An Energy-Efficient Spectrum Sensing in Cognitive Radio Network Using Fractional Optimization Model


 In wireless communication, the main challenge is to use the radio spectrum efficiently. The spectrum used for wireless radio technology is a natural resource that is limited and expensive. The tremendous growth of the market for wireless communication has led to radio spectrum scarcity. The process for conventional spectrum sensing initiates by scanning the frequency spectra for finding the spectrum holes. On the basis of the availability of spectrum holes, Secondary User (SU) can transmit data and need to perform periodic sensing for a seamless connection. In this work, to detect spectrum holes with improved energy utilization, we have proposed the Fractional Optimization Model (FOM) which is the combination of Gray wolf optimization and Cuckoo search algorithm to detect the spectrum holes with improved energy utilization. In this paper, the model is made to obtain energy efficiency while considering different spectrum sensing states. The energy efficiency is improved by optimizing the parameters such as transmission power, sensing bandwidth, and power spectral density using the Fractional GWO-CS optimization algorithm. With the proposed novel FOM, the spectrum holes can be detected with the optimized transmission power, sensing bandwidth, and power spectral density values. The proposed model will be implemented in the working platform of Matlab by optimizing the energy efficiency of spectrum sensing in terms of transmission power, spectrum sensing bandwidth, and power spectral density compared which will be compared with existing optimization methods.

term Cognitive Radio was first utilized by Mitola et al in [3]. Since the Cognitive radio network has the advantage of sensing the spectrum holes without any intricate, it can effortlessly adapt to the surrounding radio environment by applying its intelligence. Hence, it can seamlessly access the licensed spectrum more effectively and efficiently [4]. To enhance energy efficiency in all aspects many works have been implemented by the researchers.
Nevertheless, some of them lack efficiency and some attain local optimization instead of global search optimization very easily. So this paper introduces the Fractional optimization model which combines the GWO and fractional CS algorithm to enhance the random walk to avert the local optimization problem. Thus this method effectively provides the best solution that is an optimized solution.
The proposed FOM (GWO-CS) algorithm is compared with existing works like Adaptive PSO, Hybrid PSO-GSA, and EH-HCRSN methods by exploiting spectrum sensing parameters and graphically represented the better performances of our proposed work. The prime focus of our proposed work is given below.
 To achieve the EE by maintaining a trade-off between sensing bandwidth and power spectral density of spectrum. EE is considered as the proportion of opportunistic throughput and average energy fetched during spectrum sensing and transmission of data.
 To achieve optimization of EE functions with the aid of our proposed FOM( GWO-CS) method by performing analysis by considering each variable as a subproblem.
Our paper is organized as follows: Section 2 presented the related works that are related to our work. In section 3 we discussed the proposed methodology which compromises the algorithms used and different parameters that are included in the analytical representation of our proposed work. Section 5 presented the simulation results of our proposed work along with the existing work, followed by the conclusion in section 6.

