GAO Hongyuan,DU Yanan,and LI Chenwan

College of Information and Communication Engineering,Harbin Engineering University,Harbin 150001,China

1.Introduction

At present,with the rapid growth of wireless communication applications,energy harvesting(EH)and spectrum efficiency have attracted growing attention in the wireless communication domain[1].EH communication systems powered by renewable sources have become increasingly attractive because they are considered to be a helpful technique that can significantly alleviate energy deficiency[2].Compared with a conventional battery-powered communication system,EH could provide an unlimited energy supply from ambient radio-frequency signals in a much more convenient manner than existing energy-constrained wire-less communication systems such as heterogeneous cellular networks.On the other hand,improving spectrum efficiency is difficult in wireless communication due to the increase in wireless equipment and services.

It is known that cognitive radio(CR)is considered to be a promising technology to improve spectrum efficiency through spectrum sensing and spectrum sharing.However,CR needs to consume more energy to finish exclusive functionalities.Thus it is essential to use the EH technique in the CR network to increase the energy and spectrum efficiency.

Cooperative communication is a hot topic of the telecommunication domain. For a CR network, the primary user(PU)and the secondary user(SU)actively look for op-portunities for better transmission[3].In cooperative com-munication of CR systems,when PUs are bustling,SUs can be used as relays to improve the transmission abilities of PUs,which will lead to more opportunities for the transmission of secondary SUs.In this way,SUs have more data transmission opportunities in case the licensed channels are occupied by PUs.Most of the existing cooperative communication systems only consider cooperative communication for the transmission of information,which do not consider the coordinated transmission of information and energy for the cognitive system[4,5].

EH is a hot topic in CR systems despite the fact that the energy transfer has unavoidable losses.A CR system powered by radio frequency(RF)EH technology is sparking more attention.In[6],the authors designed a CR network with a good spectrum and energy efficiency to be used as a secondary transmitter for EH.In[7],the author designed a new two-way relay information transfer protocol which can decrease the outage probability of the primary network.In[8],secondary transmitters can harvest energy from primary transmitters then transmit data by using the harvested energy,and a stochastic-geometry model was proposed which could show the relationship be-tween primary transmitter density and the secondary net-work’s throughput.In 2014,Yin et al.proposed two time slot modes for the cooperation between information transformation and EH[9],which is the latest progress in this research direction.For time slot modes in[9],the PU only transmits a fixed amount of data within a time slot,and the secondary user just harvests energy from ambient signals.

In this article,a cooperative CR system that operates in the time-slotted mode is considered.In the model,the energy from ambient radio signals can be harvested by the SU transmitters.For one thing,an SU can make use of the PU’s spectrum by helping PU transmit data,for another,an SU can obtain energy from PU and the other ambient signals without using additional energy supply equipment.And we deduce the maximal achievable throughput formula in case of the coexistence of information transfer and EH.

The maximal throughput problem based on the designed best cooperative mechanism(BCM)can be regarded as a continuous optimization problem,and many intelligent algorithms can be applied to improve the estimation accuracy,such as the genetic algorithm(GA)[10],the artificial bee colony(ABC)[11],the particle swarm optimization(PSO)[12],the quantum-inspired bacterial foraging algorithm(QBFA)[13],the quantum-behaved particle swarm optimization(QPSO)[14]and the hybrid cuckoo search algorithm(HCSA)[15].The above intelligent algorithms have the weakness of slow convergence rate and poor convergence value for complex optimization problems.

Therefore,it is important to design an effective cooperative method based on a novel intelligent algorithm.The fireworks algorithm(FA)[16]has a good optimization performance, but the convergence value is not accurate enough for the complex continuous optimization problems.And some research has been done to improve FA for more perfect optimization capability.In[17],a study on accelerating FA was presented by introducing the elite strategy,and the authors discussed the influence on FA under different approximation models,sampling methods and sampling numbers.The enhanced fireworks algorithm(EFWA)[18],the adaptive fireworks algorithm(AFA)[19]and the cultural firework algorithms(CFA)[20]are designed to enhance the performance of FA through new designed evolutionary operators.In EFWA,several improved operators are designed for the evolutionary process of sparks.In AFA,adaptive amplitude is introduced to FA to improve the global convergence performance.In CFA,the knowledge strategy is introduced to FA,then FA is used to design two kinds of digital filters.However,the improvements obtained by these methods are slight.Thus designing a new FA to ameliorate the convergence performance is very important.According to the theory of FA and quantum computation,QFA is proposed.In the QFA,we design the entirely new explosion equations compared with the FA[16],which improves the search ability and overcomes the drawbacks of FA.The global convergence analysis of the QFA in a probabilistic version is also presented.QFA is applied to solve the proposed BCM difficulty,and the proposed method is called QFA-BCM.We can see that QFA-BCM can obtain the optimal throughput performance and amplify the domain of application from the simulation results.

