Minimal Throughput Maximization for

MIMO Cognitive Radio Networks Using

Particle Swarm Optimization

1

Abd Elhamed M. Dawoud,

1

Mona Shokair,

1

Mohamed Elkordy and

1

Said El Halafawy.

Faculty of Electronic Engineering, El-Menofia University

Menouf 32952, Egypt

Corresponding author’s email

:

abd.elhamed@el-eng.menofia.edu.eg

Abstract—Due to the scarcity of the available

spectrum bands, Cognitive Radio (CR) has been

proposed as a promising paradigm. One of the most

important research area is how to maximize

Secondary User (SU) system throughput while

assuring the Quality of service of Primary User (PU)

system. Multiple-Input-Multiple-Output (MIMO) is

an efficient technique, exploiting space diversity,

used for increasing SUs throughput. The

contribution is to maximize the minimal throughput

among SUs, in particular the uplink of the

infrastructure-based Cognitive Radio Networks

(CRNs), through proposing a power allocation

technique based on Particle Swarm Optimization

(PSO) for MIMO systems in CR networks.

Maximum-Minimum Throughput-based Power

Assignment (MMTPA) and Equal Power

Assignment (EPA), using the average minimal

throughput among all SUs and also the complexity

to measure performance, approaches are used for

comparison. The simulation results show that the

proposed approach outperforms the two other

schemes, in addition, an increase in the total

throughput of SU system.

KEY WORDS: Cognitive radio networks, MIMO,

Particle Swarm Optimization, and Throughput

.

I. INTRODUCTION

Due to the rapid growth of wireless technologies,

the increasing demand for higher bandwidth

applications and the crowded spectrum. CR had

been introduced by J. Mitola [1], as a promising

solution. CR has the ability to utilize efficiently

the spectrum as its network entities are aware of

their environment and can communicate

intelligently in such a manner that their

transmission and reception parameters can be

changed dynamically avoiding the interference

with licensed or unlicensed users [2-4]. Therefore,

CR has attracted much attention from researchers

[5-8].

Actually, there are three main approaches for CR

to exploit the available spectrum bands named

underlay spectrum sharing, overlay (opportunistic

spectrum access) and sensing-based spectrum

sharing, respectively. For underlay spectrum

sharing, the spectrum band is shared among all

PUs and SUs yielding co-channel interference

between SUs and PUs and so that the transmitted

power of SUs system must be controlled in such a

way to reduce interference with PUs system and

protect the quality of service (QoS) of licensed

PUs [9-10]. From the point of view of overlay,

SUs only has the right to use the empty spectrum

bands after the process of sensing [11-12].

Sensing-based spectrum sharing is a hybrid

scheme in which SU firstly sense the spectrum,

then adjusts its transmitted power according to

PU’s status [13]. Underlay spectrum sharing is the

most common used scheme so the transmitted

power of SUs must be assigned carefully in order

to maximize SUs throughput, under power and

interference constraints, and not to affect the QoS

of PUs. Through the literature, there are many

optimization techniques that have been used to

find SUs optimal transmitted power. EPA is the

simplest one among them, where equal power is

assigned to each one of SUs. The assigned

constant power doesn’t affect the QoS of each

PUs [14]. Another scheme named MMTPA in

which [14] the minimal power of all SUs is

maximized in order to have the same QoS of each

SUs.

In fact, OFDM has been recognized as the

promising candidate in Cognitive Radio Network

(CRN) due to its flexibility of resource allocation.

2016 International Conference on Selected Topics in Mobile & Wireless Networking (MoWNeT)

978-1-5090-1743-0/16/$31.00 ©2016 IEEE

In seeking to have a superior data throughput and

more reliability, Multiple-Input-Multiple-Output

(MIMO) [15-16] has been adopted in modern

communication systems without using additional

transmit power or spectral bandwidth because of

its ability to exploit space diversity. For this

reason, researchers had been implemented MIMO

system for CRNs to improve the performance of

SUs under cochannel interference [17-18].

In this paper, a proposed power allocation

technique based on PSO will be suggested to

maximize the minimal throughput among SUs

considering that the deduced interference from

each one of SUs should be under the allowed

threshold level and guaranteeing the QoS of the

user of Pus and SUs. Therefore, we use the

capacity pound of SUs under co-channel

interference to measure the SUs throughput. In

fact, there are different required QoS for different

SUs and consequently variable throughput for

each SU. The minimal throughput among SUs

will be used to quantify system performance. For

comparison, the minimal throughput gained by

PSO will be compared with that achieved by

MMTPA and EPA. Simulation results show that

the proposed PSO power allocation scheme

outperforms the EPA and MMTPA as it gives the

maximum minimum throughput and also

maximize the throughput of each one of SUs but

with more complexity.

