cooperative cognitive radio with obstacles on the sensing
TRANSCRIPT
Cooperative Cognitive Radio with Obstacles on the Sensing
Channels
Abdul Haris Junus Ontowirjo1,2
, Wirawan1, and Adi Soeprijanto
1
1Department of Electrical Engineering, Faculty of Electrical Technology, Institut Teknologi Sepuluh Nopember,
Surabaya 60111, Indonesia 2Department of Electrical Engineering, Faculty of Engineering, Universitas Sam Ratulangi, Manado 95115, Indonesia
Email: [email protected]; {wirawan, adisup}@ee.its.ac.id
Abstract—This paper investigates the performance of
cooperative cognitive radio with obstacles on the sensing
channels. The analysis focuses on weighted summation
combining in the fusion center. In this paper we propose
Rayleigh, Rician, and Nakagami-m channel models to handle
the presence of obstacles in the sensing channels. The analysis
is based on the central limit theorem. The results are presented
in the form of relation between detection probability and SNR
with decision threshold as the parameter and the relation
between detection probability and decision threshold with SNR
as the parameter. Index Terms—Cooperative cognitive radio, spectrum sensing,
fusion center, weighted summation, decision threshold, energy
detection.
I. INTRODUCTION
Measurements show that spectrum utilization by
licensed Primary Users (PUs) is inefficient [1]. Cognitive
radio [2], [3] is a technology which has inherent
capability to increase the efficiency of inefficient
spectrum utilization by allowing unlicensed Secondary
Users (SUs) access the spectrum band during idle time.
The Cognitive Radio Network (CRN), all the SUs, must
release the spectrum band as soon as the PU be active. It
means the SUs do not interfere the PU and it is said the
SUs utilize the spectrum band in opportunistic fashion. In
order to keep the SUs from interfering the primary
network, the network of PU, spectrum sensing is essential
to detect the spectrum holes, the idle licensed spectrum
sub-bands. Different spectrum sensing techniques have
been proposed. Among them are matched filter detection
[4], the cyclostationary detection [5], the energy detection
[6]-[9], and covariance based detection [10]. Among the
proposed detection techniques for spectrum sensing, the
energy detection is the most common practical one due to
its simplicity.
With a single SU, the instantaneous Signal-to-Noise
Ratio (SNR) of the received signal may become too low
to make the sensing result due to the fading, shadowing,
and the hidden node problem. Cooperative approach has
been introduced to overcome this challenge. Several
Manuscript received August 1, 2018; revised April 2, 2019. Corresponding author email: [email protected].
doi:10.12720/jcm.14.5.396-401
different SUs cooperatively detect the spectrum holes. As
the number of involved SUs increases, the probability
that all of the cooperating SUs are simultaneously in a
deep shadowing or fading is reduced [11]. Furthermore,
the multiple distributed SUs provide the diversity gain.
The diversity gain, in turn, greatly improves the global
performance and efficiency [12].
We consider the Cooperative Cognitive Radio (CCR)
of Fig. 1. The model consists of one PU, K SUs, and a
Fusion Center (FC). The black thick vertical lines
represent the obstacles on the related channels. Each SU
senses the spectrum band of interest through an
individual sensing channel, applies energy detection
technique, that is, computes the amount of energy of the
signal received from PU for specified time interval, and
sends it to the FC via perfect (error-free) reporting
channel. The FC collects the information on the energy of
PU's signal received by all SUs, combines them, and
applies some rule to make the global decision considering
the occupancy of the spectrum band. If the messages sent
by the SUs are in form of local binary decision about the
present or the absent of the PU, then the FC combining
rule is called hard combining method [9]. If the messages
sent to the FC are the local test statistics, the FC
combining rule will be a soft combining method [4], [13].
If every SU forwards the signal from PU to FC and the
test statistics is computed by the FC then it is still said
that the FC performs soft combining method [14]-[16].
Fig. 1. Cooperative cognitive radio with obstacles
Even if only binary decisions are transmitted by the
SUs to the FC for hard combining, there may be
significant communication overhead related to the
protocol used in transmitting the sensing results.
