An Energy Eﬃcient Cooperative Spectrum Sensing for Cognitive Radio-Internet of Things with Interference Constraints

Spectrum sensing plays a very important role in Cognitive Radio based Internet of Things (CR-IoT) networks for utilization of the licensed spectrum accurately. However, the performance of the conventional Energy Detector (ED) method is compromised in a noise-uncertain environment owing to interference constraints, i.e. the CR-IoT user interference with the licensed Primary User (PU) on the same licensed band. To overcome this drawback, we proposed an energy eﬃcient Cooperative Spectrum Sensing (CSS) for a CR-IoT network with interference constraints using a novel ED method. In this method, each CR-IoT user is capable of spectrum sensing that makes both the local decision and the weight factor based on the sequential approach; we calculate the weight factor against each CR-IoT user based on the Kullback Leibler Divergence award score. After the local decision and the weight factor are made, each CR-IoT user transmits its measured both the local decisions, and the weight factor to a Fusion Center (FC), which is made a ﬁnal decision about the PU activities based on the hard fusion rule. The simulation results demonstrates that the proposed ED method obtains an improved detection performance, an enhanced sum rate, a spectral eﬃciency, an energy eﬃciency,


Introduction
Nowadays the Internet of Things (IoT) is one of the most rising network applications that connects the billions of networking devices across the globe to the Internet world and permits connectivity among devices, all networking appliances can collect and share data continuously over the internet to achieve better value and services [1][2][3][4][5][6]. Nevertheless, there are several challenges that abate the outgrowth of IoT networks such as its requires greater bandwidth for connecting a lot number of hybrid communication devices and services, ensuring the security of a massive number of heterogeneous devices and networks, high implementation cost, lack of adequate spectrum and more energy required than the conventional communication systems [7][8][9][10][11]. Cognitive Radio (CR) technology is developed to solve the spectrum shortage due to increasing wireless devices and networks [12][13][14]. It promotes the use of the radio frequency band by permitting Secondary User (SU) to allow the licensed spectrum of the Primary User (PU) [15][16][17][18][19][20]. In a Cognitive Radio based IoT (CR-IoT) network [4,21,22], each CR-IoT user is conveniently using the idle licensed frequency bandwidth when the licensed user is absent in the CR-IoT networks. Basically, each CR-IoT user detects the unoccupied licensed channels and selects the one that is most appropriate for data transmission. To overcome the unacceptable conflict between the PU and the CR-IoT user, the CR-IoT user leaves the licensed spectrum as soon as possible when the PU returns to transmit data in the network [23,24]. The unoccupied licensed spectrum detection is a very important part in the CR Network (CRN) to overcome the unacceptable conflict between the PU and the SU [25,26].
Licensed spectrum detection approaches can be classified into many groups, including non-coherent spectrum sensing, coherent spectrum sensing, Non-Cooperative Spectrum Sensing (NCSS), and Cooperative Spectrum Sensing (CSS). In a non-coherent spectrum sensing, for the purpose of spectrum sensing it is not require any previous knowledge about the PU signal [27]. In a coherent detection scheme, PU signal detection requires perfect prior knowledge of the PU signal, e.g. synchronization message, presenter, spectral scattering sequences, training and pilot patterns [28]. In non-cooperative detection, CR-IoT users do not need to exchange sensing information with other CR-IoT users [29]. In this method, the performance of spectrum detection is reduced due to concealed terminal issues, multi-path fading, and shadow impact [30]. In CSS techniques [31,32], where group of CR-IoT users cooperatively execute spectrum detection to mitigate the multi-path fading, hidden terminal problem, and shadowing effects. In CSS technique, each CR-IoT user sends the spectral detection result of the PU signal to the respective Fusion Center (FC) individually. Thereafter, the FC uses the fusion rule on the collected spectrum detection outcomes of the CR-IoT users to take a final global decision. In the end, the FC transfers a final global decision to all CR-IoT user about the appearance and non-appearance of the PU signal in the CR-IoT networks [33][34][35].
Numerous spectrum sensing methods have been investigated under varying conditions, including matched filter method [36], cyclostationary feature method [37], entropy-based method [39,40], eigenvalue-based method [38], and Energy Detection (ED) method [41,42]. The matched filter method and cyclostationary feature method are both easy to understand and execute. However, both require reliant prior knowledge of PU signals, e.g., the carrier frequency, the modulation technique, amplitude, and phase of the PU signal [43]. The ED method is one of the simplest methods to calculate the received signal energy of the PU signal without any previous information about the PU signal [44]. Therefore, it is the most commonly used method for spectrum sensing in CRNs. However, the ED is very susceptible to noise fluctuations and needs a absolutely right understanding of the influence of noise signal power at the receiver side of the CR-IoT user for proper identification of PU signal. As a result, the detection performance of the ED method is degraded in noise uncertainty environments and low Signal to Noise Ratio (SNR) value [45].