Background Research
In Wireless communication the performance can be further enhanced by endorsing the characteristics of Cognitive Radio user/ Secondary user without interrupting the actions of Primary units. Researchers have employed different approaches that manage the spectrum management function which compromises spectrum sensing, identification of the spectrum from the band, and allocation of the spectrum for the CUs. R Rajaguru et al. [5] presented a cooperative spectrum sensing technique along with the characteristic-based cluster classifier which exploits the merging of clustering with the expected maximization (EM) algorithm and reinforcement learning techniques. The application of this method refines the sensing outcomes by minimizing the proportion of error, false alarm rate, and missed identification nevertheless with computational overhead. The dynamic correlation between the secondary users in cognitive radio sensors based on their statistical analysis was described by Amrit Mukherjee et al. [8]. The time delay in prediction can be reduced with the aid of Gaussian Copula theory and advanced particle swarm optimization algorithm for the same set of channels and provides Energy Efficient sensing method along with computational overhead for individual SUs. Generally in cooperative spectrum sensing, CRs most researchers concentrate on improving spectral efficiency, nevertheless, they ignore the energy consumption. Cong wang et al. [10] proposed a hybrid spectrum sharing scheme to improve the mean Energy Efficiency of the SUs. The sensing time and the number of cooperative SUs are optimized by the joint optimization method and hence it maintains the detection accuracy.
However, the information held by the channel shows some error.
A wireless multiple-access channel function has been proposed by Arash Ostovar et al. [6] to demonstrate the availability of primary users along with the mean energy-efficient optimization problem of the cognitive radio systems. This method reduces the energy usage of secondary users and improves the performance metrics of Energy Efficient optimization.
However, the proposed method is not applicable to networks beyond 5G, since the coverage performance increases with the exploitation of non-orthogonal multiple access and OFDMA methods. Errong Pei et al. [7] presented an Energy Harvesting module incorporated with node heterogeneous Cognitive Radio for spectrum sensing. This method exploits the Cross entropy-based spectrum sensing algorithm to reduce the deployment cost of the network and thereby improves the energy utilization efficiency. Zan Li et al. [9] were described a novel cognitive radio network using energy harvesting techniques, which exploits the Partially Observable Markov Decision (POMDP) framework along with a Markov Decision Process (MDP)frameworks to improvise the spectrum efficiency and energy efficiency. This method is not effective for the CR network with multiple SUs and PUs. Feiyu YAN et al. [30] proposed an energy-efficient cooperative spectrum sharing based energy harvesting cognitive radio network to achieve energy efficiency by merging Dinkebalch's method and convex optimization technique. This method effectively accomplishes the high effective EE and better QoS. However, the simulation has been carried between the proposed approach and benchmark scheme and didn't analyze with other approaches. In the massive Multiple-input multiple-output (MIMO) cognitive network the energy efficiency can be accomplished by energy-efficient power control algorithms which were proposed by Manman Cui et al. [31].
This method exploits the bisection based fractional programming to achieve the maximum network EE and efficient iterative algorithm based sequential convex programming to accomplish the optimal transmit power with a slight rising of circuit power consumption. Table 1 illustrates the algorithms that were utilized in previous work along with their merits and limitations. Usually, the conventional method follows the scanning of frequency spectra to detect the spectrum holes [11]. The available spectrum holes initiate the secondary user to transmit the data and thereby perform periodic sensing for coherent connection. The spectrum sensing process is initiated by sensing the available unoccupied channel. After detecting the unoccupied channel, the SUs transmit the data through that channel and thus perform the  Our proposed method exploits the continuous spectrum sensing scheme i.e., it senses the spectrum coherently without any interrupts. To explore the proposed method we are considering the bandwidth W for SU and segmenting it into two bands: WS for spectrum sensing and WT for the transmission of data with the availability of minimal energy outside the band [12]. The SU transmits data by using the bandwidth WT and halts the transmission if it detects any PU on its way. Thus the transmission of data by SU over the bandwidth WT is totally based on the presence of PU. Meanwhile, the spectrum sensing performed by the bandwidth WS is continuous. Thus this is termed as an effective spectrum sensing scheme.
For an instance, consider the PU utilizes Orthogonal Frequency Division Multiple Access (OFDM) along with the Quadrature Amplitude Modulation (QAM) scheme. While the SU exploits the OFDM technique to avert the spectral leakage [13] during data transmission incorporated with subcarrier spacing for the bandwidth WT same as that of the PU. Since the subcarrier for spectrum sensing is orthogonal [14] to the subcarrier for data transmission we can ignore spectral leakage by SU which occurs during sensing and immediate data transmission.

