Recent Efficient Iterative Algorithms on Cognitive Radio Cooperative Spectrum Sensing to Improve Reliability and Performance

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Introduction
Radio spectrum is a precious resource and characterized by fixed allocation policy.However, most of allocated spectrum is underutilized by licensed users [1].Conversely, the rapid development of ubiquitous wireless technologies increases the demand for radio spectrum.Federal Communications Commission (FCC) used the Static Spectrum Allocation (SSA) scheme to allocate spectrum bands to users exclusively since licensed users do not occupy radio spectrum or even at least whole of it all the time.As a solution to the spectrum inefficiency problem, cognitive radio (CR) is an exciting and emerging technology, which has attracted a great deal of attention in recent years to enhance the utilization of limited resources [1].In CR network, licensed or primary users (PUs) coexisted with the unlicensed or secondary users (SUs) in the same frequency band to achieve better spectrum utilization [2].Also, a key technology that can help mitigate the scarcity of spectrum is CR [3,4].In other words, SUs can opportunistically access the licensed spectrum without causing interference to the PUs.By using this access strategy, the spectrum resources can be assured to enhance the spectrum efficiency thus significantly increases the number of users using wireless services, which can greatly resolve spectrum scarcity problem.However, detection performance may be affected by shadowing effect and the hidden terminal problem and SU may not detect the activity of the PU within the short interval of sensing period [5].Thus, to solve this issue, cooperative spectrum sensing (CSS) was proposed by [6,7]; it is based on continuing to monitor the spectrum periodically to overcome hidden terminal and shadowing problems for minimizing interference.The wellestablished local sensing mechanism for spectrum sensing in CR networks is energy detection.It does not require the prior  knowledge about the signal of PU.Also, it has short sensing time and represents a simple technique, low implementation cost, and compatibility with legacy primary systems.The energy detectors measure received signal's power to check the existence of PU with unknown power strength, waveform structure, and frequency location (with as less complexity as possible).The results that are collected from energy detectors will be forwarded to a fusion centre (FC), where the global decision on the existence of PU will be taken based on two methods, namely, soft decision fusion (SDF) and hard decision fusion (HDF) [8][9][10][11].Also in [12], SDF-based linear CSS methods were applied to find the ideal weights.Different conventional approaches implemented at the FC to maximize probability of detection (  ) and minimize probability of error (  ) were as follows: equal gain combining (EGC), maximal ratio combining (MRC), normal deflection coefficient (NDC), modified deflection coefficient (MDC), and OR-Rule [12,13].EGC scheme is one of the simplest SDFbased weighting schemes and it does not require any channel estimator, but it still performs much more accurately than the conventional HDF techniques.Here, weights of each path are individually assigned at fusion centre and are reversely related to the number of SUs.In MRC, the allocated weighting vector is correlated to the quality of the received PU signal at the global fusion centre.Thus, if the received signal-to-noise ratio (SNR) of a particular SU at the fusion centre is high, a larger weighting coefficient is assigned.On the other hand, a small weighting coefficient is assigned when its corresponding SNR values are low to reduce the negative contribution to the final sensing decision due to shadowing or deep fades over the SU-FC links.Deflection coefficient (DC) measures detection performance and it is formulated based on two hypotheses  0 and  1 and categorized into two groups, first NDC and second MDC.The NDC weighting schemes formula is based on hypothesis  0 which means that the PU is absent and the MDC uses hypothesis  1 [13].Iterative algorithms, such as genetic algorithm (GA), particle swarm optimization (PSO), and imperialistic competitive algorithm (ICA), overcome conventional models in cognitive radio cooperative spectrum sensing (CRCSS) issue (ICA is the advanced method so far) [13][14][15].This research considers iterative algorithms based on SDF method which is performed at the FC to reduce global   and increase   and then compared with each other.In addition, it has been shown that ICA-based method provides better convergence performance and lower complexity than other existing iterative SDF-based schemes.

