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Energy Detector with Adaptive Optimal Threshold for Enhancing
Spectrum Sensing in Cognitive Radio Network
M.V.S. Sairam
1
, Raju Egala
2
1
Professor, Department of Electronics and Communication Engineering, Gayatri Vidya Parishad College of Engineering
(A), Visakhapatnam, PIN: 530 048
2
Assistant Professor Department of Electronics and Communication Engineering, Gayatri Vidya Parishad College for
Degree and PG Courses (A), Rushikonda, Visakhapatnam, 530 045
DOI : https://doi.org/10.51583/IJLTEMAS.2024.131218
Received: 31 December 2024; Accepted: 04 January 2025; Published: 10 January 2025
Abstract: Cognitive radio (CR) is a promising solution to resolve the crisis of spectrum underutilization. Spectrum sensing is an
indispensable aspect of CR network (CRN). Energy detection method is being recognized as a simple and reliable step for
spectrum sensing. The significant factor of the energy detector (ED) is threshold, whose optimum value depends on signal to
noise ratio (SNR). However, in a wireless environment, where the received signal is severely degraded due to the uncertain noise,
reliable spectrum sensing is not guaranteed.
The key metrics of the CRN are total spectrum sensing error probability, throughput, and energy efficiency. For each SNR value,
there exists an optimal threshold that minimizes total spectrum sensing error probability and maximizes throughput as well as
energy efficiency. Therefore, the threshold of ED should be adaptive in CRN. This paper presents an optimal adaptive threshold
by utilizing spectrum sensing errors for each metric in CRN.
Keywords: Cognitive radio, SNR, Optimal threshold, primary user, secondary user, spectrum sensing, throughput, energy
efficiency.
I. Introduction
According to a Federal Communications Commission (FCC) survey, only 30% of assigned spectrum is utilized [1]. FCC
recognized CR as the candidate to resolve the spectrum underutilization. The CRN includes the following essential functions [2]:
Spectrum sensing: identify unused licensed spectrum
Spectrum management: selecting the preeminent available spectrum band
Spectrum sharing: coordinating the spectrum band with other users
Spectrum mobility: quitting the spectrum band when a licensed user is detected and searching for other available user
CRN allows secondary users (SUs), who are using unlicensed spectrum, to utilize the licensed spectrum band assigned to the
primary user (PU) when the spectrum band is provisionally not being used. Therefore, spectrum sensing is an imperative feature
in CR network [3-5]. Spectrum sensing methods are divided in to synchronous detection and non-synchronous detection. The
methods of synchronous detection are matched filter detection and cyclostationary feature detection [6].
Energy detection is a non-synchronous detection method. The more practical method for spectrum sensing is energy detection [7-
11]. Authors in [7] presented an analysis of the ED method and the detection threshold is optimized to minimize the total error
rate. The inappropriate choice of the threshold of the ED leads to a significant decline in the performance of CR. Authors in [8]
explore this situation and presented optimal threshold values in ED. According to [12], the ED method is sensitive to noise
uncertainty, and therefore this method requires an estimate of noise power, which is a challenging task [13].
The steps involved in ED are as follows:
Step 1: Filtering the received signal to select the preferred spectrum band
Step 2: Squaring the selected signal over the observation period
Step 3: Integrating the output of the squared signal
Step 4: Comparing the output of integrator with threshold of the ED to take decision on the status of PU
Threshold setting methods are based on either constant false alarm probability or constant missed detection probability.
Increasing the threshold leads to an increase in the probability of missed detection, and decreasing the threshold leads to an
increase in the probability of false alarm. Therefore, optimization of these two errors is contradictory goal. Further, since the data
transmission time in CR is reduced due to sensing time, the throughput is reduced and energy consumption is increased. Total
spectrum sensing error probability (sum of false alarm probability and missed detection probability), throughput, and energy
efficiency (ratio of throughput and energy consumption) are three key metrics in a CRN. These key metrics are governed by false
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alarm and missed detection errors. In Industrial applications, where the effect of noise is severe, one should consider the total
error as the key metric. One should consider throughput a key metric in decisive applications like health monitoring. In greenfield
perspective, one should consider energy efficiency as the key metric. Therefore, the threshold of energy detection should be
adaptive to the environment and application of the wireless communication.
