粒子群算法 ------马哥

WIRELESS COMMUNICATIONS AND MOBILE COMPUTING

https://www.wendangku.net/doc/3113252572.html,put.2009;9:875–881

Published online6May2008in Wiley InterScience

(https://www.wendangku.net/doc/3113252572.html,)DOI:10.1002/wcm.633

Cognitive radio adaptation using particle swarm optimization

Zhijin Zhao,Shiyu Xu,Shilian Zheng*,y and Junna Shang

Telecommunication School,Hangzhou Dianzi University,Hangzhou310018,China

Summary

One of the basic capabilities of cognitive radio is to adapt the radio parameters according to the changing environment and user needs.This paper proposes a new adaptation method which uses particle swarm optimization (PSO)to optimize cognitive radio parameters given a set of objectives.The procedure of the proposed method is presented and multicarrier system is used for simulation analysis.Experimental results show that the proposed method performs far better than genetic algorithm(GA)-based adaptation method in terms of convergence speed, converged?tness values,and stability.The proposed method can also provide the tradeoffs of the objective functions,and the resulting parameter con?guration is consistent with the weights of the objective functions. Copyright#2008John Wiley&Sons,Ltd.

KEY WORDS:cognitive radio;particle swarm optimization;genetic algorithm

1.Introduction

Cognitive radio technology is receiving signi?cant attention in wireless communications?eld in recent years[1–3].In general,cognitive radios have three basic parts that make it cognitive:the ability to sense the RF spectrum,geographical surroundings and the user’s needs,the capacity to learn and the ability to adapt to the outside world[4].Research done at Virginia Tech has developed a cognitive radio engine to perform all of these tasks[1].This paper focuses solely on the adaptation mechanism,which is a method to adjust the radio parameters.

In Reference[4]the adaptation mechanism which uses a genetic algorithm(GA)[5]is discussed in detail.Their simulation results validate that their GA implementation does in fact change the radio parameters to different settings based on a set of objectives.The work presented in Reference[6]goes beyond just demonstrating that the GA outputs a selection,but also provides the numerical analysis of the relationships between the environmental para-meters and the transmission parameters.A GA-based adaptation method for multicarrier system is also presented in Reference[6].However,GA is quite poor at hill climbing and it behaves even worse when the chromosomes are too long to exploit. In contrast,another emerging population-based optimization method,particle swarm optimization (PSO)[7–11],is easier to be understood and to be implemented.PSO has the characteristics of both evolutionary computation and swarm intelligence. This paper presents a new adaptation method which uses discrete PSO to optimize parameters given a set of objectives for cognitive radios.As can be seen in the rest of the paper,the proposed method per-forms far better than the GA-based adaptation method.

*Correspondence to:Shilian Zheng,Telecommunication School,Hangzhou Dianzi University,Hangzhou310018,China. y E-mail:lianshizheng@https://www.wendangku.net/doc/3113252572.html,

The structure of the paper is organized as follows. In Section2,the problem of cognitive radio parameter adaptation is formalized.Section3focuses on the adaptation method based on discrete PSO.Section4 presents some simulation results.Finally,conclusions are drawn in Section5.

2.Cognitive Radio Adaptation

The cognitive radio adjustable parameters are denoted as a??a1;a2;ááá;a n ,where n is the number of parameters.Examples of radio adjustable parameters are power,center frequency,modulation type,symbol rate,etc.In order to communicate successfully,the radio must balance multiple objectives and constraints to?t the speci?c channel condition,to meet user needs,and to obey the regulatory requirements[4]. We denote the objective functions which a cognitive radio needs to optimize as f??f1;f2;ááá;f m ,where m is the number of objective functions.The objective functions are designed to re?ect the current link quality[4],examples of which are transmitting power, bit error rate(BER),and data rate.The weight vector w??w1;w2;ááá;w m is used to represent the relative importance of the objective functions in the decision-making process,where w i denotes the importance of the i th objective function.In this framework,the cognitive radio adaptation process becomes a multi-objective optimization problem,that is,how to adjust radio parameters to optimize multi-objective func-tions given the weight vector.

To simplify the problem,we transform the multi-objective functions into a single objective function. Suppose all the objective functions in f??f1;f2;ááá;f m have been normalized to the range [0,1],then the multi-objective functions can be transformed into the following objective function:

f?