System Model
SDF-based CSS is applied to enhance reliability of detection done by SUs when local CSS is used, and, hence, local spectrum sensing can be accomplished via energy detection without any prior information of the PU signal [16].Figure 1 demonstrates the centralized CSS SDF-based scenario, where  SUs (as relays) send their measurements on the activity of PU to FC to make decision on the presence of PU [10].
Figure 1 is modelled as channels starting from the PUs to FC which are assumed to be Rayleigh fading (different gains) and noise is AWGN with different variance in each path.During the entire frame duration, it is assumed that the PUs present in different time in channel; thus, the CSS process can be given as binary hypothesis testing: where [] is the signal that is received at the CR user, [] is the transmitted PU signal,  refers to the gain of the sensing channel, [] is additive white Gaussian noise (AWGN) with zero mean, and  0 and  1 are the hypotheses demonstrating the PU absence and PU presence in the frequency band of interest, respectively.Cognitive radio networks (CRNs) are mathematically modeled under two main criteria: Mini-Max [15] and Neyman-Pearson [14] criterion, which are individually defined as follows.

Neyman-Pearson Criteria
This criterion was introduced based on the problem of the most efficient tests of statistical hypotheses [17].This section applied Neyman-Pearson criterion as opportunity of minimum interference that happened by SU to PU in active position: where  is the decision statistic and  is the decision threshold (value of  is constant based on the fixed known   and the final   ).To the benefit of the readers and avoiding reputation, the particular structure involving CRCSS, which is actually shown in Figure 1, is mathematically formulated in the Appendix: Equation ( 5), in SDF-based collaborative sensing, offers a solid measure of detection capability for a fixed set of false alarm probabilities.

Mini-Max Criteria
Mini-Max method is able to trade off between spectrum utilization and interference in PU [10,13].In other words, we plan to minimize   and probability of mismatch   which are unwanted in any communication detection task.For simplicity, let us assume that   is the same as   .Based on these definitions, the probability of misdetection is defined as   = 1 −   = {decision =  0 |  1 }.Total   is derived in the Appendix and characterized as below: It is discernible that maximization of   ( ⃗ ) and minimization of   ( ⃗ ) are very dependent on ⃗ .As mentioned before, this research will investigate optimal weighting vector for above objective functions with the help of GA, PSO, and ICA that will be explained in detail in the following.

GA-Based Cooperative Spectrum Sensing
GA is one of the stochastic iterative search algorithms that follow natural evolution.It has been used for several engineering applications, such as solving complicated nondeterministic problems as well as machine learning.GA is a populationbased method in which each individual in the population evolves to create new individuals that form new populations.This evolutionary procedure iteratively goes on until no improvement on the fitness score is achieved and then the optimal individual (fitness score) is achieved from the last updated population.
In this paper, GA-based technique has been proposed; an initial population of pops (possible alternatives) is produced randomly such that each individual is normalized to fulfill the limitations.Here, our main objective is to discover the best set of weighting coefficients to maximize detection reliability.When the maximum number of generations is reached (predefined level), GA process is ended and the weighted vector values that minimize the probability of error are obtained as the best solution.If we assume that there are  SUs and  1 ,  2 ,  3 , . . .,   are the soft decisions of SU 1 , SU 2 , . . ., SU  on the presence of PUs and  →   is the weighting vector of the individual that consists of  1 ,  2 ,  3 , . . .,   , the fitness value for the th individual is defined as follows: and   stands for probability of error.The principal functions of the GA are selection, crossover, and mutation.For selection, the idea is to choose the best chromosomes for reproduction through crossover and mutation.The smaller the fitness value (probability of error), the better the solution obtained.In this paper, "Roulette Wheel Selection" method has been used.The probability of selecting the th individual or chromosome   can be written as The chromosomes with the minimum probability of error value will be transferred to the next generation through elitism operation.The next step after the selection procedure