Hence, designing a system with an adaptive threshold is a challenging issue in the communication environment. In this paper, we
focus on presenting the optimal threshold values, which maximize the performance of each metric of CR under different SNR
values.
The remainder of this paper is organized as follows. In section 2, spectrum sensing is reviewed. In section 3, minimization of the
total spectrum sensing error probability is presented. In section 4, maximization of throughput and energy efficiency is presented.
The results are presented in section 5, and finally conclusions are drawn in section 6.
Spectrum sensing Preliminaries
We consider a CR network with one PU and one SU with ED as illustrated in Figure 1. PU is utilizing a licensed spectrum band for
transmitting data, and SU performs spectrum sensing to know the status of the PU. If the PU is absent (the channel is idle), the SU
transmits the data in licensed spectrum band of the PU. If the PU is present (the channel is occupied), the sensing is being continued
for every predetermined time slot until the SU finds an unutilized licensed band. The SU makes the final decision on the presence
or absence of the PU using ED. In ED, the received signal,
is used to evaluate the energy of the signal. The energy is then
compared to the threshold
to decide the status of the PU. Setting the proper threshold is a challenging task, as it has to
differentiate between the signal and noise. If
, the channel is assumed to be idle, on the contrary, the PU is assumed to be
occupied.
Fig. 1 Cognitive radio network
Analytically, signal detection can be formalized as a hypothesis test:
= hypothesis when channel is idle
= hypothesis when channel occupied by the PU
= signal transmitting from the PU
= signal received at the SU
= complex channel gain of sensing channel between PU and SU
= additive white Gaussian noise (AWGN)
In a binary hypothesis test, if
is accepted when
is true, it is called type I error. If
is accepted when
is true, it is called
type II error. The probability of making a type I error,
is called the probability of false alarm
and the
probability of making a type II error,
is called the probability of missed detection
In AWGN channel,
and
can be represented, respectively, as [14]
Where,
= time-bandwidth product of the ED
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= threshold of the ED
= SNR at SU
= probability of detection which is described as the probability that the detector states the presence of PU, when the
PU is actually present
= incomplete gamma function which is specified by
= complete gamma function
= th order generalized Marcum Q - function, which is specified by
Where,
is the
order modified Bessel function
Minimization of Total Spectrum Sensing Error Probability
Minimizing the false alarm errors to afford more spectrum access opportunities and minimize missed detection errors to afford
more protection to PU are indispensable in spectrum sensing. In this section, we explore the minimization of the total spectrum
sensing error probability. In Figures 2 and 3,
and
, respectively, versus
, are presented. From Eq. (3)
and Figure 2, it can be observed that the performance of
is independent of SNR.
Fig. 2 False alarm probability vs. Threshold (SNR = -5 dB, 0 dB, 5 dB)
Fig. 3 Missed detection probability vs. Threshold (SNR = -5 dB, 0 dB, 5 dB)
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It is clear that, from false alarm stand point one should use high threshold, whereas from missed detection point, one should use
low threshold. Hence, a careful trade-off is to be considered while setting the threshold.
In the present work, the total spectrum sensing error probability, which is formulated as the sum of
and
, is
considered as one of the key metrics. In Figure 4, the total spectrum sensing error probability
is
presented versus
in varying-SNR environment. It is perceived that there indeed exists a threshold to make
minimum. The significance of selecting threshold is explained by dividing the each curve into two regions
. When the threshold of the energy ED is taken
in the left half of the
, missed detection errors are minimum.
in the right half of the
, false alarm errors are minimum.
at
, both missed detection errors and false alarm errors are minimum
Fig. 4 Total error probability vs. Threshold (SNR = -5 dB, 0 dB, 5 dB)
Minimum missed detection and false alarm errors must be jointly sustained to optimize detection performance in SNR varying
environment. It is perceived that there indeed exists a threshold to make
minimum.
Maximization of Throughput and Energy Efficiency
Refer to Table I for the main notation. In CRN, there are four possible scenarios between PU and SU. Throughput and energy
consumption for each scenario are presented in Table II.