Therefore, hard combining method does not significantly
decrease the bandwidth requirement comparing its soft
counterpart. The difference in the resource usage between
hard combining strategy and the soft combining one may
Journal of Communications Vol. 14, No. 5, May 2019
©2019 Journal of Communications 396
be small [17]. Complex coupling relation between the
local quantization rule and the fusion combining rule is
the most important task in hard combining technique and
that is not present in soft combining technique. The soft
combining technique (soft-fusion policy) can achieve
optimal diversity, providing a higher diversity gain and
better detection accuracy compared with the hard
combining one (decision-fusion policy) [18].
Obstacles can considerably reduce the performance of
cognitive radio in practice. Hence, the fading channel that
occurs in most of the realistic wireless environments,
degrade the performance of the channels. CSS is analyzed
superficially by [19]. In [15] the performance analysis of
CSS in CR over Nakagami-m channels is studied. In [20]
the performance analysis of CSS is examined for
multipath fading channels based on energy detection. In
[6] the analysis is based on fast-fading and block-fading
channels where only the average SNR is available. In [9]
block flat-fading channels are assumed in the model for
analyzing the CSS and in [7] Nakagami-m fading
channels are assumed with MRC reception.
This paper describes the effect of the presence of
obstacles on the sensing channels. The work presents a
performance analysis of spectrum sensing over multipath
fading for a system with obstacles between PU and SUs
as depicted in [21]. Specifically, we suggest the use of
available channel models as Rayleigh channels, Rician
channels, and Nakagami-m channels and the use of
Central Limit Theorem (CLT) to derive the closed-form
expression of the performance measures.
II. SYSTEM AND CHANNEL MODELS
We consider a CCR with K secondary users, {𝑆𝑈𝑘}𝑘=1𝐾 ,
which cooperatively observe the presence and the
absence of the primary signal, 𝑠[𝑛], transmitted by PU,
with a specified frequency, via independent sensing
channels, in certain successive observation intervals.
Each interval consists of N samples which is selected
based on the bandwidth-observation time product. The n-
th received signal sample at 𝑆𝑈𝑘 , 𝑦𝑘[𝑛] , for 𝑘 =1,2,⋯ , 𝐾 and 𝑛 = 1,2,⋯ ,𝑁, can be written as
𝑦𝑘[𝑛] = {𝑤𝑘[𝑛] 𝐻0
ℎ𝑘𝑠[𝑛] + 𝑤𝑘[𝑛] 𝐻1 (1)
where the null hypothesis, 𝐻0, represents the absence of
PU and the alternative hypothesis, 𝐻1 , represents the
presence of PU. Noise samples are zero mean complex
Gaussian random variables with variance 𝜎𝑘2.
𝑤𝑘[𝑛]~𝐶𝑁(0, 𝜎𝑘2) (2)
where ℎ𝑘 is the flat fading channel gain between PU and
𝑆𝑈𝑘 . The energy of the primary signal, 𝑠[𝑛], from PU,
during observation, is
𝐸𝑠 =∑|𝑠[𝑛]|2𝑁
𝑛=1
(3)
The channels with obstacles have no line-of-sight
(LOS) component in their propagation paths. The fading
amplitude of each channel, |ℎ𝑘|, can be approximated by
Rayleigh distribution. The SNR, 𝛾, distribution is [22]
𝑓𝛾(𝛾) =
1
𝛾𝑒𝑥𝑝 (−
𝛾
�̅�) , 𝛾 ≥ 0,
(4)
where �̅� = 𝐸[𝛾] is the expectation value of 𝛾 . The
channels with no obstacle have one strong direct LOS
component in their paths. They can be considered as
Rician channels approximately. The SNR distribution is
[22]
𝑓𝛾(𝛾) =𝜅 + 1
�̅�𝐼0 (
𝛾𝜅(𝜅 + 1)
�̅�) 𝑒𝑥𝑝 (−
𝛾(𝜅 + 1)
�̅�− 𝜅),
𝛾 ≥ 0 (5)
where the function 𝐼0 is the modified Bessel function of
0-th order and 𝜅 is the ratio of the power in the LOS
component to the power in the non-LOS multipath
components. It can be seen that for 𝜅 = 0 , Ricean
distribution becomes Rayleigh distribution so it can be
used to approximate the channels without LOS
component as well.