Grey Wolf Optimization Algorithm
GWO is a metaheuristic algorithm that portrays the characteristics of grey wolves and their hunting nature with clear categorization of labor and mutual coordination. These creatures are at the top of the food chain and usually, they tend to live in a group of 7 to 12 [23]. They follow a strict protocol for the hierarchical management system which is depicted in figure 2.
Due to this hierarchical management system and their coordination, they efficiently hunt the prey. In figure 2,  is the layer for the head wolf and it is the most powerful and capable individual. This wolf usually directs the other group members for distributing the food, team's predation actions, and other decision-making jobs. To maintain those processes α wolf requires assistance hence it set β and δ layers wolf to its abetting. The main responsibility of these two layers of wolves is to assist and control the behaviors of other members. The bottom-most layer of the pyramid is the ω layer which occupies the majority population of the group and they maintain the interrelationship of the population and looking after the young ones. Moreover, group hunting is another important social characteristics of grey wolves. The different phases followed by the grey wolf hunting are listed below [24]; The hunting and social hierarchical methods are illustrated numerically in the following section to design GWO and thereby perform optimization.

Numerical expression and Algorithm a) Social hierarchy
Numerically the social hierarchy of wolves can be designed by considering α as the fittest solution and β as the second fittest solution and δ as the next best solution, while ω is considered as the least solutions by exploiting the GWO. Meanwhile, the hunting is directed by α and performed by the assistants β and δ. Usually, ω follows higher levels of wolves.

Algorithm
Initialize the population of Grey

b) Targeted prey
During the hunting process, the grey wolves used to target the prey to be hunt. This has been done to easily attack the prey. this can be numerically expressed as follows [23].
Here T A  and T C  represent the coefficients vectors, TP X  denotes the position vector of the targeted prey, W X  represents the position vector of the grey wolf and t denotes the current iteration [23].
The components a  mentioned in equation (14)

c) Hunting
After targeting the prey the wolves try to hunt it. They have the capability to identify the position of the prey and encircle them. Then the hunting process is guided and directed by the head wolf α. The β and δ might have follows the α. Sometimes they involve in the hunting process without the guidance of α. Mathematically the location of the prey can be optimized by considering the α, β, δ as the three best solutions and ignoring the other search agents including the ω. Hence the updated position of the prey depends on α, β, and δ and can be expressed as From equations (5), (6), (7) it can be said that the α, β, δ decides the new location of the prey and other wolves arbitrarily decides the location of the prey.

Cuckoo Search Algorithm
The Cuckoo Search Algorithm is also a population-based metaheuristic algorithm that has been proposed by Yang and Deb to solve the mathematical optimization problems [25]. It was followed and taken from the inspiration of the constraint brood parasitism behavior of some cuckoo species. Usually, they lay eggs in the nest of host birds (other species). While laying eggs there is a probability that some hosts can easily identify the intruding cuckoo and make direct disputes. After discovering the eggs those hosts can expel it away or sometimes they simply leave that nest and build it anywhere else. Moreover, some species of cuckoos (new world brood-parasitic Tapera ) can change the color, size pattern according to the host species. These behaviors of Cuckoo search can be adopted for various optimization problems.
The probability of leaving the nest by the host can be denoted as PL and can be given as, [26]. Meanwhile, the identification of the eggs of cuckoos by the host may cause two possibilities. The first possibility is the host abandon and builds the new nest. The second one is that it expels the cuckoo's eggs away.
To make the CS algorithm more efficient it exploits Levy flight random walks [26] in the place of isotropic random walks. Thus the CS is more efficient than the GA and PSO algorithms. Therefore CS algorithm can be numerically expressed by assuming several assumptions [25]:  here an egg denotes a solution  besides the number of host nests is a fixed one  The cuckoo lays one egg in each random nest  The nest with high-quality eggs are chosen as the best nest to carry over to the next generation PL is the probability of the discovery of an egg by the host bird and it represents the replacement of cuckoo's eggs with new egg in the new generation. Hence the CS algorithm is exploited to perform the iterative process to replace the cuckoo eggs (the solutions) in the nests with new better eggs. It can be explained in the following sub-sections.

