensor
lifetime is greater than a constant is calculated as:
, (24)
where denotes the number of times that the sensor has
performed sensing between the times of performing the
MCCSS. This paper assumes that because the least
number of sensors is assumed and all the sensors participate in
the MCCSS
3
. Also, and denote the initial energy and
consumption energy of the sensor n, respectively. The is
calculated from (9) and (10). Therefore, the tail probability in
(24) is calculated as:
(25)
The result shows that the probability that the sensor to the
3
This assumption can be extended to a scenario in which the number of
sensors is more than the least required number. Under that assumption, in each
of the sensing durations, a minimum required number of sensors are selected
for sensing and the other sensors keep silent in order to save energy.
FC distance is lower than a threshold, is equal to the
probability that the sensor lifetime is greater than . We call
the threshold distance as :
(26)
Because the position of the sensors over the network was
modeled as a Poisson process with parameter , the distance
of the sensors from the origin of the network is an Exponential
distribution random variable with parameter [23] [25].
Now, we calculate a closed-form expression for the sensor
lifetime distribution as:
(27)
For calculating the network lifetime distribution, it is
emphasized that the network lifetime is the number of times
that the MCCSS is performed with and
about all the PUs. Therefore, the network lifetime is the time
until the first sensor is off. Because if one sensor is off, the
number of live sensors is lower than the minimum number of
nodes needed to guarantee to perform the MCCSS with the
desired GDP and GFP. Hence, the network lifetime is a
random variable denoted as , and the probability that it is
greater than a constant is calculated as:
, (28)
in which is the random variable denoting the lifetime of a
sensor , and is another random variable
denoting the lifetime of a sensor with the shortest lifetime.
Using the fact that the sensors lifetime are independent
random variables, and using (27), the network lifetime tail
probability is calculated as:
(29)
Therefore, a closed-form expression for the WCSN lifetime
distribution is calculated as:
, (30)
when the average number of sensors per unit area is , and
the number of sensors, N, calculated from (23).
VII. SIMULATION RESULTS
In this section, the obtained results for the minimum
number of sensors, and also, the distribution for the network
lifetime are verified through computer simulations using
MATLAB. Monte-Carlo method is used with 10000 number
of iterations. A circular region with a radius of R is assumed in
which an FC is located in the center, the sensors and PUs are
distributed uniformly, in which the number of sensors is
determined from (23) and the number of PUs varies from one
to ten. The IEEE 802.15.4/Zigbee is used for the cognitive
sensors [27]. The Nyquist sampling frequency for ED is
assumed. The other parameters are presented in Table 2.
Table 2 The values of simulation parameters [27]
=20mW
7
It is noted that this paper determines the least number of
sensors for satisfying the detection quality. Furthermore, it
statistically analyzes the CCDF of the WCSN lifetime. To the
best of our knowledge, determining a closed expression for the
least number of sensors needed for CSS on multiple channels,
and the CCDF of lifetime in a WCSN has not been
investigated in the previous works. Also, unlike [21], this
paper assumes multiple PUs with unknown positions. Thus,
we compare the results with [21], assuming a similar scenario
with one PU.
First, the minimum number of sensors, required for
satisfying the constraints on the GDP and GFP, are plotted in
Fig.1, versus the number of channels for two different
measures of the ED thresholds () and different constraints on
the GDP. The minimum number of sensors plotted in this
Figure is calculated from (23). This plot indicates that the
minimum required number of sensors increases when the
number of PUs goes up. However, it illustrates that the
presented expression for the minimum number of sensors does
not have a linear relation with the number of PUs. This
relation could be explained by the fact that the PUs might be
placed anywhere over the area as a Poisson process; hence the
positions of PUs are independent. Therefore, according to the
Poisson process property [25], the probability, that at least one
sensor is located in an enough-short distance from the PUs, are
independent of the PUs' locations, and accordingly, the
obtained minimum for the number of sensors (in (21)) does
not have a linear relation with M. An evident result that can be
deduced from this plot is that, at a fixed number of channels, if
the constraint on the GDP is tight while the ED threshold level
is fixed, the more sensors should be used to satisfy the
constraints. Also, Fig.1 represents that, at a fixed number of
channels, if the ED threshold level increases while the
constraint on the GDP is fixed, the minimum required number
of sensors increases. It is because of the decrease in the DP of
sensors with increasing in the ED threshold level [6].