Table I Notations
Notation
Meaning
: PU’s throughput when SU is absent
: SU’s throughput when PU is absent
: PU’s throughput when SU is present
: SU’s when PU is present
: Energy consumed by SU to accomplish spectrum sensing
: Energy consumed by PU to transmit data
: Energy consumed by SU to transmit data
Table II Throughput and Energy Consumption for Each Scenario
λ
λ
λ
λ
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Scenario
PU status
CR Decision
Channel
occupancy
Through-put
Energy
1
Present
Present
only by PU
2
Absent
Simultaneously
by PU and SU
3
Absent
Absent
only by SU
4
Present
neither by PU
nor by SU
0
Let us describe
as the probability for which the channel is idle and
as the probability for which the channel is
occupied so that
. The average channel throughput
is the sum of throughput
of PU and SU. From Table II,
can be delineated as
In CR network, each time frame contains a sensing slot
and a data transmission slot
, where is the total time frame
as illustrated in Figure 5.
Fig. 5 Spectrum sensing frame of CR
The CR remains idle in the data transmission slot when PU is present and transmits data in the data transmission slot when it is
absent. In a conventional system, the entire frame is used for data transmission; however, in CRN, a portion of the frame is
reserved for sensing. Consequently, throughput is reduced and energy consumption is increased. Throughput of SU when PU is
absent can be written as given below.
Throughput of SU when PU is present can be simplified to (under missed detection)
Where,
= SNR of the SU
= SNR of the PU
Eq. (7) can be simplified to
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Where,
The average energy consumption
is the sum of energy consumed by spectrum sensing, PU
data transmission and SU data transmission. From Table II,
can be expressed as
The above Equation can be simplified to
Where,
From Eq (10) and Eq (11), Energy efficiency can be written as
The throughput and energy efficiency are key metrics of CRN. Throughput and energy efficiency versus the threshold are
presented, respectively in Figures 6 and 7, for different SNR values. The simulation parameters are indexed in Table III.
Table III Simulation Parameters
Parameter
Value
10
20
10
15
0.15
40
10
0.5
0.5
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Fig. 6 Throughput vs. Threshold (SNR = -5 dB, 0 dB, 5 dB)
Fig. 7 Energy efficiency vs. Threshold (SNR = -5 dB, 0 dB, 5 dB)
It is clear from Figures 6 and 7 that if the threshold is fixed and the SNR increase, then throughput and efficiency also increases.
Consequently, desired maximum throughput and maximum efficiency could be fixed; to do so, the threshold must be recalculated
as a function of SNR. Spectrum and energy efficiency are primary resources in wireless environments [15-22]. In this context, the
authors focus on optimizing threshold levels in CR systems to enhance these resources. The performance of the proposed work is
discussed in the subsequent section.
II. Results and Discussion
It is clear from Figures 4 and 5 and 6 that there lies only one optimal threshold value for each metric. Table 4 shows the optimal
threshold of each metric under different values of SNR.
Table IV Performance of Key Metrics of Cr
SNR
Total spectrum sensing error
Throughput
% Efficiency
Minimum value
Maximum value
Maximum value
-5 dB
0.9189
4
12.55
16
49.07
1
0 dB
0.7693
5
12.68
8
49.79
1
5 dB
0.4455
6
13.55
8
53.55
4
From Table IV, it can be concluded that the larger the value of SNR, the lower the total spectrum sensing error probability and
higher the maximum throughput as well as maximum energy efficiency. For instance, when SNR is 0 dB, the value of total
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spectrum sensing error probability is 0.7693 and decreases to 0.4455 when SNR increases to 5 dB. Moreover, when SNR rises
from 0 dB to 5 dB, maximum throughput and maximum efficiency increase from 12.68 to 13.55 and 49.79% to 53.55%,
respectively. It is clear that information of SNR is adequate for selection of an optimal threshold.
III. Conclusion and Future scope
In this paper, we presented optimal threshold values for total spectrum sensing error probability, throughput, and energy
efficiency. As SNR value increases, the performance of the CR metrics is enhanced. For instance, when SNR increases from 0 dB
to 5 dB, the total spectrum sensing error probability decreases from 0.7693 to 0.4455, the throughput increases from 12.68 to
13.55, and energy efficiency increases from 49.79% to 53.55%. Therefore, CR should adapt its operating parameters to the
variations of the wireless communication environment.
Future research in CR networks could focus on advancing adaptive thresholding techniques for energy detection using deep
learning models. This includes optimizing threshold adaptation algorithms based on real-time data.
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