The CSS technique was studied in order to resolve the issue of spectrum sensing for CR-IoT networks. In [46], the detection performance of CSS have been analyzed under a situation in which malicious users transfer a wrong detection result to the FC, i.e. malware attacks. In [47], the authors introduced the eigenvalue-based CSS scheme to enhance the spectrum detection performance under the effects of impulsive noise distributions. In [48], the authors analysed the blind CSS methods for interweave CRN. In [49] each CR-IoT user used the CSS technique to sense the PU signal, they are used noisy reporting channel to send the sensing results to the FC. In [50], the authors used the Kullback-Leibler divergence (KLD) technique to calculate the weight value for each CR-IoT user according to their local sensing result and the FC uses the local sensing results and weight value of each CR-IoT user to make the final global decision about the appearance and non-appearance of the PU's signal in CR-IoT networks. In [51], each CR-IoT generates their local spectrum sensing result about the appearance and non-appearance of the PU's signal in the network. The FC collected the local detection results. Thereafter, the FC applies weights to the local spectrum detection results of the CR-IoT users. Finally, the FC makes the final global decision based on the KLD techniques and this decision sends to the CR-IoT users. The authors proposed sub-optimal recursive search algorithm to maximize energy efficient licensed spectrum detection for a CRN by optimizing sensing and transmission time in [52]. Its minimizes the interference between PU and cognitive user transmission. However, their paper considered only one PU and one SU; for the large number of SUs, this scheme is not capable of ensuring optimal spectrum detection performance. In [53], the authors proposed the Conventional Col- laborative Compressive Sensing (CCCS) approach for better energy efficiency spectrum sensing in CRNs. Their paper optimized the parameters value to enhance the energy efficiency of the CCCS scheme. The authors introduced the energy efficient spectrum sensing approach using Dempster-Shafer (D-S) theory in CR Sensor Networks (CRSNs) to maximize detection accuracy and minimize energy consumption in [54]. In [55], the authors proposed a twoway dynamic spectrum sensing scheme which the energy efficiency for data transmission in CR-IoT networks are maximized. Moreover, the proposed an energy efficient power assignment approach is to improve the spectrum detection performance and throughput. In [56], the authors proposed a hybrid PSO (Particle Swarm Optimization)-GSA (Gravitational Search Algorithm) which is maximized the energy efficiency of the spectrum detection by identifying the licensed spectrum, the power spectral density and the transmission power.
In summary, the current research has some drawbacks as shown in Table  1: (i) a typical CR-IoT network in which all CR-IoT users are participating to sense the PU licensed channel for scenario I which did not to consider interference constraints e.g., perfect channel conditions; and (ii) an improved detection performance, an enhanced the sum rate, an improved spectral efficiency, a lowest energy efficiency and a lowest global error probability for scenario II has not been analyzed regarding with both interference constraints e.g., imperfect channel conditions and flexible sensing time e.g., sequential scheduling. The proposed ED method overcomes these drawbacks.
The major achievements of this article are summarized in the following points: -We propose an energy efficient CSS scheme for CR-IoT networks with interference constraints II. The sum rate in the proposed scheme using a novel ED method is an analyzed and an evaluated. The feasibility of the proposed ED method is evaluated when compared with the conventional ED method for scenario I, e.g., detection performance and sum rate. -We examine the sequential approach [2] in which the flexible sensing time period is obtained by each CR-IoT user, which enhances the detection performance, however with the limited number of samples due to noise uncertainty [27] and interference robustness. In addition, we evaluate the weight factor from the KLD award score based on the flexible sensing time slot. -The detection performance of the proposed ED method is analyzed for both CR-IoT users and an FC based on the hard fusion rule. -Depending on the enhanced detection performance, (i) the sum rate of the licensed primary network, and the unlicensed CR-IoT network, is evaluated for the conventional ED method and the proposed ED method using the hard fusion rule under different channel environments, and (ii) the global error probability is also evaluated for the conventional ED method and the proposed ED method with interference constraint for scenario II. -Moreover, the spectral efficiency and the energy efficiency are analyzed depend on both the sum rate and the detection performance for the conventional ED method and the proposed ED method with interference constraint for scenario II. -Eventually, the simulation results show that the proposed ED method obtains an improved detection performance, an enhanced sum rate, an improved spectral efficiency, a lowest energy efficiency and a lowest global error probability compared to other conventional ED methods with interference constraints for scenario II.
The rest of this article is structured as follows. The proposed system model for scenario I and scenario II explains in Section 2. The conventional ED method for scenario I is discussed in Section 3. Moreover, we describe the detection performance, the sum rate, the spectral efficiency, an energy efficiency, and the global error probability. In Section 4, the proposed scheme based on a novel ED method for scenario II is analyzed of the flexible sensing duration, the weight factor based on the KLD award score, the detection performance, the sum rate, the spectral efficiency, an energy efficiency, and the global error probability. The simulation validation with the value of parameters and their affects are discussed in Section 5, here, the proposed ED method illustrates improved detection performance, enhanced sum rate, spectral efficiency, energy efficiency, global error probability, and total time when compared to other conventional ED methods. Finally, in Section 6, our finding and possible future work are discussed.
For ease of comparison, in Table 2, we list our generally used notations with description as follows:

System Model
For a CR-IoT network, spectrum sensing become an essential and fundamental method to identify the unused spectrum allotted to the PUs. An explanation of the proposed system model for scenario I, and scenario II are discussed in this section.