For a better illustration, in Fig.2, the minimum number of
sensors is plotted versus the ED threshold level at a different
number of PUs. Although the direct effect of does not
appear in (23), it has a reverse relation with (from (13)),
and accordingly, it has an almost linear relationship with the
minimum number of sensors. It is noted that practically
increasing the ED threshold level decreases the DP of sensors.
To compare the obtained results of this article with other
existing works, the results of [21] has been plotted in Fig.2,
for the case that only one PU is under-monitor, because [21]
assumed a WCSN performing CSS in only one channel. A
worthy note is that this paper obtains an expression for the
minimum number of sensors for satisfying the detection
quality constraints, while existing works ( [21]) only consider
the numerical solutions. Moreover, we assumed that there is
no information about the position of PUs, the PUs-to-sensors
distances, the radio propagation conditions, and the SNR in
the PUs-to-sensors links but in [21], the minimum number of
sensors is calculated with assuming the known position of the
PU. The assumed model in this paper is a complicated
problem that has not been considered in the previous works, to
the best of our knowledge. Although, it shows that the
minimum number of nodes from [21] is lower than the results
of this paper. Because in [21], the minimum number of
sensors is calculated with assuming the known position of the
PU (the PU is located at the origin), and hence, the known
SNR in the PU-to-sensors links (assuming only path-loss
channel). Therefore, if the PU's position is not known, we
need to use more sensors to ensure that if the PU is located in
every desired point of the area, the constraints on the GDP and
GFD about the PU are satisfied. However, the known PU's
position and SNR in the PU-to-sensors links are not available
for some scenarios assuming mobile PUs, military uses, or
emergency networks. Also, it is observed that if the number
of PUs goes up (assuming other parameters fixed), the number
of required sensors increases because it should satisfy that
there is at least one sensor at a distance lower than around
each of the PUs. In the following plots, we evaluate the
statistically-obtained results for the minimum number of
sensors required for satisfying the constraints on the GDP and
GFP, and the network lifetime probability. To this end, we
designed an iterative algorithm that has been described in
Fig.3. The average results obtained from the algorithm are
plotted and discussed in the following Figures.
Fig.1. The least number of sensors versus the number of PUs for two
different thresholds of energy detectors ().and
different constrains on the GDP ().
Fig.2. The least number of sensors versus threshold levels of ED for
different number of PUs ().
[21]
8
In Fig.4, we evaluate the obtained results for the minimum
number of sensors required for satisfying the constraints on
the GDP and GFP. To this end, we consider a network with
the number of sensors calculated from (23). The sensors are
distributed randomly over the network based on the uniform
distribution. Then, the average obtained GDP (over 10000
times realization of the network) is plotted. The plot shows
that the average provided GDP satisfies the problem
constraint, i.e. all the average provided GDP are higher than .
It is noted that the number of sensors is calculated from (23) if
it satisfies (12), therefore, it is clear that the constraints on the
GFP are satisfied; hence, the average provided GFP has not
been plotted. In this plot, when the ED threshold level goes up
(at a fixed number of PUs), the average provided GDP is
greater. According to (13), when the ED threshold level goes
up, the becomes shorter; hence the number of required
sensors is greater. Also, when the number of PUs goes up (at a
fixed ), the average provided GDP increases; because the
number of required sensors is greater, according to (23).
To evaluate the quality of detection, in Fig.5, the receiver
operating characteristic (ROC) curve (i.e. the average GDP Vs
the average GFP) are plotted, at different number of sensors,
in which sensors are selected randomly for sensing two
different channels number. This plot validates the achieved
results, for the least number of sensors that have been plotted
in Fig.1, satisfy the desired detection's quality constraints.
In Fig.6, the obtained tail probability for the network
lifetime, in (29), is plotted, assuming the number of sensors is
determined from (23). It is observed that the tail probability
has little increase due to increasing M or . The more the
number of PUs, the more the number of sensors required for
satisfying the sensing quality constraints. Also, the higher
threshold level of ED leads to lower sensors' DP; hence, more
sensors required for satisfying the GDP constraint. Therefore,
increasing M or increases the average lifetime. The average
network lifetime can be calculated from Fig.6 as the number
of iterations in which the tail probability is equal to 0.5.
Finally, we evaluate the obtained distribution for the
network lifetime. We consider a network with the obtained
number of sensors from Fig.1, and then the sensors are
distributed based on the uniform distribution over the network.
Fig.7 plots the average provided lifetime over 10000 times
realization of the network. It is observed that the average
lifetime from the obtained distribution in (29) (it can be
calculated from Fig.6) is confirmed by the results of the
average provided lifetime in realization in Fig.7.