International Journal of Distributed Sensor Networks
Before crossover parent 1 Before crossover parent 2 (m) (p) After crossover offspring 1 After crossover offspring 2 [13].
is crossover.The crossover starts with pairing to produce new offspring.A uniformly distributed random number generator has been selected to make the row numbers of chromosomes as mother () or father ().Here, a random population of chromosomes is shown in matrix , with pops being the total number of chromosomes and  being the number of secondary users: It starts by randomly selecting a variable in the first pair of parents to be the crossover point.In Figure 2,  is the crossover point and  is a value randomly chosen in the range of [0, 1].As for the GA crossover operation, two parents are chosen and the new offsprings are formed from combinations of these parents.For crossover scheme used in our proposed algorithm is a hybridization of an extrapolation method with a crossover method to enhance the quality of obtainable solutions [18].The GA crossover operation is graphically explained in Figure 2.
For parent 1 () offspring 1 (), For parent 2 () offspring 2 (), The next step after crossover is the mutation operation.The total number of variables that can be mutated equals the mutation rate times the population size.The row and column numbers of variables are nominated randomly and then these nominated variables are replaced by new random ones.For instance, if the mutation rate is 60% and the population size is equal to 5 chromosomes as shown in matrix , then the total number of variables that have to be mutated is 0.6 * 5 = 3 variables.Assume that the following pairs have been selected randomly from  : row = [4 3 5] where row is the row index and col is the column index of the population.Then, the variables to be mutated can be highlighted, as shown in matrix  below:

Mini-Max Criteria for Genetic Algorithm
The GA-based optimization algorithm for SDF-based CSS can be outlined as follows.
Step 1. Adjust  = 0 and arbitrarily make pops number of digits-long chromosomes, such that  is equal to the number of cognitive users in the network.
Step 4. Compute the fitness value of every normalized decoded weighting vector,  →   , rank their corresponding chromosomes according to their fitness value, and identify the best chromosomes ⌊pops * elite⌋, where elite ∈ [0, 1] and ⌊⋅⌋ denotes floor operation.
Step 6. Construct a new set of population pops by concatenating the newly ⌈pops * (1−elite)⌉ reproduced chromosomes with the best ⌊pops * elite⌋ found in ( − 1).
Step 7. Decode and normalize the chromosomes of the new population pops as in Steps 2 and 3, respectively.
Step 8. Evaluate the fitness value of each chromosome as in Step 4.
Step 9.If it is equal to a predefined number of generations (iterations) gener, then stop.Otherwise, go to Step 5.

Neyman-Pearson Criteria for Genetic Algorithm
Step 1.It remains the same as Mini-Max criteria step.
Step 2. It remains the same as Mini-Max criteria step, but the condition must satisfy the condition, which is used to maximize the detection probability.
Step 3. It remains the same as Mini-Max criteria step.
Step 4. It remains the same as Mini-Max criteria step.
Step 5.It remains the same as Mini-Max criteria step.
Step 6.It remains the same as Mini-Max criteria step but this time reproduced chromosomes with the best ⌊pops * elite⌋ found in ( − 1) (higher value).
Step 7. It remains the same as Mini-Max criteria.
Step 8.It remains the same as Mini-Max criteria.
Step 9.It remains the same as Mini-Max criteria.

PSO-Based Cooperative Spectrum Sensing
PSO algorithm, invented by Kennedy and Eberhart in 1995 [16], is conceptualized from social performance of a group of fishes and birds.This amazing algorithm imitates the performance of these organizations.

Mini-Max Criteria for Particle Swarm Optimization Algorithm
In this section, the objective is to explain how to minimize the objective function   ( ⃗ ) with   ≤  ≤   , where   = 0 and   = 1 are lower and upper limits on .The steps involved in the PSO algorithm are as follows.
Step 3. The objective functions' values achieved in Step 2 are compared in this step and their smallest value is chosen.
Next, the particle position equivalent to the minimum value is considered as P best,0 and iteration number is set to  = 1.
Step 4. The velocity of the th particle at the th iteration is updated based on the following equation: where  1 and  2 are individual and social learning acceleration coefficients, respectively, and  1 and  2 are uniformly distributed random numbers in the range of 0 to 1 which present stochastic components to the algorithm.At the th iteration, P best, demonstrate the most powerful particle position that minimizes the objective function.The best-qualified position among all iterations is called global best position and is expressed by G best .
Step 5. Update the th particle's new position as and the objective functions' value for each of the particle positions created in this step is again calculated as 2 ) , . . .,   ( ⃗ Step 6.The values of the objective functions obtained in Step 5 are compared and the particle position corresponding to minimum value of the objective function is defined as P best, .
The value of G best will be replaced by the value of P best, if the following condition is satisfied as follows: Step 7. Check the convergence of the algorithm.Whenever algorithm converges to a stable value, the procedure is ended.
Otherwise, update the iteration number  =  + 1 and repeat the process as in Step 4.