A. Initialization
Consider the nests are initialized with eggs (solutions). The nth solution is considered as 0 n X can be initialized as [26], which provides the quality of solutions. After estimating the best fitness value from the initial population can be denoted as Fmax.

B. Procedures followed for iteration
Some procedures are followed to ensure the existence of the nests with the best solutions to the next generation. It can be described as follows:  At iteration t, {t=1,2,…}, the nth solution is produced from the previous iterative solution t n X by exploiting the Levy flights walk as below [24,25]: Here  is an entry-wise multiplication and S  is a step size-related to the dimension of the solution and is greater than 1.
) ( m n X t m  is an arbitrarily selected solution. 0  is approximately equal to 0.01 as mentioned in [27] to improve the searchability of Cuckoo.
is considered as the Levy flight random walk with the step size of S acquired from Levy distribution. Next, we have to estimate ) ( vy e L  as below [26]: Where, From [28] the local random walk can be obtained as below, Where, o X and p X are different random solutions selected for the random permutation. The H is the Heaviside function and is a random number obtained from a uniform distribution, and r is the step size. PS is the switching probability utilized to achieve a balance between global and local random walk. Its value is assumed to be 0.25 in [28].

Fractional GWO-CS Optimization Algorithm
The Fractional GWO-CS Optimization algorithm is utilized to enhance the optimization of Step:1 Initialization

Estimation of EE for total opportunistic throughput and energy consumption during spectrum sensing and data transmission
To estimate the total energy consumption during the spectrum sensing the proposed method calculates the signal sampling values initially. Signal sampling is a method to measure the instantaneous values of the continuous-time signal in a discrete form [15]. Thus signal sampling contributes highly to the energy consumption the estimation of energy per sampling period is an unavoidable one. Let us consider ES be the energy consumed per sampling period by the secondary user while spectral sensing and PT be the power spectral density (PSD) of the SU signal consumed while transmitting the data in the channel. Further, the maximum transmission power of the SU can be denoted as PT,Max, which is distributed evenly over the bandwidth WT.
Consider two hypotheses for energy detection based spectrum sensing CR model and can be given as [16] [17], Here gain. Also, hypothesis B0 means the primary user is inactive, and B1 represents that the primary user is active in using the channel.
Then on C , the probability of detection and off C the probability of false alarm is used to denote the probability that the channel is probably inhabited by the PU or not i.e., whether it belongs to B0 or B1. Thus by considering these values the cognitive radio sensor determines if the channel is busy or idle. Besides, the maximum value on C protects the primary user transmission from the interference with the SUs, and the minimum value off C offers the SUs to utilize the idle channel. Since 1   off on C C the probability of detection and probability of false alarm can be estimated as in Eqs. (2) and (3).
Here d q and f q denotes the detection and false alarm probability by an energy detector.
The static energy detection technique used for spectrum sensing can be given as [19], [20], . Consider,  be the detection threshold and so the probability of detection and false alarm can be denoted by Eqs. (19) and (20) correspondingly, Q function represents the probability that a Gaussian random variable of zero mean and unit variance attains a value higher than the prescribed value. Numerically it can be expressed as [22], Since the increasing value of detection probability affects the false alarm probability, so taking a threshold value for the probability of detection (qd th ) so that qd th <qd [17]. So the equation for the probability of false alarm can be reframed as, The Ds can be estimated based on the monotonically decreasing Q function and 2FpDs integer values and can be given as, Since the spectrum sensing energy efficiency is completely depends on the spectrum sensing parameters the following hypothesizes can be made: 1. Spectrum is busy: The SU exactly detects the existence of PU and so the probability can be given as . on C is the probability of the existence of PU. Meanwhile, the SU halt transmitting the data, and hence the energy consumption can be given as, Since there is no transmission of data by SU the opportunistic throughput for SU is equal to 0 i.e., c1=0. Hence the energy consumption purely depends on spectrum sensing.