Fig.4. The average GDP versus threshold level of energy detector for
different number of PUs.
Fig.5. The ROC curve for two different channel number ().
counter number1=0;
While (counter number1 <= 10000)% Monte-Carlo method with 10000
times realization of the network
Step1: The number of sensors calculated from (23).
Step2: The sensors are distributed randomly over the network based on
the uniform distribution.
lifetime number counter=0, Initial energy of sensors=
Step3: while (all the sensors are on) % This is the stop criteria (the
network lifetime is the time until the first sensor is off).
1. The sensors are randomly divided into M clusters (every
cluster cooperatively sense one of the PUs).
2. Each node senses the specified channel and generates a
decision bit.
3. The sensors send their decision bit to the FC.
4. FC combines the received bits using OR rule and
determines the final decision about the channels.
Lifetime number counter= lifetime numbercounter+1;
5. Update the remaining energy of sensors.
end
counter number1= counter number1+1;
end %
Fig.3. The proposed algorithm for evaluating the average lifetime
Fig.6. The tail probability of the network lifetime ().
9
VIII. CONCLUSION
This paper considered a WCSN, in which sensors are used
to sense the transmission activities of multiple PUs. For
reliable sensing results, the cooperative spectrum sensing
scheme was assumed. Analyzing the WCSN lifetime and
reducing the consumption energy was investigated in the
paper, for scenarios in which the position of the sensors and
PUs are not known. The results can be applied for military
uses or emergency applications. In this paper, the Poisson
process was used to model the number of sensors and PUs.
First, a closed-form expression for the minimum number of
sensors to satisfy the global detection probability and global
false alarm probability about all the PUs was determined.
Then, assuming a network composed of the number of
sensors, some statistical analysis for the network lifetime was
presented, and a closed-form expression for the
complementary cumulative density function of the network
lifetime was concluded. Finally, computer simulations were
conducted to evaluate the presented statistical results. The
simulation illustrated that the expression for the minimum
number of sensors satisfy the detection quality an also,
indicated that the network lifetime distribution is verified by
the average provided lifetime using the Monte-Carlo method.
REFERENCES
[1]
I. Akyildiz, W. Lee, M. Vuran and S. Mohanty, " NeXt
generation/dynamic spectrum access/cognitive radio wireless
networks: A survey," Computer Networks, vol. 50, no. 13, pp. 2127-
2159, 2006.
[2]
O. B. Akan, O. B. Karli and O. Ergul, "Cognitive Radio Sensor
Networks," IEEE Network, vol. 23, no. 4, pp. 34-40, July/Agust 2009.
[3]
A. Alfahham and M. Berekovic, " Energy efficient cooperative
spectrum sensing in Cognitive Radio Sensor Network Using FPGA:
A survey," in 21st Conference of Open Innovations Association
(FRUCT), Finland, 2017.
[4]
A. Ghasemi and S. Sousa, "Spectrum sensing in cognitive radio
networks: requirements, challenges and design trade-offs," IEEE
Communications Magazine, vol. 46, no. 4, pp. 32-39, April 2008.
[5]
N. Arora and R. Mahajan, "Cooperative Spectrum Sensing Using
Hard Decision Fusion Scheme," International Journal of Engineering
Research and General Science, vol. 2, no. 4, pp. 36-43, 2014.
[6]
K. Cichoń, A. Kliks and H. Bogucka, "Energy-efficient cooperative
spectrum sensing: a survey," IEEE Communications Surveys &
Tutorials, vol. 18, no. 3, pp. 1861-1886, 2016.
[7]
F. Awin, Y. Alginahi, E. Abdel-Raheem and K. Tepe, "Technical
issues on cognitive radio-based Internet of Things systems: A
survey," IEEE Access, vol. 7, pp. 97887-97908, 2019.
[8]
S. Althunibat, M. Di Renzo and F. Granelli, "Towards energy-
efficient cooperative spectrum sensing for cognitive radio networks:
An overview," Telecommunication Systems, vol. 59, no. 1, pp. 77-91,
2015.
[9]
F. Awin, E. Abdel-Raheem and K. Tepe, "Blind spectrum sensing
approaches for interweaved cognitive radio system: A tutorial and
short course," IEEE Communications Surveys & Tutorials, vol. 21,
no. 1, pp. 238-259, 2018.