Scenario I
The proposed system model is composed of a CR-IoT network (unlicensed), and a primary network (i.e., licensed) which is depicted in Fig. 1. The primary network is composed of the primary receiver (i.e., PU Rx), and the primary transmitter (i.e., PU Tx). The execution of the PU activities i.e., ON or OFF are represented by the Time Division Multiplexing Access (TDMA). Whilst, in a CR-IoT network (i.e., secondary network), it includes an FC and a lot of (M) CR-IoT users (unlicensed). Just in Fig. 1 (a) for scenario I, the CR-IoT user refers to an unlicensed CR-IoT user who wants to access the PU spectrum without interference constraints from the casing, whereas the PU is referred to as the spectrum's licensed user.

Scenario II
In this Fig. 1 (b) for scenario II, the CR-IoT user refers to an unlicensed CR-IoT user who wants to allow the PU spectrum opportunistically with casing interference. As a result, this interference is degraded the detection performance of the proposed ED method.
As a result, depend on the transmission of the PU activities, the received signal is evaluated by the i th CR-IoT user under hypotheses as follows [57]: where z i (l) indicates the received signal in the l th sampling time by the i th CR-IoT user, h i (l) indicates the channel gain between the PU Tx and the i th CR-IoT Rx, x i (l) indicates an additive white Gaussian noise of the i th CR-IoT user, i.e., x i (l) 0, σ 2 x,i , and s (l) indicates the transmitted PU signal that is used the Binary Phase Shift Keying (BPSK) modulation technique; here l = 1, 2, · · · , N x , and i = 1, 2, · · · , M. Moreover, during the sensing phase, the stationary channel is considered.

Conventional Energy Detection Method for Scenario I
For the conventional ED method based CSS in CR-IoT networks for scenario I where the analysis of detection performance is addressed in the sub-section 3.1, the analysis of sum rate is provided in sub-section 3.2, the spectral efficiency is discussed in the sub-section 3.1, and the energy efficiency is discussed in sub-section 3.4. Moreover, the global error probability is discussed in the subsection 3.5.
The received signal energy during the sensing phase of the conventional ED method is evaluated and compared with the predetermined threshold value [17,18], which is illustrated in Fig. 2.  [17] Now, the continuous signal power in time-domain that occupies the specific bandwidth is calculated by each CR-IoT user to achieve the decision statistics of the conventional ED method as described in the following: First, to choose the specified signal frequency, the obtained signal is filtered by a bandpass filter, and the outcome of that filter is converted by an analog to digital converter (ADC) as a produce the analog signal; Secondly, this analog signal is to produce the discrete time signal using sample and hold circuit; and Finally, this discrete time signal is independently summation and squared to calculate its own signal energy obtained by the conventional ED method [58]. Therefore, the calculated energy of the i th CR-IoT user is given by the following formula: where z i l fs is the received signal at the l th sample of the i th CR-IoT user, N s indicates the signal samples during the sensing phase that defines as N s = 2τ s f s ; here, f s indicates the sampling frequency, and τ s indicates the sensing time slot during the sensing phase. For all CR-IoT users in CR-IoT networks, thus, the duration of the inflexible sensing time slot, τ s , is widely to use as shown in Fig. 3.

Analysis of detection Performance
If N s > 300, then the measured obtained signal of the CR-IoT user, e i , should be Gaussian random variable under both hypotheses based on the Center Limit Theorem (CLT) that is mathematically defined as follows: where τ c s denotes the inflexible sensing time slot for the conventional ED method, and γ i denotes SNR of the i th CR-IoT user that is mathematically defined as γ i = p 2 s σ 2 x,i ; here p s denotes the signal power of the PU transmitted signal.
By comparing e i to a predetermined threshold value, λ I i,ED using the Eq. 4, the detection probability, p I d,i , and the probability of false alarm, p I f,i of the i th CR-IoT user is calculated as follows: and where Q (θ) is a Gaussian tail function which is mathematically given by ∞ θ e − η 2 2 dη. Therefore, the probability of a false alarm, p I f,i refers to the probability where the CR-IoT user wrongly claims the presence of the PU, even if the PU is really absent on the licensed spectrum for scenario I; whilst the detection probability, p I d,i refers to the probability where the CR-IoT user correctly claims the presence of the PU, even though the PU is really present on the licensed spectrum for scenario I.
After the sensing phase, each CR-IoT user forwarded its own local decision toward the respective FC during the fixed reporting time slot, which are integrated with the local decisions in terms of achieving the global decision on the spectrum allocation of the PU [57]. Now, the detection performance of the global decision, i.e., p I f,F C /p I d,F C , at the FC for scenario I is calculated by and where β I is the predetermined decision threshold at the FC for scenario I.