This paper is organized as follows.For Section 2,the optimal cooperation model of CR with EH is designed.In Section 3,QFA is proposed and its convergence analysis and function testing are presented.In Section 4,QFABCM is proposed for the EH CR network.In Section 5,an evaluation of QFA-BCM and the simulation curves with different system parameters are presented.Finally,conclusions and the future jobs are described in Section 6.

2.BCM of CR with EH

2.1 BCM model of CR with EH

We assume a cooperative CR system that consists of two parts.One is the PU system and the other is an SU system.There are a primary transmitter and a primary receiver in the PU system.For the SU system,there are a secondary transmitter and a secondary receiver in the network.The PU transmits its own data to the primary receiver through a licensed channel at any time.For each timeslot,the PU transmits its own data to the primary receiver by the licensed spectrum.To avert the conflict between the PU and the SU,once the PU uses the licensed spectrum,the SU is forbidden to use the PU’s spectrum to transmit its own information.While the licensed channel is used by the PU,the SU collects energy from the ambient environment and the radio signals.In this article,the save-then-transmit protocol is proposed for the SU.In every time slot,the SU costs part of the time with the save-ratio to harvest energy to help its own transmission.

In this cooperative CR system,when the PU uses a licensed channel to transmit its own data,the SU will act as a cooperative relay to assist the data transmission of PU.Therefore,the throughput of the PU is enhanced and the speed of data transmission for the PU is accelerated.Thus,it is a good method for the SU to create more time for itself,even if the PU has always occupied the licensed channel.Due to the cooperative mode of the PU and the SU,the PU’s throughput can be improved and the licensed channel will be vacated for the SU to transmit its data.Therefore,cooperative communication between the SU and the PU can be seen as a potential possibility to improve the throughput of the PU and the licensed spectrum will be idle earlier and more chance will be provided for the SU to transmit its own data.For each timeslot,the energy harvested by SU should be used up to assist the PU to relay its data in the cooperative process.

We propose a novel cooperation mode in Fig.1.Compared with[9],the SU harvests energy in two modes:one mode is harvesting energy from the PU,the other is harvesting energy from the ambient signals.Moreover,the amount of data transmitted by PU within each timeslot will be not fixed.

Fig.1 Timeslot structure with cooperative mode of information and EH

For the cooperative mode of time slot structure in Fig.1,a timeslot can be separated into three parts in accordance with different functions,and the description of each part is shown as follows:

During the time interval(0,ρ1T],where 0 ≤ ρ1＜ 1,the PU starts its own process of data transmission,the SU harvests its own energy from ambient radio signals,and there is non-cooperative relationship between the PU and the SU.

During the time interval(ρ1T,(ρ1+2ρ2)T],where 0≤ ρ2＜ 1,the SU acts as a cooperative relay of PU,which can enhance the throughput of PU and end the data transmission of PU as soon as possible.The cooperative mode abides by decode and forward(DF)protocol[21].For the first half part(ρ1T,(ρ1+ ρ2)T]in the cooperative mode,the PU’s transmitter should transmit its data to the PU receiver and the SU’s transmitter.The PU receiver can be seen as a destination and the SU’s transmitter can be seen as a relay.The SU receives information and harvests energy at this time.In the second half of the cooperative interval((ρ1+ρ2)T,(ρ1+2ρ2)T],the SU transmitter works as a relay to transmit the PU’s data to the PU receiver[9].

During the time interval((ρ1+2ρ2)T,T],when the PU transmits all of its own data,the SU can transmit its own data by using the licensed channel.Due to the fact that this article is concerned about the optimization based on short-term throughput,the SU must consume all its harvested energy in each timeslot.