[10]
R. Deng, J. Chen, C. Yuen, P. Cheng and Y. Sun, "Energy-Efficient
cooperative spectrum sensing by optimal scheduling in sensor-aided
cognitive radio networks," IEE Transactions on Vehicular on
Technology, vol. 61, no. 2, pp. 716-725, 2012.
[11]
M. Monemian, M. Mahdavi and M. Omidi, "Optimum sensor
selection based on energy constraints in cooperative spectrum sensing
for cognitive radio sensor networks," IEEE Sensors Journal, vol. 16,
no. 6, pp. 1829-1841, 2015.
[12]
A. Bagheri, A. Ebrahimzadeh and M. Najimi, "Sensor selection for
extending lifetime of multi-channel cooperative sensing in cognitive
sensor networks," Physical communication, vol. doi.org/10.1016,
2017.
[13]
M. Najimi, A. Ebrahimzadeh, S. Hosseni Andargoli and A. Fallahi,
"Lifetime Maximization in Cognitive Sensor Networks Based on the
Node Selection," IEEE Sensors Journal, 2014.
[14]
S. Maleki, G. Leus, S. Chatzinotas and B. Ottersten, "To AND or to
OR: on energy-efficient distributed spectrum sensing with combined
censoring and sleeping," IEEE Transactions on Wireless
Communications, vol. 14, no. 8, pp. 4508-4521, 2015.
[15]
M. Usman, D. Har and I. Koo, "Energy-efficient infrastructure sensor
network for ad hoc cognitive radio network," IEEE Sensors Journal,
vol. 16, no. 8, pp. 2775-2787, 2016.
[16]
X. Liu, B. Evans and K. Moessner, "Energy-efficient sensor
scheduling algorithm in cognitive radio networks employing
heterogeneous sensors," IEEE Transactions on Vehicular Technology,
vol. 64, no. 3, pp. 1243-1249, 2014.
[17]
V. Srividhya and T. Shankar, "Energy proficient clustering technique
for lifetime enhancement of cognitive radio–based heterogeneous
wireless sensor network," International Journal of Distributed Sensor
Networks, vol. 14, no. 3, pp. 1-18, 2018.
[18]
E. Pei, H. Han, Z. Sun, B. Shen and T. Zhang, "LEAUCH: low-
energy adaptive uneven clustering hierarchy for cognitive radio
sensor network," EURASIP Journal on Wireless Communications and
Networking, pp. 1-8, 2015.
[19]
M. Zheng, L.Chen, W. Liang, H. Yu and J. Wu, "Energy-efficiency
maximization for cooperative spectrum sensing in cognitive sensor
networks," IEEE Transactions on Green Communications and
Networking, vol. 1, no. 1, pp. 29-39, 2016.
[20]
J. Ren, Y. Zhang, Q. Ye, K. Yang, K. Zhang and X. Shen, "
Exploiting secure and energy-efficient collaborative spectrum sensing
for cognitive radio sensor networks," IEEE Transactions on Wireless
Communications, vol. 15, no. 10, pp. 6813-6827, 2016.
[21]
M. Najimi, A. Ebrahimzadeh, S. Andargoli and A. Fallahi, "Energy-
efficient sensor selection for cooperative spectrum sensing in the lack
or partial information," IEEE Sensors Journal, vol. 15, no. 7, pp.
3807-3818, 2015.
[22]
B. Hamdaoui, B. Khalfi and M. Guizani, "Compressed wideband
spectrum sensing: Concept, challenges, and enablers," IEEE
Communications Magazin, vol. 56, no. 4, pp. 136-141, 2018.
[23]
A. Papoulis and P. Unnikrishna, Probability, random variables and
stochastic process, Boston: McGraw-Hill, 2002.
[24]
L. Gunter and P. Mathew, Lectures on the Poisson Process,
Cambridge University Press, 2017.
[25]
J. F. C. Kingman, Poisson Processes, Clarendon Press, 1992.
[26]
T. Yang, Y. Wu, L. Li, W. Xu and W. Tan, "Fusion Rule Based on
Dynamic Grouping for Cooperative Spectrum Sensing in Cognitive
Radio," IEEE Access, pp. 51630-51639, 2019.
[27]
D. Han and J. h. Lim, "Smart home energy management system using
IEEE 802.15.4 and zigbee," IEEE Transactions on Consumer
Electronics, vol. 56, no. 3, pp. 1403-1410, 2010.
Fig.7. The average provided lifetime for a network assuming the
number of sensors are determined fromFig.2 ().