Analysis of Sum Rate
The sum rate, R I of the conventional ED method for scenario I, can be estimated based on the global detection performance (p I f,F C /p I d,F C ) as follows: where α, R I P U , and R I CR−IoT,i are the primary activity factor, the channel capacity of the PU link, and the channel capacity of the i th CR-IoT user, respectively.
The channel capacity of the i th CR-IoT user, and the channel capacity of the PU link are defined, respectively as follows: and where W denotes the licensed channel bandwidth in bps/Hz.

Analysis of Spectral Efficiency
In this sub-section, the spectral efficiency (SE) of the conventional ED method without interference constraints for scenario I at the FC is evaluated which can be defined as follows: where V I SE is the SE for scenario I in b/s/Hz.

Analysis of Energy Efficiency
In this sub-section, the energy consumption (EE) of the conventional ED method without interference for scenario I at the FC is evaluated that is calculated as where V I EE is the EE of the conventional scheme without interference for scenario I in b/s/J, and P is the transmitted power in J.

Analysis of Global Error Probability
In this sub-section, the global error probability, p I e of the conventional ED method without interference for scenario I at the FC is evaluated which is formulated as follows: where α is the primary activity factor of the PU. The whole idea is demonstrated by the Algorithm 1, which verifies the inflexible sensing time slot, τ c s = τ s (see line 3) as the conventional ED method without interference for scenario I is not being utilizing the reporting framework. After that, the probability of false alarm (see line 4), and the detection probability (see line 5) are determined in the conventional ED method without interference for scenario I. Then after that, a global decision, p I f,F C /p I d,F C at the FC is computed (see line 7/line 8). Finally, the sum rate, spectral efficiency, energy efficiency, and global error probability are computed based on the global detection (p I f,F C /p I d,F C ) at the FC (see lines from 9 to 12).

Proposed Energy Detection Method for Scenario II
For the proposed ED method based CSS with interference constraints in a CR-IoT network for scenario II where the utilization of the reporting framework is explained in the sub-section 4.1, the analysis of weight factor of each CR-IoT user is discussed in the sub-section 4.2, the analysis of detection performance is explained in the sub-section 4.3, the analysis of the sum rate is provided in sub-section 4.4, the spectral efficiency is derived in the sub-section 4.5, and finally, the energy efficiency is discussed in sub-section 4.6. Moreover, the global error probability is discussed in the sub-section 4.7 and the total time is discussed in sub-section 4.8.

Algorithm 1
The conventional ED method based CSS scheme without interference constraints for scenario I Input: Ns, M, T, fs, τr, and τs Output: Estimate the probability of false alarm, p I f,F C , the detection probability, p I d,F C , the sum rate R I , the spectral efficiency, V I SE , the energy efficiency, V I EE , and the global error probability, p I e 1: Initialize M, Ns, and τs 2: for i = 1 to M do 3: Calculate: τ c s = τs 4: Calculate

Analysis of Flexible Sensing Time
In flexible sensing time slot, the 2 nd CR-IoT user is utilized the fixed reporting time slot (τ 1 r ) of the 1 st CR-IoT user as obtaining the flexible sensing time slot (τ 2 s ), i.e., τ 2 s = τ 2 s + τ 1 r ; the 3 rd CR-IoT user is utilized the fixed reporting time slots of both the previous the 2 nd CR-IoT user (τ 2 r ), and 1 st CR-IoT user (τ 1 r ) as obtaining the more flexible sensing time slot (τ 3 s ), i.e., τ 3 s = τ 3 s + τ 1 r + τ 2 r ; etc as well, as depicted in Fig. 4. We conclude that the flexible sensing time slot (τ p s ) is then obtained for all CR-IoT users, except for the 1 st CR-IoT user. Currently, the flexible sensing time slot, τ p s , of the proposed ED method is calculated by each CR-IoT user in a CR-IoT network with interference constraints for scenario II which is seen in Fig. 4 of the following format [2]: where τ s , τ p s , and τ r are the non-flexible sensing time slot for each CR-IoT user, the flexible sensing time slot of the proposed ED method, and the fixed reporting time slot for each CR-IoT user, respectively. The packet format of the proposed ED method for scenario II where the flexible sensing time slot is obtained based on the reporting framework as depicted in Fig. 4. As a result, based on the flexible sensing time slot, τ p s using the KLD award score, each CR-IoT user to sense the PU licensed spectrum more efficiently. Now, we can calculate the KLD award score, δ of the proposed ED method using the flexible sensing time slot, τ p s with interference constraints for scenario II which is defined as between the two normally distributed functions f (ψ) and f (ψ) [5,50,51,59] as follows: It is essential to confirm the KLD award score, δ expression of the two Gaussian distributions of e i (H 1 ), and e i (H 0 ) using H 1 , and H 0 , respectively. Under two hypotheses (H 1 /H 0 ), the means in Eq. 4 are updated by the flexible sensing time slot (τ p s ) which are given bȳ  i (H 0 ) and σ 2 i (H 1 ) in Eq. 4. After evaluating the updated means and variances from in Eq. 17 and Eq. 18, each CR-IoT user of the proposed scheme computes the weight factor (Ω i ) based on the KLD award score (δ) using the flexible sensing time slot, τ p s is given as follows: where Ω i is the weight factor at the i th CR-IoT user of the proposed ED method for scenario II.