The rest of this paper is organized as follows: the

system model and throughput calculation are

presented in Section II. Where MMTPA and EPA

schemes will be discussed in Section III. The

proposed PSO power optimization scheme is

highlighted in Section IV. Simulation results will

be presented in Section V. Finally, a conclusion

will be in Section VI.

II. SYSTEM MODEL AND

THROUGHPUT CALCULATION

A. SYSTEM MODEL

Suppose a CRN consist of ܭ cochannel SUs

coexist with ܮ PUs pair in the same spectrum band

and share the same frequency band in underlay

paradigm. Each ܷܵ

(the ݅

௧

SU) has a single

MIMO transmitter and a single MIMO receiver

(transmitter ݅ and receiver݅, respectively). Each

transmitter composes of ܯ transmit Antennas and

each receiver contains of ܰ receive antennas. For

a given SU, each transmit antenna has the same

shared transmitted power. An independent

Rayleigh flat-fading MIMO channel is assumed.

It can be represented by ሺܯൈܰሻ channel matrix

ofܪאԧ

ெൈே

. Now, consider a transmitted signal

vector ݔ

ሺݐሻאԧ

ெൈூ

from transmitter݅, then for

eachܷܵ

, the received signal at the receive

antenna array can be expressed by:

ݕ

ൌܪ

ݔ

݊

ߟ

ߤ

(1)

Where ݕ

ൌሺݕ

ሻאԧ

ேൈூ

represents the received

signal vector for the receiver݅, ܪ

ൌሺܪ

ሻא

ԧ

ேൈெ

is the channel matrix between the

transmitter ݅ and receiver ݅ , ݊

ൌሺ݊

ሻאԧ

ேൈூ

represents the additive white noise vector in the

channel, ߟ

ൌሺߟ

ሻאԧ

ேൈூ

is the vector

corresponding to the co-channel interference from

other SUs and ߤ

ൌሺߤ

ሻאԧ

ேൈூ

represents PUs

co-channel interference vector. Moreover, each

element of channel matrix ܪ

is assumed to be an

independent complex random Gaussian variable

and can be modeled

as݄

ேǡெ

̱ࣝࣨሺͲǡͲǤͷ݁ݎ݀݅݉݁݊ݏ݅݊ሻ.

Furthermore, we assume that a full channel state

information (CSI) is known to the receiver and is

not known to transmitter, and each element of ݊

is independent of each other.

Actually, there will be mutual co-channel

interference among PUs and SUs and to assure the

QoS of PUs the co-channel interference form SUs

should be below the given threshold which can be

expressed as:

σܲ

ୀ

ୀଵ

ܩ

ǡ

Ȳ

for ݈ൌͳǡʹǡǥǥǤǡܮ (2)

Where ܲ

represents the transmit power ofܷܵ

,

ܩ

ǡ

is the power gain between the transmitter of

݅

௧

SU and the receiver of ݈

௧

PU, and Ȳ

is the

introduced interference threshold value from all

SUs on ݈

௧

PU.

B. THROUGHPUT CALCULATION

In order to quantify the throughput, we first

calculate the capacity of MIMO system in CRN

under co-channel interference. Then, use the

capacity pound (in b/s/Hz) to determine the

throughput. For eachܷܵ

, the channel capacity,

according to [16-17], can be expressed as:

ܥ

ൌ

ଶ

݀݁ݐቀܫ

ே

ீ

෨

ೕǡ

ெ

ܪ

ܪ

ு

ሺܴ

ሻ

ିଵ

ቁ ്݆݅

(3)

where ܫ

ே

represents an identity matrix, ܩ

෨

ǡ

is the

power gain between ܷܵ

transmitter and

ܷܵ

receiver, ܪ

ு

represents the Hermitian

transpose of the channel matrix, and ܴ

is the

correlation matrix that is given by:

ܴ

ൌ߃ሾ݊

݊

ு

ሿ߃ሾߟ

ߟ

ு

ሿ߃ሾߤ

ߤ

ு

ሿ (5)

According to [18], if there are a large number of

interfering sources, the correlation matrix can be

denoted as:

ܴ

՜ሺߙ

ߚ

ߛ

ሻܫ (6)

Where, for eachܷܵ

, ߙ

represents power of

noise, ߚ

represents total co-channel interference

power from other SUs, and ߛ

represents total

interference power from PUs, respectively.