Missed Detection:
To determine the energy consumed by the missed detection phase, we have to consider the probability i.e., is equal to , since that can be alternatively filled by both SUs and Pus. It can be given as, Here too the opportunistic throughput of SU is equal to zero since there exists interference between the PU and SU transmissions. Hence c2=0.

False Alarm: False alarm means the SU doesn't pass data even if the channel is vacant.
Hence the probability of false alarm can be given as Since there is no transmission of data the opportunistic throughput is equal to 0 i.e., c3=0.

4.
Useful Detection: It is the most necessary situation since the SU exactly spots the vacant channel to perform the data transmission and the probability can be denoted as The energy consumption is based on the spectrum sensing and data transmission and can be estimated as Moreover, the opportunistic throughput of SU can be determined by using equation Here, P0 is the noise power spectral density. The total energy consumed by bandwidth WT of SU can be estimated as, The overall opportunistic throughput can be estimated as, EE can be defined as the ratio of total opportunistic throughput to the total energy utilized and can be given as, (32)

Step 2: Energy Efficiency
The energy efficiency of the Cognitive Radio system depends on two terms i.e., sensing bandwidth and Power spectral density (PSD) and it can be given as,

Step 3: Solution Updation Using Fractional CS-GWO
The updated version of location/ solution by exploiting CS-GWO can be obtained by Where W=1, and by applying the newly updated location of prey by exploiting GWO of equation (6) and enhanced version of random walk of CS of equation (9) in equation (34), it can be modified as, Fractional order is exploited to enhance the random walk of the cuckoo search algorithm. This also adapted to the harmonization of diversification and intensification of CS.
In order to calculate the fractional order of CS, we adopted the fractional calculus definition determined by Grunwald-Letnikov. Mathematically it is implemented by [29]   determines the Grunwald-Letnikov fractional derivative of order   .
) (t  denotes the gamma function. Equation (13) can be discretely formulated as: Here, the sampling period can be denoted by T and the number of terms from the previous section can be marked as g (memory window).   indicates the coefficient of derivative order. For β=1 the equation (30) can be reformulated as, shows the difference between the two followed events. Now equation (9) can be reformulated with the aid of (39) as shown below.
Besides for the generalized case equation (18) can be rewritten as with any derivative order of   and a number of memory terms as g.
By assuming sampling period T=1 in equation (30) and can be exploited to reframe the equation (33) as, On the basis of equation (34), the updated solution for FO-CS can be expressed as, Consider the first four terms of g (g=4) for the derivative order of   the location can be updated as By applying equation (44)  Thus the opportunistic throughput which in turn leads to the optimization of the EE function.

Experimental Analysis
The correlation of EE of CRN among transmitted power, sensing time, bandwidth, and power spectral density can be computed by employing MATLAB simulation. Here we use MATLAB 2018 platform on a laptop with Core i7-6500U CPU, 2.5GHz speed, and 6 GB of RAM. We have conducted a simulation of about 40 runs in order to acquire the statistics of energy efficiency obtained via the proposed Fractional Optimized Model (Fractional CS-GWO), Adaptive PSO [8], Hybrid PSO-GSA [11], and EH-HCRSN [7] approach. Each algorithm performs almost 200 iterations for each execution. To achieve a better EE it is necessary to obtain the joint optimization of sensing bandwidth and power spectral density.
The unit of EE function is bits/Joule.