Analysis of Detection Performance
Now, we can estimate the detection probability p II d,i , and the probability of false alarm, p II f,i of the i th CR-IoT user in the proposed ED scheme for scenario II by compared to the received signal, e i with the predetermined local decision threshold, λ II i,ED , is given by Eq. 17 and Eq. 18 as follows: and Therefore, the probability of a false alarm, p II f,i refers to the probability where each CR-IoT user wrongly claims the presence of the PU, though if the PU is really absent on the licensed spectrum for scenario II, whilst the detection probability, p II d,i refers to the probability where each CR-IoT user correctly claims the presence of the PU, even though the PU is really present on the licensed spectrum for scenario II.
After the sensing phase of the proposed scheme for scenario II, each CR-IoT user forwards its local decision towards the respective FC during the fixed reporting time slot (τ r ), which are integrated with the local decisions in terms of achieving a global decision on the PU's spectrum occupancy. The detection performance at the FC as like the global decision, i.e., p II f,F C /p II d,F C based on the weight factor (Ω i ) and the local decision (p II f,i /p II d,i ) of the i th CR-IoT user for scenario II is calculated by and where β II is the global decision threshold at the FC for scenario II.

Analysis of Sum Rate
After calculating the detection performance at the FC based on the flexible sensing time slot (τ p s ) in the previous sub-section, now the sum rate is evaluated when considering numerous premises. During the transmission phase, the CR-IoT Tx transmits its own relevant information towards the respective CR-IoT Rx based on round robin scheduling approach [5]. In the case of the non-false alarm, if the PU is absent, each unlicensed CR-IoT user is correctly sensed the absence of the PU; then each unlicensed CR-IoT user is likely to allow the licensed spectrum of the PU for a certain amount of time , as described by the probability of 1 − p II f,F C . In another side, in the case of detection, the CR-IoT users should not interfere with the PU transmission. Consequently, the sum rate based on the round robin scheduling approach of the proposed scheme for scenario II is defined as follows: where R II is the sum rate in Hz or b/s, and α is the primary activity factor, that is defined as α ∈ [1, 0]. Moreover, R II CR−IoT , and R II P U are the channel capacity of the CR-IoT link for scenario II, and the channel capacity of the PU link for scenario II, respectively. Now, we can calculate the channel capacity of the CR-IoT link, R II CR−IoT , and the channel capacity of the PU link, R II P U which are expressed as follows: and where SN R CR−IoT,i , T, and SN R P U , indicates the SNR of the CR-IoT Tx & the CR-IoT Rx link of the i th CR-IoT user, the total frame length, and the SNR of the PU Tx and the CR-IoT Rx link, respectively.

Analysis of Spectral Efficiency
Now, the spectral efficiency (SE) of the proposed ED method with interference constraints (scenario II) at the FC is calculated in this sub-section which can be defined as follows: where V II SE is the SE for scenario II in b/s/Hz.

Analysis of Energy Efficiency
In this sub-section, the energy efficiency (EE) of the proposed ED method with interference constraints (scenario II) at the FC is calculated which can defined as follows: where P, and V II EE indicates the transmit power in J, and the energy efficiency (EE) for scenario II in b/s/J, respectively.

Analysis of Global Error Probability
Now, the global error probability, p II e of the proposed ED method for scenario II at the FC is calculated in this sub-section which is given as follows:

Total Time Analysis
In this sub-section, if the number of CR-IoT users (M) is increased then the total time, τ II t of the proposed ED method for scenario II is also increased which is consisting of the sum of the fiexed reporting time, τ r , and the sensing time, τ s [48]. Therefore, the total time of the proposed ED scheme for scenario II is defined as follows: where τ i r is the reporting time of the i th CR IoT user i.e., τ i r = τ r , and τ II t is the total time of the proposed ED scheme for scenario II; here, the reporting time, τ r and the sensing time, τ s of the proposed ED method for scenario II are same, i.e., τ r = τ s . Therefore, we can see from Eq. 30, the total time, τ II t of the proposed ED method for scenario II is only depend on the M. If M is increased by the number of CR-IoT users, the detection performance of the proposed ED method is improved while the total time required is also increased.
The whole idea is demonstrated by the proposed Algorithm 2. In Algorithm 2, it checks τ p s = τ s + M τ r (see line 8) as the proposed ED scheme for scenario II is being utilizing the reporting framework. Then it updates the means and variances based on the flexible sensing time slot (τ p s ) (see line 10/ line 11). Also, it computes the weight factor based on the updated the means and variances (see line 12