Neyman-Pearson Criteria for Particle Swarm Optimization Algorithm
Step 1.It remains the same as Mini-Max criteria step.
Step 3. Find the maximum value of the objective function in Step 2 and set its corresponding particle position as P best,0 .Set the iteration number  = 1.
Step 4. It is like Step 3 in Mini-Max criteria.
Step 5. Update the th particle position at the th iteration using Evaluate the values of objective function corresponding to new particle positions as   (w 2 ), . . .,   (w ()  ).
Step 6. Find the maximum value of the objective function in Step 5 and set its corresponding particle position as P best, .If P best, ≥ G best , replace G best with P best, .
Step 7. If the algorithm is converged to a stable value, stop the process.Otherwise, set the iteration number as  =  + 1 and repeat from Step 4.

Imperialistic Competitive Algorithm
ICA is inspired from imperialistic competition and human's sociopolitical evolutions [19][20][21].The optimization targets in this research are, respectively, maximizing probability detection and minimizing the probability of error in the Neyman-Pearson and Mini-Max criteria.ICA begins with an initial population consisting of countries that are considered as individuals in other iterative-based algorithms.This population is divided into two groups, a group with the finest (in Neyman-Pearson highest and in Mini-Max lowest) objective function values, power, which is chosen to be the imperialists, whereas the remaining group is their colonies.Then the colonies are distributed among the imperialists according to each imperialist power.Figure 4(a) depicts the initial colonies for each empire when superior empires have larger quantity of colonies, for example, imperialist 1.As an imperialist grows stronger, it will own more colonies.Empire is formed from an imperialist with its colonies in ICA language when each individual colony will try to discover better position to be named as imperialist of its empire.This method is fulfilled in ICA by moving the colonies towards their imperialist, named assimilation.It is possible that a colony turns out to be more powerful than its imperialist during assimilation, so the colony displaces the imperialist and the imperialist becomes one of its colonies.Moreover, it may be seen that, through imperialistic competition, the most powerful empires attempt to raise their power, while weaker ones are losing their power to break down.Both structures head the algorithm to steadily converge into a single empire, in which the imperialist and all the colonies have similar culture.

Neyman-Pearson Criteria for Imperialistic Competitive Algorithm
Step Step 2. In this step, countries are divided into imperialists ( imp ) and colonies ( col ), and we select  imp from the most powerful countries (Neyman-Pearson criteria need to use maximization algorithm).The colonies will be distributed among the imperialists according to their power.This research proposes Boltzmann distribution [10] with suitable selection pressure coefficient (): in which ( imp ) represents the probability of imperialist power (∑  imp  imp = 1).It is known from the GA part that the best quantity for selection pressure () is obtained when the sum of the half of the best countries probability is almost 0.8.The power of the imperialists is portion of  col , which should be controlled by  imp .Number of colonies for each empire is arbitrarily picked from  col in terms of power of its empire's imperialistic competition: Initial number of empire's colonies Step 3.This step is imperialistic competition such that each imperialist tries to extend its colonies.Figure 4(b) illustrates that all colonies travel to their related imperialist ( is unit of colony move).The new position of this colony is shown in darker blue.Amount of  is uniformly selected; that is,  = (0,  × ), where 0 <  ≤ 2 is the assimilation coefficient and  is the distance between the colony and imperialist.In Figure 4(b), assimilation deviation () is a uniform random distribution number that can be picked from −/2 <  < /2.
In the next sections, the optimum values of parameters will be given.We replaced the assimilation deviation with a random vector as follows to show the implementation of ICA: in which base vector () is the vector from the previous position of the colony pointing to the imperialism.Also, rand and ⊗ sign represent random vector generator and elementby-element multiplications, respectively.Unavoidably, the colony is departed minus of consuming the classification of  because these random values are not essentially identical.Stating a new vector in order to have the suitable exploration capability (search area) satisfies the utilization of .
Step 4. Exchange the position of a colony and its imperialist if the colony in empire possesses lower cost than imperialist.It means that while colonies are moving toward imperialist, one colony is capable of getting a better position (get more power) than imperialist.
Step 5. Calculate the total cost of all empires.Generally, imperialist cost affects the cost of each empire, but, to have an accurate view of an empire, the average cost of empire's colonies should not be eliminated.Below we have modeled this fact by stating the total cost of each empire: where positive number, , is less than one (0 <  ≤ 1).Slight value of  has less effect of empire's colonies on the whole cost of empire.
Step 6. Select the most vulnerable colony from weakest empire and deliver it to one of the most powerful empires.
Step 7. When all colonies of an empire are delivered to other powerful empires, the only remaining country, that is, imperialist, automatically joins the best empires as a simple colony.
Step 8. Stop the algorithm whenever one empire remains.Otherwise, go to Step 2. The result of the problem is the final imperialist.