X m

i?1

w i f ie1T

where w i!0(1i m)and P m

i?1

w i?1.

3.Parameter Adaptation Using PSO

3.1.Background of PSO

PSO is inspired by observing the bird?ocking or?sh school[7].Scientists found that the synchrony of ?ocking behavior was through maintaining optimal distances between individual members and their

neighbors.Thus,velocity plays an important role of

adjusting each other for the optimal distance.Further-

more,scientists simulated the scenario in which birds

search for food and observed their social behavior.

They perceived that in order to?nd food the indivi-

dual members determined their velocities by two

factors,their own best previous experience and the

best experience of all other members[7].This is

similar to the human behavior in making decision

where people consider their own best past experience

and the best experience of how the other people

around them have performed[8].

According to the above concept,Kennedy and

Eberhart[7]developed the so-called PSO for optimi-

zation of continuous nonlinear functions.In their

paper,birds are called particles,each representing a

potential solution.All particles have their position,

velocity,and?tness value.To?nd the optimal solu-

tion,each particle adjusts its?ying according to its

own?ying experience and its companions’?ying

experience.Shi and Eberhart[9]named the former

the cognition part and the latter the social part.

3.2.The Parameter Adaptation Method

Based on Discrete PSO

In the above discussion,PSO is restricted in real

number space.However,many optimization problems

are set in a discrete number space.Besides,research-

ers frequently cast?oating-point problems in binary

terms and solve them in such a discrete number space

[10].To meet the need,Kennedy and Eberhart[10]

developed a discrete binary version of PSO.Discrete

PSO essentially differs from the continuous PSO

in two characteristics.First,the particle is composed

of the binary variable instead of the real number.

Second,the velocity must be transformed into the

change of probability,which is the chance of the

binary variable taking the value1[11].

The following notation is needed in discrete PSO.

The number of particles in the population is denoted

as N P.Let x t i??x t i1;x t i2;ááá;x t iD be the position of particle i(1i N P)at iteration t,where D is the

number of bits to represent a particle and x t id2f0;1g is the d th(1d D)bit of the position of particle i. Note that x t i is similar to the chromosome using binary encoding mechanism in GA,and it is treated as a potential solution of the optimization problem.The structure of x t i is shown as in Figure1for the adapta-tion problem in cognitive radios,where L j is the

876Z.ZHAO ET AL.

number of bits used to encode parameter a j ,1 j n .The number of bits used to encode a parameter is determined by the range and the expected precision of the parameter.The velocity of particle i at iteration t is denoted as v t i ??v t i 1;v t i 2;ááá;v t iD ,v t id 2R .Each par-ticle in the swarm is assigned a ?tness value indicating the merit of this particle such that the swarm evolu-tion is navigated by best solutions.Let p t i ??p t i 1;p t i 2;ááá;p t iD be the best solution that particle i has obtained until iteration t ,and p t g ??p t g 1;p t g 2;ááá;p t gD be the best solution obtained from p t i in the population at iteration t .The objective function provides the mechanism for evaluating the ?tness of each particle.In this paper,we directly use the objective value computed from Equation (1)as the ?tness value of the corresponding particle (solution).

As in continuous PSO,each particle adjusts its velocity according to the cognition part and the social part.The current velocity of the d th bit of the i th particle is updated as follows:v t id

?

v t à1id

t

c 1r 1p t à1

id

à

x t à1id

à

á

t

c 2r 2p t à1

gd

à

x t à1id

e2T

where c 1and c 2are acceleration coef?cients,and r 1and r 2are uniform random numbers distributed in [0,1].

Equation (2)speci?es that the velocity of a particle at iteration t is determined by the previous velocity of the particle,the cognition part,and the social part.For the velocity value of each bit in a particle,Kennedy and Eberhart [10]claim that higher value is more likely to choose 1,while lower value favors the 0choice.Furthermore,they constrain the velocity value to the interval [0,1]by using the following sigmoid function:

S ev t id T?

1

1texp eàv t id T

e3T

where S ev t id Tdenotes the probability of bit x t id taking 1.If r

random number uniformly distributed in [0,1].The continuous-valued particle swarm algorithm always limit v t id by a value V max which is a parameter of the system.In the discrete version V max is retained to avoid S ev t id Tapproaching 0or 1,that is,v t id 2?àV max ;tV max .Note that smaller V max allows a higher mutation rate.In practice,V max is often set at 4[8].