Simulation Results and Discussion
The simulation findings with the relevant explanation is discussed in this section. Numerical assessments were carried out and contrasted with those of many other conventional ED methods employing Monte Carlo test to evaluate the detection probability of the proposed ED method. MATLAB R2020b is used to run simulations, and the findings are computed from an average of 20 × 10 3 − 50 × 10 3 independent simulation loops. Table 3 summarizes the simulation parameters that are required.
First for scenario I, the detection performance of the conventional ED method, and the proposed ED method are evaluated; then, their performance is depicted in Fig. 5a. The performance achieved when the SNR, i.e.,γ is −4dB, the predetermined sample, N x ) is 25, the flexible sensing time slot, τ p s is 10ms, and the non-flexible sensing time slot, τ c s is 5ms. The cooperative detection performance is drawn by Receiver Operating Characteristic (ROC) curves for the proposed ED method, and the conventional ED method for scenario I under the flexible and non-flexible sensing time slots which is shown in Fig.  5a. In τ p s , the detection probability of the conventional scheme is an enhanced. For instance, if p I f,F C is 0.20 for the conventional ED method for scenario I, then the detection probability, p I   better detection performance (29% when τ c s = 5ms and τ p s = 10ms) than the conventional ED method for scenario I. Fig. 5b illustrates the ROC curve of the cooperative detection performance obtained based on different sensing time slots, i.e., τ c s , and τ p s , of the proposed ED method and the conventional ED method with interference constraints for scenario II. Within the flexible sensing time slot, τ p s of the conventional ED method, the detection probability enhances as shown in Fig. 5b. For instance, if p II f,F C is 0.20 of the conventional ED method for scenario II, then the detection probability, p II d,F C with fixed sensing time slot (τ c s = 5ms), and the detection probability, p II d,F C with flexible sensing time slot (τ p s = 10ms) are 0.48 and 0.50, respectively. Similarly, if p II f,F C is 0.20 of the proposed ED method for scenario II, then the probability of detection, p II d,F C with fixed sensing time slot (τ c s = 5ms), and the detection probability, p II d,F C with flexible sensing time slot (τ p s = 10ms) are 0.78 and 0.81, respectively. Because of the weighted factor, Ω i of the proposed ED method for scenario II, the detection performance is an improved in the proposed scheme. It is clearly seen in the proposed ED method and the conventional ED method by contrasting all ROCs at the FC where the proposed ED method has a much better detection performance (31% when τ c s = 5ms and 30% when τ p s = 10ms) than the conventional ED method for scenario II.
At the FC, by comparison of the detection performance is shown in Fig.  5a as well as Fig. 5b; here, both are demonstrated that with τ c s = 5 ms, the proposed ED method for scenario I is detected the licensed PU's spectrum with 89% detection performance, while the conventional ED method for scenario I is detected the licensed PU's spectrum with 60% detection performance that is listed in Table 4. Fig. 6 shows the detection probability, and the probability of false alarm of the proposed ED method versus SNR for scenarios I, where N = 20 and τ s = 10ms and τ r = 5 ms. We can seen from Fig. 6a, the detection perfor- Table 4: Detection performance of the proposed ED method, and the conventional ED method at a FC, when both scenario I, and scenario II are considered; here, the probability of false alarm (p I f,F C = p II f,F C ) is 0.20.
Schemes e.g., detection probability τ c s = 5ms τ p s = 10ms The conventional ED method for scenario I 0.60 0.65 The proposed ED method for scenario I 0.89 0.94 The conventional ED method for scenario II 0.50 0.57 The proposed ED method for scenario II 0.82 0.89 mance of the proposed ED method increases significantly as the SNR value are increasing. For instance, for N s = 20, the probability of detection is 44% when SN R = −9dB, 68% when SN R = −6dB, and 90% when SN R = −3dB; whereas the detection performance of the conventional scheme slightly increases as SNR value increases. Again for instance, for the conventional ED scheme with N s = 20, the probability of detection achieves 0% for SN R = −9dB, 5% for SN R = −6dB, and 15% for SN R = −3dB. Furthermore, we seen that the p I f,F C of the proposed ED method significantly decreases as the SNR value increases as depicted in Fig. 6b. However, we clearly seen from this simulation where the detection performance of the conventional ED method did not perform well whereas the SN R value is −8 dB. Therefore, it is seen that the conventional ED method is not sufficient for low SNR value, i.e., SN R ≤ −8 dB.  (b) SNR vs. p I f,F C for scenario I Fig. 6: SN R vs. the detection probability, and the probability of false alarm at FC when scenario I is only considered. Fig. 7 demonstrates probability of false alarm, and the detection probability of the proposed ED method versus the SINR value for scenario II, where N = 20 and τ p s = 10ms and τ r = 5 ms. We can seen that the probability of detection of the proposed ED method significantly increases when the SIN R  (b) SINR vs the probability of false alarm for scenario II Fig. 7: SIN R vs. the detection probability, and the probability of false alarm at FC when scenario II is only considered.