Substituting (6) into (5) with ߚ

ൌσܲ

ஷ

ܩ

෨

ǡ

the

channel capacity (in b/s/Hz) of ܷܵ

can be denoted

by:

ܥ

ൌ

ଶ

݀݁ݐ൬ܫ

ே

ீ

෨

ೕǡ

ெ൫σ

ೕಯೕ

ீ

෨

ǡೕ

ାఈ

ାఊ

൯

ܪ

ܪ

ு

൰

(7)

Furthermore, according to [19 theorem 1], we

have

ܥ

ܰ

ଶ

൬ͳ

ீ

෨

ೕǡ

ெே൫σ

ೕಯೕ

ீ

෨

ǡೕ

ାఈ

ାఊ

൯

ԡܪ

ԡ

ଶ

൰

(8)

In addition, applying the expectation over ܪ

elements in (8). Then, for eachܷܵ

the capacity

pound, as given in [14], can be denoted by:

߃ሾܥ

ሿܰ

ଶ

൬ͳ

ீ

෨

ೕǡ

൫σ

ೕಯೕ

ீ

෨

ǡೕ

ାఈ

ାఊ

൯

൰ (9)

And the maximum achievable data rate can be

determined by the right hand side of (9). Since the

throughput represents the actual date rate and

always changes with time, transceivers and

environment. It is appropriate to use the capacity

pound to quantify the throughput. Consequently,

for each ܷܵ

the throughput ܶ

(In b/s/Hz) can be

denoted by:

ܶ

ൌܰ

ଶ

൬ͳ

ீ

෨

ೕǡ

൫σ

ೕಯೕ

ீ

෨

ǡೕ

ାఈ

ାఊ

൯

൰ (10)

III. MMTPA AND EPA SCHEMES

A. MMTPA SCHEME

The aim of MMTPA is to maximize the minimal

throughput among all SUs while ensuring the total

co-channel SUS interference does not affect the

QoS of all PUs. Setting ܶ

ൌܶ

ሺሻ whereൌ

ሼܲ

ሽ represents the power set ofܲ

. Therefore,

MMTPA aims to find the optimal value of the

power set ܲ

כ

ൌሼܲ

כ

ሽ which satisfies the

following optimization problem:

Problem 1

Maximize ሼܶ

ሺܲሻሽ

Subject to σܲ

ܩ

ǡ

Ȳ

݈

ୀ

ୀଵ

In fact, a proposition found in [14 proposition 1]

is implemented in order to simplify the process of

finding the optimal value

כ

. According to [14],

for an uplink infrastructure-based CRN where all

SUs are connected to the same base station (BS),

therefore, the noise power and the interference

power from all PUs to all SUs’ receivers will be

constant as all SUs’ receivers are located in the

same BS i.e. ߙ

ൌߙ

ൌߙ,ߛ

ൌߛ

ൌߛ and

σܲ

ܩ

෨

ǡ

ൌσܲ

ܩ

෨

ǡ

. Therefore, the

optimization problem had reduced to simply

optimizing the transmit power of the

representative SU in order to maximize its

throughput and keep the ratio of the transmit

power of any other SU to the representative SU

constant. Therefore, problem 1 can be

reformulated to be:

Problem 2

Maximize

ீ

෨

ǡ

ሺିଵሻீ

෩

ǡ

ାሺఈାఊሻ

Τ

Subject to ܲ

σܨ

ܩ

ǡ

Ȳ

ୀ

ୀଵ

for all l

where ܩ

෨

ǡ

represents the power gain between the

transmitter and the receiver of the representative

SU, ܲ

is the transmit power of representative SU

and ܨ

ൌܩ

෨

ǡ

ܩ

෨

ǡ

ൗ. Further, in order to

maximizeܲ

, the author [14] chooses ܷܵ

such

that

ܩ

෨

ǡ

ܩ

෨

ǡ

for all i (11)

Figure 1. Flowchart of PSO algorithm.