2.2 Maximal throughput of the BCM

For this part,we will derive the objective functions and constraints for throughput maximization for joint PU and SU based on the proposed cooperative mechanism.The EH save ratio is the ratio of EH time during a timeslot.Suppose Rptand Rstrepresent the PU’s and SU’s throughput in each timeslot,respectively.Rptwill be decided by Rpand Rc,where Rpand Rcdenote the instantaneous non-cooperative transmission rate and the instantaneous cooperative transmission rate of PU in a timeslot.According to[9],Rpcan be expressed as

where Yprepresents the PU’s fixed energy supply rate and γpdenotes the channel-to-noise power gain ratio between the PU’s transmitter and receiver.

According to[9]and[21],we are concerned that the transmitter of SU can be fully decoded(i.e.,there is no er-ror in the repetition-coded scheme),and Rc,which denotes the PU’s instantaneous cooperative transmission rate may be derived as

where γsrepresents the channel-to-noise power gain ratio from the transmitter of PU to the transmitter of SU,rprepresents the channel-to-noise power gain ratio from the transmitter of SU to the receiver of PU,and wsis the power allocated by SU for the process of cooperative relay communication.

According to[22]and the designed timeslot structure,the instantaneous non-cooperative transmission rate of SU can be written as

where ρ1represents the EH save ratio of SU from ambient signals,ρ2represents the SU’s EH save ratio from the signals of PU,Xsprepresents the SU’s EH rate which harvests energy from the PU’s signal,Xsrepresents SU’s EH rate which harvests energy from ambient signals and rsrepresents the channel-to-noise power gain ratio from the SU’s transmitter to the SU’s receiver.

When a CR system is not restricted by the fixed amount of PU’s data,the throughput of PU and SU during a timeslot should be

where Qpminis the PU’s minimal target throughput required during a timeslot.

There are three constraints that should be strictly enforced in(4).The first constraint is that the energy consumed by relay transmission must be no more than the energy gathered by SU.The second constraint is that the PU’s non-cooperative and cooperative transmission duration should be no more than a timeslot’s duration.Thirdly,the PU’s achieved throughput should be no less than the minimal target throughput of PU in each timeslot.

3.Design and convergence proof of QFA

3.1 The proposed QFA

FA is an intelligent algorithm which has a powerful capability of exploration and exploitation in the searching process.By introducing quantum computing theory to generate sparks,it can increase the diversity of the whole population,and the purpose is to find some domains where more excellent solutions may exist.

In the QFA,a firework’s explosion process should be regarded as a process of searching in the local space.Each firework’s position or spark’s position denotes a latent solution and we can evaluate the fitness of each position through the objective function.It is assumed that the QFA is proposed to solve the minimum value optimization problem:

Considering the characteristics of quantum bits and the superposition of states,quantum computation theory is employed to QFA,which can increase the rate of convergence and improve the convergence value.In the QFA,the evolution process is accomplished by updating the fireworks’quantum positions and sparks’quantum positions,then the quantum positions can be mapped into the corresponding positions.Thus,the adaptable performance of fireworks and sparks can also be reflected by the quality of their quantum positions.A quantum position consists of a series of quantum bits.[zkd,xkd]Tis a quantum bit,where(d=1,2,...,D).We define the kth firework’s quantum position or spark’s quantum position as

In QFA,the quantum position’s evolution is completed by using the simulated quantum rotation gate,whereis a quantum rotation angle.The d th main quantum bit position of the k th quantum position

is updated by

In the QFA,for each explosion,n positions are selected.When n fireworks are let off,the sparks are generated in two methods.Sort the objective function values of fireworks in an ascending order.The numberof the sparks generated by the i th firework in the first method is related to the i th firework’s position for the l th iteration,and the number of the sparks generated in the second method iswhich can be set according to the real problems.can be got by

The specific description of the sparks which are produced by the first evolutionary method is as follows:suppose that the ith(i=1,2,...,n) firework will producesparks,and the kth spark’s quantum position at the current iteration can be initialized byrepresents the ith firework’s quantum position at the l th iteration.