value is increasing as shown in Fig. 7a. For example, the detection probability is 35% when SIN R = −9dB, 51% when SIN R = −6dB, and 78% when SIN R = −3dB; whereas the detection probability of the conventional ED scheme slightly increases with increasing SIN R. For example, for N s = 20, the detection probability is 0% when SIN R = −9dB, 4% when SIN R = −6dB, and 8% when SIN R = −3dB. Moreover, according to Fig. 7b, we have seen it with increasing SINR, then the p II f,F C of the proposed ED method is decreased. For example, for N s = 20, the p II f,F C is 68% when SIN R = −9dB, 48% when SIN R = −6dB, and 20% when SIN R = −3dB; whereas the p II f,F C of the conventional ED method slightly decreases when the SIN R value is increasing. For example, for N s = 20, the p II f,F C is 100% when SIN R = −9dB, 98% when SIN R = −6dB, and 92% when SIN R = −3dB. However, we can see from this simulation where the detection performance of the conventional ED method did not perform well when the SIN R value is −8 dB. Therefore, it is seen that the conventional ED scheme did not perform well when the low SIN R value is considered i.e., SIN R ≤ −8 dB. Fig. 8a demonstrates the sum rates of the proposed ED method, and the conventional ED method without interference constraints for scenario I that depends on the p I f,F C . The sum rate of the proposed ED method for scenario I is better when compared with the conventional ED method for the whole value of the p I f,F C . Consequently, the sum rate ROC defines a quasi concave function of the p I f,F C for the PU activity factor (α). As a result, for the scenario I, the sum rate of the proposed ED method achieved 2360Hz, while the sum rate of the conventional ED method achieved 1921Hz under the non-    Fig. 8b shows the sum rates of the proposed ED method, and conventional ED method with scenario II depends on the probability of false alarm which is a function of the p II f,F C . For the entire range of the p II f,F C , the sum rate of the proposed ED method achieved a higher compared to the conventional ED method. Therefore, the sum rate of the proposed ED method for scenario II achieved 2149Hz, whilst the sum rate of the conventional ED technique achieved 1700Hz when the non-flexible sensing time slot (τ c s = 5ms), the number of samples (N s = 20), and the probability of false alarm (p II f,F C = 0.2). Moreover, the sum rate of the conventional ED method for scenario II is 1792Hz, whilst the sum rate of the proposed ED method is 2280Hz at the probability of false (p II f,F C = 0.2) with the number of samples (N s = 20) and the flexible sensing time slot (τ s = 10ms). Therefore, we argue that as compared to the sum rate of the conventional ED method when the number of samples (N s = 20), and the no-flexible sensing time slot (τ c s = 5ms) or the flexible sensing time slot (τ p s 10ms) for scenario II, the sum rate of the proposed ED method achieved an enhanced.
The spectral efficiency of the conventional ED method and the proposed ED method demonstrates in Fig. 9 when both scenario I and scenario II are considered. For scenario I, the spectral efficiency of the proposed ED method achieved a better when compared to the conventional ED method due to its higher sum rate as shown in Fig. 9a. Here, we clearly seen as the V I SE of the proposed ED method (8.4bps/Hz) achieved a higher compared with the conventional ED method (6.5bps/Hz), where p I f,F C is 0.1, and the sensing time slot (τ p s ) is 10ms for scenario I. Similarly, the spectral efficiency of the  proposed ED method (7.5bps/Hz) obtained a higher compared by the conventional ED method (5.8bps/Hz) for scenario II, where p II f,F C is 0.1, and the sensing time slot (τ p s ) is 10ms as shown in Fig. 9b. Therefore, we argue that the V II SE of the proposed ED method (7.5bps/Hz) for scenario II obtained a lower compared with the proposed ED method (8.4bps/Hz) for scenario I due to the interference constraints is considering in scenario II which degrades the detection performance of the PU spectrum.
In Fig. 10, it demonstrates the energy efficiency of the conventional ED method, and the proposed ED method when both scenarios are considered, i.e., I, and II. For scenario I, the energy efficiency of the proposed ED method achieved a higher compared to the conventional ED method because of its higher sum rate as shown in Fig. 10a. Here for scenario I, we clearly seen that the energy efficiency of the proposed ED method (1.30bps/J) is a better when compared to the conventional ED method (1.04bps/J), where the flexible sensing time slot (τ p s ), and the probability of false alarm (p I f,F C ) are 10ms, and 0.1, respectively. Similarly for scenario II, the energy efficiency of the proposed ED method (1.2bps/J) is a better when compared to the conventional ED method (0.94bps/J), where the sensing time slot (τ p s ) is 10ms, and p II f,F C is 0.1. Finally, we argue that the energy efficiency of the proposed ED method for scenario II achieved a lower compared with the proposed ED method with scenario I due to the scenario II is considering the interference constraints which degrades the detection performance.  Fig. 10: Energy efficiency curves vs. the probability of false alarm at FC for the conventional ED method, and the proposed ED method when scenario I and scenario II are considered. Fig. 11 shows the global error probability for the conventional ED method, and the proposed ED method when scenario I and scenario II are considered. We shown in Fig. 11a, the global error probability for both the proposed ED method and the conventional ED method decreases as the probability of false alarm decreases as like 0.3 to 0.0.   Fig. 11: Global error probability curves at FC of the conventional ED method and the proposed ED method when scenario I and scenario II are considered.
Therefore, in terms of the global error probability for scenario I, the proposed ED method achieves 50% compared to 70% with the conventional scheme at p I f,F C = 0.1, when the sensing time slot (τ p s ) is 10ms. Similarly, we observed from Fig. 11b, it is clearly seen as the p II e of the proposed ED method for sce-nario II achieves 60% compared to 80% with the conventional ED method at p II f,F C = 0.1, when the sensing time slot (τ p s ) is 10ms. Therefore, we conclude from Fig. 11a and Fig. 11b, in terms of the global error probability, the proposed ED method (60%) for scenario II achieves a higher compared to the proposed ED method (50%) for scenario I due to the interference constraints is considering in scenario II which also degrades the global error probability.