The problem of obstacles also can be approached by
Nakagami-m distribution which has SNR distribution as
[22]
𝑓𝛾(𝛾) =
𝑚𝑚𝛾𝑚−1
�̅�𝑚Γ(𝑚)𝑒𝑥𝑝 (−
𝑚𝛾
�̅�) , 𝛾 ≥ 0 (6)
where Γ(⋅) is the Gamma function and m is the
Nakagami-m fading parameter. We can see that for m = 1
the distribution reduces to Rayleigh fading so it can be
used to model the channels with obstacles. For𝑚 =(𝜅 + 1)2/(2𝜅 + 1) the distribution is approximately
Rician fading which can be used to represent the channels
without obstacle.
The instantaneous SNR at the k-th secondary user is
𝛾𝑘 =
𝐸𝑠|ℎ𝑘|2
𝜎𝑘2 (7)
and its average value is
�̅�𝑘 = 𝐸[|ℎ𝑘|
2]𝐸𝑠
𝜎𝑘2 (8)
Each secondary user, 𝑆𝑈𝑘 , performs energy detection
on the received signal, 𝑦𝑘[𝑛], to produce test statistics, 𝑌𝑘,
𝑌𝑘 = ∑|𝑦𝑘[𝑛]|2
𝑁−1
𝑛=0
(9)
According to the central limit theorem (CLT) [23], for
a large 𝑁 (the number of samples), 𝑌𝑘 is asymptotically
normally distributed,
𝑌𝑘~𝑁(𝜇𝑌𝑘 , 𝜎𝑌𝑘2 ) (10)
Journal of Communications Vol. 14, No. 5, May 2019
©2019 Journal of Communications 397
The probability distribution function (PDF) of 𝑌𝑘 then
can be expressed as
𝑓𝑌𝑘(𝑥) =
1
𝜎𝑌𝑘√2𝜋𝑒𝑥𝑝 (−
1
2[𝑥 − 𝜇𝑌𝑘𝜎𝑌𝑘
]
2
) (11)
where the local test statistics mean, 𝜇𝑌𝑘, and the local test
statistics variance, 𝜎𝑌𝑘, are [24]
𝐸[𝑌𝑘] = 𝜇𝑌𝑘 = {
𝑁𝜎𝑘2 𝐻0
𝑁(1 + 𝛾𝑘)𝜎𝑘2 𝐻1
(12)
and
𝑉𝑎𝑟[𝑌𝑘] = 𝜎𝑌𝑘
2 = {𝑁𝜎𝑘
4 𝐻0𝑁(1 + 2𝛾𝑘)𝜎𝑘
4 𝐻1 (13)
respectively.
All SUs send their local test statistics to FC via
independent and perfect reporting channels. FC applies
weighted summation rule and combines linearly all 𝑌𝑘 to
generate a single global test statistics 𝑍,
𝑍 =∑𝛽𝑘𝑌𝑘
𝐾
𝑘=1
(14)
where 𝛽𝑘 is the weight applied to each channel. Since all
𝑌𝑘 are normal random variables, their linear combination
is normal too. We can see that equal gain combining
(EGC) and maximum ratio combining (MRC) are two
special cases of weighted summation combining. If all
weights are unity, 𝛽𝑘 = 1 for all 𝑘, then we have EGC
and if each weight is proportional to the SNR at 𝑆𝑈𝑘 ,
𝛽𝑘 ∝ 𝛾𝑘 , then we have MRC. The distribution of the
global test statistics can be expressed as
𝑍~𝑁(𝜇𝑍, 𝜎𝑍2) (15)
where the global test statistics mean, 𝜇𝑍 = ∑ 𝛽𝑘𝜇𝑌𝑘𝐾𝑘=1 ,
and the global test statistics variance, 𝜎𝑍2 = ∑ 𝛽𝑘
2𝜎𝑌𝑘2𝐾
𝑘=1
are expressed in detail as
𝐸[𝑍] = 𝜇𝑍 =
{
𝑁∑𝛽𝑘
𝐾
𝑘=1
𝜎𝑘2 𝐻0
𝑁∑𝛽𝑘
𝐾
𝑘=1
(1 + 𝛾𝑘)𝜎𝑘2 𝐻1
(16)
and
𝑉𝑎𝑟[𝑍] = 𝜎𝑍2 =
{
𝑁∑𝛽𝑘
2
𝐾
𝑘=1
𝜎𝑘4 𝐻0
𝑁∑𝛽𝑘2
𝐾
𝑘=1
(1 + 2𝛾𝑘)𝜎𝑘4 𝐻1
(17)
respectively.