In conclusion,the adaptation method using PSO algorithm proceeds as follows:

Step 1.Set t ?0,and randomly generate x t id and v t id ,where x t id 2f 0;1g ,v t id 2?àV max ;tV max .

Step https://www.wendangku.net/doc/3113252572.html,pute the ?tness value of each particle in the population according to Equation (1),and set p t i ??x t i 1;x t i 2;ááá;x t iD and p t g ??x t g 1;x t g 2;ááá;x t gD ,where g is the index of the particle which has the highest ?tness value.

Step 3.Set t ?t t1,and update v t id according to Equation (2).If v t id >V max ,then set v t id ?V max ;if v t id <àV max ,set v t id ?àV max .

Step 4.Randomly generate a real number uniformly distributed in [0,1],if it is smaller than S ev t id T,then x t id ?1;else,x t id ?0.

Step https://www.wendangku.net/doc/3113252572.html,pute the ?tness value of each particle in the population according to Equation (1).For particle i ,if it’s ?tness value is greater than the ?tness value of p t à1i ,then p t i ??x t i 1;x t i 2;ááá;x t iD .If particle i ’s ?tness

value is greater than the ?tness value of p t à1

g

,then p t g ??x t i 1;x t i 2;ááá;x t iD .

Step 6.If t equals to the prede?ned maximum itera-tion,then the algorithm is terminated;else,go to step 3.

4.Simulation Analysis 4.1.

Multicarrier System Design

We simulated a multicarrier system with 32subcar-riers similar to Reference [6].The transmitting power ranges from 0to 25.2dBm with an increment of 0.4dBm.The noise ?oor is assumed to be à85dBm and a constant path loss from the transmitter to the receiver is assumed to be 85dB.In addition,each subcarrier is assigned a random attenuation value which ranges from 0to 1to simulate a dynamic channel.The symbol rate is assumed to be 1Msps.The modulation types considered in the simulation are BPSK,QPSK,16QAM,and 64QAM.In this case the total search space is 25632and it needs 256bits to represent a potential solution.Three

objective

Fig.1.The structure of the position of particle i .

COGNITIVE RADIO ADAPTATION USING PSO 877

functions are used which are minimize transmitting power,minimize BER,and maximize data rate.They are de?ned as follows:

f min power?1à P=P maxe4T

f min ber?1àlog10e0:5T

log10e P beT

e5T

f max data rate?

1

N

P N

i?1

log2M iàlog2M min

log2M maxàlog2M min

e6T

where P is the average transmitting power over N

subcarriers,P max the maximum available transmitting

power, P be the average BER over N channels,M min the

minimum modulation order,M max the maximum

modulation order,M i the modulation order used in

the i th channel,and N is the number of subcarriers

(channels).Assuming a gray-coded bit assignment

and an AWGN channel model,the BER can be

computed using Equations in Reference[12].The

three objective functions are combined as follows:

f?w1f min powertw2f min bertw3f max data ratee7T

Hence,the adaptation mechanism needs to adjust the

parameters to maximize Equation(7).

Table I.Weight settings.

Weights Mode1Mode2Mode3Mode4 w10.800.150.051/3

w20.150.800.151/3

w30.050.050.80

1/3

4.2.Simulation Results

GA and PSO were compared by simulation.The parameters for the PSO algorithm were N P?30, c1?c2?2[13],and V max?4,and the iteration would be terminated after1500runs.The GA used a 30chromosome population with a crossover rate of 0.6and a mutation rate of0.001.The maximum generation was set1500.The roulette wheel selection scheme[5]and two-point crossover scheme[5]were used in GA.Four different weight settings shown in Table I were used to test the effectiveness of the proposed method.Each mode emphasizes different objectives and is appropriate for different situations

Table II.Objective values:GA versus PSO.

Iteration Mode1Mode2Mode3Mode4 GA PSO GA PSO GA PSO GA PSO 500.73230.85740.70840.75100.77710.92510.69390.7978 1000.76080.90000.70930.76200.81750.93420.71240.8392 5000.84870.94150.72410.77510.91780.94400.79080.8741 15000.87180.94440.73730.77760.92710.94440.81320.8765 Standard deviation0.008510à160.00670.00140.003810à50.008810à

16

and applications.Mode1emphasizes on minimizing power and it is for applications like text messaging. Mode2is for emergency applications and mode3is for applications requiring high throughput like broad-band video,while mode4has no preference to any speci?c objective.