Conclusion
The detection performance of the conventional ED method and the proposed ED method for CSS scheme has been presented. In the detection performance, (i) for scenario I, the proposed ED method with the flexible sensing time slot i.e., τ p s demonstrates a 8%, 38% and 47% improvement over the proposed ED method with the non-flexible sensing time slot e.g, τ c s , the conventional ED method with the flexible sensing time slot, e.g, τ p s and the conventional ED method with the non-flexible sensing time slot, i.e., τ c s , respectively; and (ii) for scenario II, the proposed ED method with flexible sensing time slot demonstrates a 10%, 43% and 46% improvement over the proposed ED method with non-flexible sensing time slot, the conventional ED method with flexible sensing time slot, and the conventional ED method with non-flexible sensing time slot, respectively. Also, with respect to sum rate, (i) for scenario I, the proposed ED method with flexible sensing time slot demonstrates a 7%, 45%, and 53% improvement over the proposed ED method with non-flexible sensing time slot, the conventional ED method with flexible sensing time slot, and the conventional ED method with non-flexible sensing time slot, respectively; and (ii) for scenario II, the proposed ED method with flexible sensing time slot demonstrates a 11%, 49%, and 54% improvement over the proposed ED method with non-flexible sensing time slot, the conventional ED method with flexible sensing time slot, and the conventional ED method with nonflexible sensing time slot, respectively. In terms of bandwidth of the spectral efficiency, (i) for scenario I, the proposed ED method with flexible sensing time slot, demonstrates a 5%, 17%, and 19% improvement over the proposed ED method with non-fixed sensing time slot, the conventional ED method with flexible sensing time slot, and the conventional ED method with nonflexible sensing time slot, respectively; and (ii) for scenario II, the proposed ED method with flexible sensing time slot demonstrates a 3%, 17% and 20% improvement over the proposed ED method with non-flexible sensing time slot, the conventional ED method with flexible sensing time slot, and the conventional ED method with non-flexible sensing time slot, respectively. In addition, in terms of sum rate of the energy efficiency, (i) for scenario I, the proposed ED method with flexible sensing time slot demonstrates a 3%, 18% and 20% better over the proposed ED method with non-flexible sensing time slot, the conventional ED method with flexible sensing time slot, and the conventional ED method with non-flexible sensing time slot, respectively; and (ii) for scenario II, the proposed ED method with flexible sensing time slot demonstrates a 3%, 24%, and 26% improvement over the proposed ED method with nonflexible sensing time slot, the conventional ED method with flexible sensing time slot, and the conventional ED method with non-flexible sensing time slot, respectively. Eventually, a global error probability of 50% obtains in the proposed ED method with flexible sensing time slot for scenario I, while 56%, 70%, and 72% global error probabilities obtains in the proposed ED method with non-flexible sensing time slot, the conventional ED method with flexible sensing time slot, and the conventional ED method with non-flexible sensing time slot, where p I f,F C is 0.1. Moreover, the global probability error of 60% obtains in the proposed ED method based on the flexible sensing time slot for scenario II, while 66%, 80% and 81% global error probabilities obtains in the proposed ED method with non-flexible sensing time slot, the conventional ED method with flexible sensing time slot, and the conventional ED method with non-flexible sensing time slot, where p II f,F C is 0.1. In the proposed ED method, the dynamic threshold will be considered under a real time environment in our future work.

Declarations Funding
This research was supported in part by the Department of Information and Communication Technology, Islamic University, Kushtia-7003, Bangladesh and by the Ministry of Science and Technology, Bangladesh.