For the k th spark,a uniform random number r1∈(0,1)is generated and is compared with probability selection threshold p1of the first evolutionary method.If r1＜p1,z(z∈{1,2,...,D})dimensions will be selected randomly,and for the d th dimension(d∈{pre-selected z dimensions of}),the d th main quantum bit position of the k th spark is updated by the following equations:

where γ1and γ2are uniform random numbers which are distributed from 0 to 1.is defined as the optimal main quantum position at the lth iteration.is the main quantum position of the quantum positionwhich is randomly selected from the excellent quantum positions.γ1and γ2reflect the influence in the evolution process brought byand bl=respectively,and the other dimensional main quantum bit position ofare kept toOtherwise,if r1?p1,for each dimension of{1,2,...,D},the dth main quantum bit position of the kth spark can be generated in the following:

where d=1,2,...,D,j ∈ [1,n/2].γ3is the uniform random number which is distributed in[A1,A2]where-1≤A1≤1 and 0≤A2≤1,and γ4∈[0,1]is a uniform random number.

Similar to the first method,for the k th spark,a uniform random number r2from 0 to 1 is generated,and we compare it with the probability selection threshold p2of the second evolutionary method.If r2＜p2,choose z(z∈{1,2,...,D})dimensions,the d th quantum bit position of the k th spark’s main quantum position can be updated in the following:

where G(0,1)stands for a random number subject to Gaussian distribution with mean 0 and variance 1.is the quantum position’s main quantum position.If r2? p2,for each dimension of{1,2,...,D},the dth main quantum bit position of the kth spark can be generated in the following.

where j∈ [1,n/2].γ5is a uniform random number which is distributed in[A3,A4]and γ6∈ [0,1]is a uniform random number.

For all sparks,the dth assistant quantum bit position of the kth quantum positioncan be computed bywhere d=1,2,...,D.Thus based on the above process,the current quantum positions of all fireworks and sparks can be described as V=The corresponding main quantum positions of V can be expressed as X=[x1,x2,...,xn+η]T.Select n quantum positions from n+η quantum positions in the set V as fireworks’initialized quantum positions for the next iteration.

The purpose of the selection operator is to maintain the diversity of the population.In each explosion,the fireworks or sparks with smaller objective function values are allowed to save and form the basis for the next iteration.The n fireworks’main quantum positions for the next generation is composed of two portions:one portion is the preferable n/2 main quantum positions selected from n+η main quantum positions in X,and the other portion is n/2main quantum positions which are chosen from the remainder η+n/2 main quantum positions according to the Euclidean distance between the main quantum positions.The Euclidean distance from the i th main quantum position xito other main quantum positions can be described in the following:

where q is the index set of the rest η+n/2 fireworks and sparks’main quantum positions.Based on the roulette selection strategy,the ith main quantum position’s selection probability is expressed as

Not only does the designed selection operator save the best quantum positions,but also it can avoid the local optimum by choosing the quantum position with higher Euclidean distance density. The n corresponding quantum positions of the selected n main quantum positions are the quantum poisons of fireworks at the next iteration,and sort them in an ascending order.The n excellent quantum positions can be expressed as

3.2 Convergence analysis of QFA

Mathematical analysis to discuss the convergence performance based on continuous space evolution algorithms follows different ideas.By using the explosive equation and the selection operator,the finite population is regarded as the approximate method for better large-population.Then we perform the convergence analysis from a probability perspective.The explosion equation is a kind of mutation which is corresponding to the increase in population diversity by quantum rotation gate operation performed on the fireworks independently,and the selection operator can save the best quantum position until the current iteration in the evolution process.Literature shows that the selection operator which saves the optimal solution can increase points’concentration in regions with objective function values superior to the average of population,and selection which is coupled with mutation is able to search for the global optimum in the multi-dimensional Euclidean space with a sequence of populations[23,24].The designed selection operator is similar to the previous work,and focuses on how explosion equations ensure that the population converges to a neighborhood which is near the optimal point.Our goal is to show that the population’s probability density function(PDF)should be closely concentrated near the objective function’s global optimal value after sufficient iterations.

Consider the continuous optimization problem which is shown in(5),which is also represented by min fR.f is called the objective function anddenotes the feasible region.D is the dimension ofR is the set of real numbers.In this section,formulate some common assumptions aboutand f.

(i)f has finite global minimal points on the feasible regionand the minimum is termed as f?.