Simulation outcomes of Optimization algorithms:
Simulations are carried out with respect to simulation parameters such as transmission power, power spectral density, sensing bandwidth, and the probability of detection. The EE curve with respect to varying transmission power for various SNR values is analyzed in figures 4(a) and 4(b). From these figures, we can inference that the value of EE rises with the value of the probability of detection, nevertheless, after reaching the peak value the EE value decreases gradually with the rising transmission power. This due to the fact that the opportunistic throughput increases with the rising transmission power and EE is directly proportional to the throughput and inversely proportional to the power including transmission power. However, for a particular constraint, the rising throughput influences the rising power level, and hence the EE function also increases. Further reaching the peak level, the rising power prevails the throughput, so the EE function shows a slight steep.
The peak value of EE function attains maximum for high SNR values since at high SNR value the probability of false alarm declined to zero and hence the detection of spectrum holes or vacant channel becomes very easy. Therefore the opportunistic throughput got improved and thereby EE also enhanced. Moreover, the proposed FOM(CS-GSW) has better exploration and exploitation value so it easily acquires the peak value or optimum value than the other approaches.

PSD vs Energy Efficiency
As similar to transmission power, the EE function increases with an increase in PSD value and after that decreases steadily with rising PSD value. Since at small PSD values, the SU has less power than QT, Max, and hence the power of SU also increases with the increase in PSD values. While SU attains the power value equal to QT, Max value then we have witnessed a steep decrease in the value of EE with respect to PSD. It was illustrated in Fig 5(a) and 5(b).
When compared to other approaches the proposed FOM(CS-GWO) shows better value in terms of peak i.e., optimum value due to its exploration and exploitation behavior.

Sensing Bandwidth vs Energy Efficiency
Unlike PSD and transmission power, the value of EE decreases with the increasing sensing bandwidth, since the higher value of sensing bandwidth provides lower transmission bandwidth. Therefore, only low opportunistic throughput value can be acquired which results in lower EE value.  When comparing the proposed method with other approaches our method succeeds in attaining peak EE value since it exhibits high exploitation ability.

Comparison of EE with respect to Convergence curves
The comparative analysis of the proposed method with respect to different approaches in terms of optimized EE is tabulated in table 2. Figures 8, 9, and 10 depict the graphical representation of the corresponding tabular representation in terms of EE varying with respect to transmission power, sensing bandwidth, PSD. Table 2

Conclusion
The emerging demands for wireless communications and devices often led to the scarcity of the radio spectrum. To manage the radio spectrum allocation effectively Cognitive radio technology provides a revolutionary solution. Currently, the spectrum allocations are controlled and managed by implementing several norms by the government. However, the cognitive radio ensures the maximum exploitation of the spectrum through opportunistic access to momentarily unexploited parts of the spectrum. This paper proposes an Energy Efficient spectrum sensing in Cognitive Radio Network by FOM method to enhance the opportunistic throughput of the system. Our proposed method uses a fractional CS algorithm to enhance the random walk to avoid the local optimization and thus improves the performances of the CS algorithm, and GWO to ensure the best solution that is to access the best spectrum holes. The simulation is conducted to estimate the Energy Efficiency function with respect to sensing bandwidth, transmission power, and power spectral density.
Simulation results illustrate the effectiveness of energy efficiency with respect to spectrum sensing in terms of transmission power, power spectral density, and sensing bandwidth for the SNR values -4dB, and 6dB. The performance analysis shows our proposed work outperforms the other approaches and hence acquires the optimal energy efficiency for spectrum sensing in CRN.

Conflicts of interest Statement: Not applicable
Ethics approval: Figure 1 Traditional spectrum sensing scheme Comparison of EE with respect to power spectral density (a) at SNR=-4dB (b) at SNR=6dB Comparison of EE with correspond to Sensing Bandwidth (a) at SNR =-4dB, (b) at SNR = 6dB Comparison of EE with respect to probability of detection (a) at SNR = -4dB, (b) at SNR = 6dB.

Figure 8
Convergence curve with respect to transmission power (a) at SNR=-4dB (b) at SNR=6dB Figure 9 Convergence curve with respect to sensing bandwidth (a) at SNR=-4dB (b) at SNR=6dB

Figure 10
Convergence curve with respect to Power spectral density (a) at SNR=-4dB (b) at SNR=6dB