The FC makes a decision based on the global test
statistics, 𝑍,
𝐻1𝑍 ≷ 𝜆
𝐻0
(18)
where 𝜆 is the decision threshold.
The performance measures of the cooperative
cognitive radio under consideration, in this case, are the
probability of false alarm, 𝑃𝑓 , and the probability of
detection, 𝑃𝑑 , then can be derived. The probability of
false alarm is the probability that the system detects the
presence of PU while in fact, it is absent. The probability
of false alarm can also be viewed as a complementary
cumulative distribution function for null hypothesis. The
probability of detection is the probability that the system
detects the presence of PU and indeed it is present. The
detection probability can also be considered as
complementary cumulative distribution function for the
alternative hypothesis.
𝑃𝑓 = 𝑃𝑟(𝑍 > 𝜆|𝐻0)
= ∫ 𝑓𝑍(𝑥|𝐻0)𝑑𝑥
∞
𝜆
= 1 − 𝐹(𝜆|𝐻0)
(19)
and
𝑃𝑑 = 𝑃𝑟(𝑍 > 𝜆|𝐻1)
= ∫ 𝑓𝑍(𝑥|𝐻1)𝑑𝑥
∞
𝜆
= 1 − 𝐹(𝜆|𝐻1)
(20)
where 𝐹(⋅) is the cumulative distribution function (CDF)
of the global test statistics, 𝑍 . In terms of the AWGN
noise, the channel SNR, the number of samples, the
weighting constant, and the decision threshold, the
probabilities of false alarm and detection can be
expressed as
𝑃𝑓 = 𝑄(
𝜆 − 𝐸[𝑍|𝐻0]
√𝑉𝑎𝑟[𝑍|𝐻0])
= 𝑄(𝜆 − 𝑁∑ 𝛽𝑘𝜎𝑘
2𝐾𝑘=1
√𝑁∑ 𝛽𝑘2𝜎𝑘
4𝐾𝑘=1
)
(21)
and
𝑃𝑑 = 𝑄(
𝜆 − 𝐸[𝑍|𝐻1]
√𝑉𝑎𝑟[𝑍|𝐻1])
= 𝑄(𝜆 − 𝑁∑ 𝛽𝑘(1 + 𝛾𝑘)𝜎𝑘
2𝐾𝑘=1
√𝑁∑ 𝛽𝑘2(1 + 2𝛾𝑘)𝜎𝑘
4𝐾𝑘=1
)
(22)
respectively. where 𝑄(⋅) is the Q-function defined as the
tail distribution function of the standard normal
distribution,
𝑄(𝑥) =1
√2𝜋∫ 𝑒𝑥𝑝 (−
1
2𝑥) 𝑑𝑥
∞
𝑥
Journal of Communications Vol. 14, No. 5, May 2019
©2019 Journal of Communications 398
The Q-function can be expressed in term of the error
function or the complementary error function.
III. SIMULATION
The performance of the CCR is analyzed by means of
detection probability vs. SNR (𝑃𝑑 vs. 𝛾) curves for
several values of threshold (𝜆),
detection probability vs. threshold (𝑃𝑑 vs. 𝜆) curves
for several values of SNR (𝛾),
For simulation purpose, the system is set up for 𝐾 = 4
users. All SUs take their local test statistics over a sensing
interval of 𝑁 = 100 samples.