Then under the above conditions,a lemma is given in the following.

Lemma 1For?δ＞ 0,after generating new positions,the probability of the event that a new position falls into the set W(δ)sat is fies

ProofFrom the conditions,it is known that if the probability of the event that a new generated spark falls into the set W(δ)satisfiesat the lth iteration, then the probability of the event that it will not occur can be expressed asAnd the probability of the event that a position with l updates but never falls into the set W(δ)can be written as

Since the selection operator can keep the optimal position,it is possible that there is a position falling into the set W(δ).Thus for?δ＞ 0,we have the following expression:

where flminis the minimal objective function value at the lth iteration.

When l in(20)tends to be in finite,the following equation holds:

Substituting(22)into(21),we get

Then the algorithm converges.Obviously,its convergence performance is irrelevant to the initialized population.

In the explosion process,sparks are generated in two methods corresponding to the increase in the diversity of population,which can be expressed by the explosion equations(9)–(12)and(13)–(16),respectively.QFA evolves towards the optimal solution through the updates of quantum positions,and quantum positions can be mapped into positions in a linear manner.The mainly generated equations about quantum rotation angles are just(9)and(13),and others have the similar generated equations as(9),but operate on different dimensions.Thus we focus on(9)and(13)to analyze.

Actually,the rotation characteristics of quantum rotation operator lead the quantum positions to evolve towards the optimal quantum position and make the positions have a high probability of falling into the set W(δ),which is more than the probability generated by the uniform random density function.Thus for?x ∈ X generated by(9)and(10),we have position follows Gaussian distributionThe probability density functionis expressed as

Upon Lemma 1 the proof is straightforward,and a conclusion that QFA can converge to the optimal solution with these explosion equations is got.

Then discuss the influence of(13)and(14)on the evolution process.Assume that the quantum rotation gate operator does not affect the probability distribution first,and then the variable of each dimension in the new quantum position follows Gaussian distribution G(0,1)around its corresponding firework.And each dimension of its mapped

Similar to the above explosion equations,the quantum rotation operator can provide a high probability of falling into the set W(δ),

It is intuitively clear that QFA can converge to the optimal solution with these explosion equations.

Note how the explosion equations and selection operator play their roles:explosion equations spread the distribution and guide the convergence of solutions to the optimal point,and the selection operator chooses the regions which have more excellent objective function values to avoid getting trapped in local optima.It means that the QF will eventually converge towards the global optimum,and its convergence performance is irrelevant to the initialized population.Namely,the QFA has the property of global convergence.

3.3 Benchmark function testing of QFA

The population size of different algorithms,i.e.,PSO,QPSO,FA,AFA and QFA is the same and the maximal iteration number is set as 1 000.In PSO,the population size is 100,two learning factors are 2,the maximum velocity of every dimension is set as 0.1 times of the absolute value of the domain boundary difference,and the other parameters can refer to[12].In QPSO,the population size is 100 and the other para-meters are con figured according to[14].In FA of[16],m=100,n=5,a=0.04,b=0.8,ξ=10-7.For AFA of[19],the other key parameters are set in accordance with[19].In QFA,the control parameter n=20,m=100,a=0.02,b=0.15,A2=0.5,p1=p2=0.5,A3=0,A4=1,ξ=10-7.

We use two classical benchmark functions to express the superiority of QFA,and two functions are given as

where-100≤yi≤100,1≤i≤D,D=50.The results are the mean of 50 simulations.From Fig.2 and Fig.3,it is clear that QFA outperforms PSO,QPSO,FA and AFA.

Fig.2 Performance of five algorithms for Griewank function

Fig.3 Performance of five algorithms for Rastrigin function

Compared with previous classical fireworks algorithms,the QFA does not use additional computation during each iteration.By using the quantum rotation gate,QFA does not need to use decision sentences to limit the boundary of each variant during the simulation processes,and some time will be saved.Thus,with the same population size and parameters,QFA must have an excellent convergence performance at the similar computational complexities.

4.BCM based on QFA

QFA is supposed to deal with the maximum optimization problem which is shown in(4).The position of each firework or spark stands for a potential solution of the maximal throughput problem of CR with EH.Since the QFA is designed for the minimum value optimization,we can transform the maximal value optimization problem of the BCM algorithm into the minimum value optimization problem of QFA.Each position represents the estimation parameter(ρ1,ρ2,ws),and the objective function of the QFA for SU throughput can be expressed as

where α denotes a positive constant whose value is very small.