Mini-Max Criteria for Modified Imperialistic Competitive Algorithm
Steps of ICA for Mini-Max are very close to Neyman-Pearson criteria.Since Mini-Max is always used for minimization, some steps are different as below while applied parameters remain the same.
Step 1.The imperialists are usually the countries with the lowest objective function values.The amount of the objective function for each of the countries generated in this step is calculated as   ( ⃗  1 ),   ( ⃗  2 ),   ( ⃗  3 ), . . .,   ( ⃗   pop ).
Step 2. The colonies will be distributed among the imperialists according to their power: Step 3. Colonies move towards imperialist states in different directions (assimilation) and  is transferred colony distance, where  ∼ (0, ž × ) and ž is the assimilation coefficient (0 < ž ≤ 2) and  is the distance of the colony and imperialist. is assimilation deviation which can be chosen from −/2 <  < /2.Figure 4(b) depicts how colonies transfer to their related imperialist.
Step 4. If a colony in empire has a higher cost than imperialist the position of a colony and the imperialist will exchange.

Classified Results and Analysis
Table 1 illustrates the general simulation parameters applied to this paper.To fulfill the low SNR environments (SNR < −10 dB) at SU and FC levels, the quantities of   and ℎ  are generated arbitrarily.Besides, it is assumed that   and ℎ  are constant over the sensing duration and the channel is a slow fading channel.Therefore, the delay requirement is short compared to the channel coherence time considered as quasi-static scenario [13].To obtain the optimal values for parameters as given in Tables 2 and 3, the set-and-test approach is used in this work.For instance,  1  1 and  2  2 in PSO or , ,  in ICA are selected in a way to promise that the particles or colonies would fly over the target about half the time [14].

Results and Analysis for Neyman-Pearson Criteria
Figure 5 shows the probability of detection of ICA-based system as well as all other methods with regard to the different false alarm probabilities.It is noticeable that ICAassisted method outperforms all other schemes with a large difference, which confirms the strength of our proposed method.For example, for the fixed   = 0.1, the value of   provided by ICA is 97.8%, which is 0.9%, 4.81%, 14.63%, 17.12%, 37.86%, and 70.26% higher than PSO, GA, NDC, MDC, MRC, and OR-Rule, respectively, and confirmed the accuracy of iterative algorithms in CRCSS in comparison with the conventional methods.
Figure 5 also reveals the comparison of convergence for ICA-, PSO-, and GA-assisted methods over 200 iterations per simulation for a given   = 0.2.It is evidently presented that the Max ICA-based method is obtained approximately after 29 iterations whereas the convergence for Max PSOand GA-based schemes is achieved over 42 and 56 iterations, respectively, which indicates the rapid convergence of the ICA.The rough enhancement of 30.8% and 48.2% of the convergence rate of ICA-assisted scheme in comparison to PSO-and GA-assisted methods validates the robustness of the algorithm for real time applications.Also, in Table 4, the mean value for each algorithm over 100 simulations is given and compared with its maximum iteration.
Table 4 compares the probability of detection for ICAand PSO-assisted scheme in which the result of the number of the population is quite observable.Generally, performing time and computational complexity of these approaches will be increased with larger number of the population.On the other hand, choosing the number of countries and particles is problem dependent and depends on different factors, like number of iterations, learning coefficient, assimilation coefficient, deviation coefficient, and so on; for example, the performance of the ICA with 25 countries is the best among all, but, in comparison with larger numbers of countries, there is still a trade-off between very slight improvements, complexity and performing time, which is well explained in Table 4.
"Not" in In other words, ICA-assisted method needs more iterations and performing time to be converged for the number of 5 and 10 populations.Additionally, convergence time is computer dependent and varies from one to another.