Fig. 2 shows how the detection probability varies as
the average SNR varies for three decision threshold
values. It is evident that better SNR leads to improvement
in the performance of spectrum sensing.
Fig. 2. Detection probability vs. SNR
The quasilinear segments of the graphs show that their
slopes are nearly close to each other. For decision
threshold 𝜆 = 2.0 , the detection probability increases
0.38 as the average SNR increases 1 dB from 0.5 dB to
1.5 dB. The detection probability increases 0.36 as the
average SNR increases with the same increment from 2.5
dB to 3.5 dB for decision threshold 𝜆 = 2.5. With the
decision threshold 𝜆 = 3.0 and with the same increment
of the average SNR, the detection probability increases
0.25 as the average SNR increases from 5.5 dB to 6.5 dB.
With this evidence, the same performance can be
achieved within different average SNR intervals by
adjusting the decision threshold value. For example if a
level of performance can be achieved when average SNR
varies between 0 dB to 4 dB by setting the decision
threshold of 𝜆 = 2.0, then the same performance can be
achieved within the interval of SNR from 2 dB to 6 dB by
adjusting threshold value 𝜆 = 2.5 and the same
performance can be achieved within the interval of SNR
from 4 dB to 8 dB by adjusting threshold value 𝜆 = 3.0,
as long as the detection probability is concerned.
Fig. 3 depicts the variation of detection probability due
to the variation of the decision threshold for several SNR
values. It is evident that the performance decreases as the
decision threshold increases as long as decision
probability is concerned.
Fig. 3. Detection probability vs. decision threshold
Journal of Communications Vol. 14, No. 5, May 2019
©2019 Journal of Communications 399
With different channel qualities, the system shows
different performance degradations. For average SNR of
4 dB, the detection probability decreases 0.52 (from 0.78
to 0.26) as decision threshold value increases 0.61 (from
2.46 to 3.07). With the same increment of decision
threshold value, the detection probability decreases 0.32
for SNR of 5 dB and decreases 0.16 when SNR is 6 dB.
IV. CONCLUSIONS
This paper has analyzed the performance of CCR with
diversity reception and obstacles on the sensing channels.
Through extensive elaboration of analytical formulas and
simulation models, we have shown that numerical results
from analytical expressions of detection probability and
false alarm probability are close to the numerical
simulation results. The closeness of analytical and
simulation results has been presented in graphical relation
between the detection probability and the SNR with
decision threshold as the parameter and graphical relation
between the detection probability and the decision
threshold with SNR as the parameter.
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Journal of Communications Vol. 14, No. 5, May 2019
©2019 Journal of Communications 400
Abdul Haris Junus Ontowirjo received
the B.Eng. degree in electrical
engineering from the Institut Teknologi
Bandung (ITB), Bandung, Indonesia, in
1991, M.Eng. degree in electrical
engineering from the Institut Teknologi
Sepuluh Nopember (ITS), Surabaya,
Indonesia, in 2010, where he is currently
pursuing the Ph.D. degree in electrical engineering.
Wirawan received the B.Eng. degree in
electrical engineering from the Institut
Teknologi Sepuluh Nopember (ITS),
Surabaya, Indonesia, in 1987, the D.E.A.
degree in signal and image processing
from the Ecole Superieure en Sciences
Informatiques, Sophia Antipolis, France,
in 1996, and the Ph.D. degree in image
processing from Telecom ParisTech, Paris, France, in 2003. He
has been with the Electrical Engineering Department, ITS, as a
Lecturer since 1989. His current research interests include
statistical signal processing, underwater acoustic
communication, and various aspects of wireless sensor networks.
Adi Soeprijanto received the B.Eng.
degree in electrical engineering and
M.Eng. Degree in control system from
the Institut Teknologi Bandung (ITB),
Bandung, Indonesia, in 1989 and 1995
respectively, and the Ph.D. degree in
power system stability from Hiroshima
University in 2001. He has been with the
Electrical Engineering Department, ITS, as a Lecturer and
Researcher since 2001. His current research interests include
power system analysis.
Journal of Communications Vol. 14, No. 5, May 2019
©2019 Journal of Communications 401