Ten independent experiments were conducted to each mode using GA and PSO,respectively.The objective function value of the particle or individual which has the highest?tness value at each iteration was recorded and the resulting average objective function values over10simulation runs were shown in Figure2.The exact average objective function values after50,100,500,and1500iterations were shown in Table II.Figure2and Table II illustrate that the PSO algorithm converges faster than GA,and the solutions optimized by the PSO algorithm have far higher objective values than those optimized by the GA.The standard deviations of the objective values after1500iterations over10runs were also given in Table II,and it can be obviously seen that the PSO algorithm is far more stable than the GA.

Figure3shows the sample adaptation results after 100iterations under different weight settings.The channel attenuation values were randomly generated. Figure3(a)shows that all transmitting powers on the subcarriers are below4dBm.The average transmit-ting power is0.875dBm,which indicates that the main goal of mode1which is minimizing power is achieved.The other two goals still have an impact on the optimal parameter set in spite of their small weights.As shown in Figure3(b),the average trans-mitting power is12.325dBm and almost all the modulation types are BPSK.This parameter con?g-uration yields a low average BER while keeping small balance on the objectives of minimizing power and maximizing data rate.Most of the BERs are approxi-mately10à3,which is a very small number when compared with the corresponding values in Figure 3(a),(c),and(d).All modulation types in Figure3(c) are optimized64QAM to provide the maximum possible data rate which is6Mbps to achieve the main goal of mode3.As shown in Figure3(d), the average transmitting power is2.6dBm,the aver-age data rate is6Mbps and the average BER is relatively high.Although mode4has no preference to any speci?c objective,the algorithm tends to mini-mize transmitting power and maximize data rate rather than minimize BER,which is because that the particle which minimizes transmitting power and maximizes data rate has far higher?tness than the particle which only minimizes BER.5.Conclusions

In this paper,a cognitive radio adaptation method has been proposed which uses PSO as the decision method.Multicarrier system is used for simulation analysis in order to examine the proposed method in such a complex scenario.Simulation results show that the proposed method converges faster than GA-based adaptation method,and the parameters optimized by the proposed method have higher?tness values than those optimized by GA,which validates the effective-ness of the proposed method.In addition,the pro-posed method is far more stable than GA,and it can also tradeoff multiple objectives and put more em-phasis on the main objective while still balancing the secondary objectives.The resulting parameter con?g-uration is consistent with the weights of objective functions.

Acknowledgment

This work has been supported by the Education Department of Zhejiang Province,China(grant No. 20050543).

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Authors’Biographies

Zhijin Zhao is currently a Professor and Dean of College of Telecommuni-cations at Hangzhou Dianzi University.She received her M.S.degree in Elec-tronic Engineering from Xidian Univer-sity,Xi’an,China,in 1984.She is the recipient of numerous honors and awards including Distinguished Tea-cher Award of Ministry of Electronics Industry of China in 1997,National

Distinguished Teacher Award in 2004,and Zhejiang Pro-vince Meritorious Service Teacher Award in 2007.She has published over 70journal and conference papers.Her research interests are in the areas of communication signal processing,adaptive signal processing,and speech signal processing.

Shiyu Xu is currently working toward his M.S.degree at Hangzhou Dianzi University,Hangzhou,China.He received his B.S.degree from Hang-zhou Dianzi University in June 2006.His research interests include cognitive radios,spectrum sensing,and genetic algorithms.

Shilian Zheng received his B.S.degree (with highest honor)and M.S.degree (with highest honor)from Hangzhou Dianzi University,Hangzhou,China,in June 2005and March 2008,respec-tively.His research interests include cognitive radios,evolutionary algo-rithms,game theory,and signal proces-sing for wireless communications.Junna Shang received her Ph.D.degree from Chinese Academy of Sciences in 2006.She is currently working at Hang-zhou Dianzi University as an Assistant Lecturer.Her research interests are in the areas of communication signal pro-cessing,satellite navigation,

etc.

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