Results and Analysis for Mini-Max Criteria
Figure 6 compares the convergence rate of ICA-assisted based scheme with other schemes.Here, the probability of error over 200 iterations is evaluated for iterative-based methods in both conditions of mean and max.The mean and max of each algorithm are achieved when the algorithms run for 100 times and the average of all results is called mean in our experiment and the best one among all these 100 simulations which results in minimum   is named as max algorithm-based simulation.As it is seen, to achieve a probability of error equal to 0.5 × 10 −4 , the mean ICA-based method requires about 23 iterations whereas the same error rate can be obtained after 38 and 124 iterations for mean PSO-and GA-based scheme, respectively.In addition, after the test duration of 200 iterations, the ICA and PSO algorithms are converging to the probability of error of about 0.2 × 10 −4 while GA achieves 0.45 × 10 −4 with the same number of iterations.The impact of different number of particles and countries in CRN simulation is also examined for ICA-and PSObased methods, which are described in Table 5.It is apparent that improvement in performance is achieved by increasing the number of population in each algorithm.It is notable that there is always a trade-off between performance and complexity in network when number of population increases.The number of fitness evaluations is simply the product of the number of generations by which the maximum SNR fitness is achieved multiplied by the number of fitness evaluations  performed in every iteration.The latter equals the population size of any of these algorithms.For instance, with ICA, the number of iterations required to achieve   is 34 and the number of countries is 20.This means that the number of fitness evaluations to find the optimal setting is 680, which is considerably low with the advancement of signal processing and computing cores.
Additionally, when the number of SUs in the system increases, the cooperation with the system will be increased.As a result, separation between two hypotheses ( 0 and  1 ) increases and the error performance of the system improves accordingly.

Conclusion
Cognitive radio cooperative spectrum sensing (CRCSS) is one of the most attractive techniques and well inspected to be acknowledged as a frequently monitoring mechanism which permits secondary users to utilize sensed spectrum holes caused by PU absence.A chief challenge encountering CSS in CR networks is to select the suitable weighting coefficient for each single SU in fusion center (FC).Subsequently, methods to adjust these coefficients are essentials for the overall detection performance of the system.This research presents best existing methods in CRCSS according to previously achieved results by other researches, namely, ICA-, PSO-, and GA-based methods in both criteria of Neyman-Pearson and Mini-Max criterion for the first time.The attained outcomes validated that the ICA-based method outperforms all other SDF-assisted techniques with its less complexity that makes this method very appropriate to real time applications.

Figure 1 :
Figure 1: Block diagram of the cooperative spectrum sensing.

Figure 4 :
Figure 4: (a) Imperialists and colonies in each empire.(b) A colony's travel toward imperialist.

Figure 5 :
Figure 5: Comparison of probability of detection over 200 iterations for fixed   = 0.2.

Figure 6 :
Figure 6: Comparison of probability of error over 200 iterations for ICA, PSO, and GA.

Table 4 : 5 :
Comparison of performance of ICA-and PSO-assisted methods for different number of population.Comparison of performance of ICA-and PSO-assisted methods for different number of population.

Table 2 :
Table 4 specifies that, in each simulation of ICAbased method, it is not able to converge during 200 iterations.Different parameter values used for testing.