The objective function of the QFA for the sum throughput of PU and SU can be expressed as

Therefore,the maximal throughput problem is converted into searching for the position which has the smallest objective function value of QFA.According to the above introduction,QFA-BCM for the minimal objective function can be summarized in the following steps:

Step 1Obtain system information of EH CR and initialize QFA parameters.Initialize the fireworks’positions and quantum positions,and set fireworks’number and other parameters.In addition,the maximal number of iterations Ngis set,then make the initial iteration number as l=0.

Step 2Then compute and evaluate the fitness of fireworks.

Step 3Calculateaccording to(7)and(8).

Step 4Each firework undergoes the explosion process.The ith firework generatessparks in the first method ac-cording to(9)–(12),and generatesparks in the second method according to(13)–(16).

Step 5Compute the new generated sparks’objective function values at the current iteration.

Step 6Choose n quantum positions between the current and previous fireworks and sparks based on the selected operator.The selected quantum position can be used as the fireworks’new quantum position for the next iteration.

Step 7If l＜Ng,set l=l+1,turn to Step 3.If not,the QFA stops,and output the quantum position of the firework which has the most excellent objective function value and obtain the maximal throughput and system parameters of EH CR.

5.Experimental simulation and analysis

To identify the superiority of the proposed QFA-BCM,a series of simulation results were presented to show the good performance of QFA-BCM.The existing two methods published in[9]are used for comparison.From[9],there is a non-cooperative mode which is named as NCP and a simple cooperative mode which is named as OCP.For QFA,the maximal iteration number is set as 200 and other parameters are set the same as Section 3.3.

For NCP and OCP,the PU’s throughput Qpis fixed as 4.

For QFA-BCM,the minimal target throughput of PU is set as Qpmin=4,which is equal or superior to NCP and OCP in each time slot,and α=0.01 in these simulations.The other parameters of CR systems for the three methods are the same,and T is set as 1 for computational convenience.

At the beginning,system parameters are set as γp=0.4,γs=100,rp=200,rs=45,Yp=100,Xsp=30,Xs=30∶4∶70,and ws∈[0,200].The simulation results of maximal throughput in different Xsare given in Fig.4 and Fig.5.It is easy to see that QFA-BCM can fulfill PU’s throughput requirements.It is shown in Fig.4 and Fig.5 that the throughput of SU is increasing while Xsincreases.We can see that at the same simulation environment,the performance of QFA-BCM is significantly better than NCP and OCP.Thus the proposed QFA-BCM is a novel and efficient scheme for CR network with EH.

Fig.4 Relationship comparison of sum throughput and Xs

Fig.5 Relationship comparison of SU’s throughput and Xs

System parameters are set as Xs～ Γ(20,5),Xsp=50,ws∈ [0,200],γp=0.3,γs=200,rp=100,Yp=100 and rs～ EXP(50),where Γ denotes the function which obeys Gamma distribution.EXP denotes the function which obeys exponential distribution,because the channel in the simulation is Rayleigh fading channel.The simulation results of the maximal throughput under different probability distributions of channel condition and EH rate are shown in Fig.6 and Fig.7.It is easy to see that the performance of QFA-BCM is better than NCP and OCP in different cases.

Fig.6 Comparison of PU and SU’s sum throughput traces with three schemes

System parameters are set as γp=0.4, γs=80,rp=200,rs=40,Yp=60∶5∶110,Xs=40,Xsp=30 and ws∈[0,200].The maximal throughput with different Ypis shown in Fig.8 and Fig.9.It can be seen that QFA-BCM is better than NCP and OCP.The proposed QFA-BCM can collect more energy from SU when compared with NCP and OCP.Therefore,there will be more energy for SU’s data transmission and cooperative communication.

Fig.7 Throughput traces of SU only with three schemes

Fig.8 Comparison of sum throughput for PU and SU in different PU’s energy supply rates

Fig.9 Comparison of SU’s throughput with diverse PU’s energy supply rates

System parameters are set as γp=0.4, γs=80,rp=180,rs=10∶3∶40,Yp=100,Xs=40,Xsp=40 and ws∈[0,200].Fig.10 and Fig.11 show the maximal throughput of three methods in different rs.We can see that the proposed QFA-BCM has the best performance in achievable throughput when compared with NCP and OCP.

Fig.10 Comparison of sum throughput for PU and SU in different rs

Fig.11 Comparison of SU’s throughput in different rs

System parameters are set as γp=3 ∶1 ∶13,γs=40,rp=200,rs=50,Xs=40,Xsp=20,Yp=100 and ws∈[0,200].Fig.12 shows the maximal sum throughput in different γp.Although NCP and OCP have the same simulation results of the achievable throughput,we can see that the achievable throughput of QFA-BCM is better than NCP and OCP.

From Figs.4–12,it can be seen that QFA-BCM can fulfill the requirements of PU and SU about throughput.When we compare QFA-BCM with previous methods,it is easy to draw a conclusion that QFA-BCM can collect the most energy among three schemes,so there will be more energy for data transmission of PU and SU.

Fig.12 Comparison of sum throughput for SU and PU in different γp

System parameters are set as γp=20, γs=200,rp=30,rs=40,Yp=80∶10∶180,Xs=20,25,30,35,Xsp=30 and ws∈[0,200].The maximal throughput with different Ypare shown in Fig.13 and Fig.14.We can get a conclusion that the achievable throughput becomes larger when Xsand Ypincrease.System parameters are set as γp=0.4,γs=100,rp=180,rs=40,Yp=100,Xsp=10∶4∶50,Xs=20,25,30,35,and ws∈[10,200].The simulation results of the maximal throughput with different Xspare shown in Fig.15 and Fig.16.It is obvious that with the increasing of Xsand Xsp,the achievable throughput is strengthening gradually.

Fig.13 Relationship of sum throughput in different PU’s energy supply rates

Fig.14 SU’s throughput with different PU’s energy supply rates

Fig.15 Relationship of sum throughput with different Xsp

Fig.16 Relationship curves of SU’s throughput with diverse Xsp

System parameters are set as γp= 1, γs=200,rp=80∶10∶180,rs=40,Yp=100,Xsp=20,Xs=20,25,30,35,and ws∈[10,200].The simulation results of the maximal throughput in different rpare shown in Fig.17 and Fig.18.It is easy to see that the throughput of SU will be increased with the increasing of rpand Xs.

Fig.17 Relationship of sum throughput with different rp

Fig.18 Relationship of SU’s throughput with different rp

From Figs.13–18,we can get a conclusion that the proposed QFA-BCM can fulfill the requirements of PU’s throughput,and the relationship between throughput and system parameters is presented.It is important for the design of CR with EH.

The simulation of Figs.13–18 is based on some certain cases.For a typical scene,the simulation results can be obtained by changing some parameters.For example,in the GSM system,the length of a frame is 4.615ms.Each frame consists of eight time slots.For each slot,the length of it is 0.577 ms,that is to say,T=0.577 ms.The transmission data rate in each time slot is156.25bit,so the the minimum transmission data of PU in each timeslot is 270.797 kbit/s,namely,Qpmin=270.797 kbit/s.According to the specific parameters,we can obtain the corresponding results by using the proposed QFA for the optimal cooperation mechanism.

6.Conclusions

Evolved from the quantum computation theory and the fireworks algorithm,QFA is proposed as a novel algorithm for continuous optimization problems,which performs well by providing a better exploitative behavior in the explosion stage of the algorithm.Then the convergence performance of QFA is derived and proved by the stochastic mathematics theory.

QFA is applied to solve the difficult problem of cognitive systems’throughput with EH,and a best cooperative scheme of QFA-BCM is proposed.It is an effective and reliable method for CR EH.

A novel timeslot structure is designed in the new mechanism.SU is not only able to harvest more energy from both ambient signals, but also able to harvest energy from PU signals, compared with other classical mechanisms and SU actively cooperates with PU to relay PU signals through simultaneous relay/EH to gain more opportunities to transmit PU’s data. In addition, our proposed mechanism introduces the flexible size of transmitted data. The simulation experiments have proved that all of these new ideas are better than the traditional schemes. Thus the mechanism we propose will have important application perspectives in the future.

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