And make the power assignment as follows:

ܲ

כ

ൌ

൛Ȳ

ൣσܨ

ܩ

ǡ

ୀ

ୀଵ

൧

Τൟ (12)

ܲ

ൌܲ

כ

ܨ

for all i (13)

Substituting (12) and (13) into problem 2, the

minimal throughput, among all SUs, achieved by

MMTPA approach can be denoted by:

ܶ

ெெ்

ൌ

ܰ

ଶ

ቆͳ

ீ

෨

ǡ

ሺିଵሻீ

෨

ǡ

ାሺఈାఊሻ୫୧୬

ቄஏ

σி

ீ

ǡ

స಼

సభ

Τቅ

ൗ

ቇ

(14)

B. EPA SCHEME

For EPA, equal level of transmitting power will

be assigned to each SU. Which means that

ܲ

ൌܲ

ൌܲfor all ്݆݅ (15)

Inserting (15) into (2), we further have

ܲൌ

൫Ȳ

σܩ

ǡ

ୀ

ୀଵ

Τ൯ (16)

Substituting (16) into (10) yields the minimal

throughput among all SUs, which can be achieved

by EPA scheme, that can be expressed as:

ܶ

ா

ൌ

൝ܰ

ଶ

൭ͳቆ

ீ

෨

ೕǡ

σீ

෨

ೕǡ

ାሺఈ

ାఊ

ሻ୫୧୬

൫ஏ

σீ

ǡ

స಼

సభ

Τ൯ൗ

ಯೕ

ቇ൱ൡ

(17)

IV. PROPOSED PSO POWER

OPTIM IZATION SCHEME

PSO algorithm is a population based global search

evolutionary algorithm inspired by the behavior

of birds and fish swarms. It was first introduced

by Dr. Kennedy and Dr. Eberhart in 1995 [20-21].

It is benefiting from the information shared

among swarm members to find the optimum

position of food, the right path to go through or

the optimum value of the optimization problem.

In PSO, the Population is called a Swarm and each

swarm member is called a Particle. Each particle

represents a possible solution of the objective

function/ optimization problem in the solution

search space. The algorithm starts with

initializing each particle with a random position

and velocity in the search space and defining

system parameters such as maximum number of

iterations, number of dimensions, swarm size and

acceleration coefficient. Then each particle

position is used as an input to fitness/objective

function to get fitness value.

A personal best (pbest) and a global best (gbest)

variables are defined that represent the particle

self-trust and social trust, respectively. Within an

iteration, the velocity and the position of each

particle are updated and the fitness value is then

evaluated using the updated position value and

compared to the current (pbest) and (g best)

values to update their values. These steps are

repeated until the algorithm finds the optimum

value of the optimization problem, the maximum

number of iterations is reached or the stopping

Figure 2. The average minimal throughput (in bps/Hz)

versus the number of SUs.

condition is achieved. Flowchart is shown in

Figure 1.

The optimization problem denoted by problem 1

aims to maximize the minimum throughput

among all SUs by optimizing the transmit power

of the SU while ensuring the QoS of PUs. Since

PSO is used as a minimization algorithm, the

problem defined in problem 1 should be

reformulated to be compatible with PSO.

Therefore, problem 1 can be reformulated to:

Problem 3

Minimize

ቊሺെͳሻൈܰ

ଶ

ቆͳ

ܲ

ܩ

෨

ǡ

൫σܲ

ஷ

ܩ

෨

ǡ

ߙ

ߛ

൯ቇቋ

Subject to σܲ

ܩ

ǡ

Ȳ

݈

ୀ

ୀଵ

Moreover, the complexity is an important issue

for power allocation besides to the performance.

The PSO can be implemented without knowing

any power gain among SUs. It is only compute the

minimal throughput in each iteration and adjust

the transmit power of each SU according to the

constraint defined in problem 3. On the other

hand, MMTPA needs to know all power gains

among SUs and compute the power level of each

SUs by (12) and (13). EPA needs only to compute

the common power level using equation (16)

without knowing any power gain among SUs.

Table 1.

ARTHIMETIC OPERATION NUMBER REQUIRED FOR

DIFFERENT POWER ASSIGNMENT SCHEMES.

Therefore, EPA yields the lowest complexity

among power assignment schemes. Table1 shows

the required number of arithmetic operation for

power assignment schemes used in an uplink

infrastructure-based CRN. Considering V

iterations is executed in PSO, it can be showed

that EPA requires the least number of arithmetic

operation while PSO requires more number of

arithmetic operation than MMTPA.

V. SIMULATION RESULTS

For the uplink of the infrastructure-based CRN

the power gain between transmitter l and receiver

i can be determined by the following

relationܵ

ܦ

ఒ

, where ܵ

models shadowing

factor and ܦ

ఒ

represents the distance between

transmitter l and receiver i and Ȝ is the path-loss

exponent.

Table 2. SIMULATION PARAMETERS.

In our simulation, all shadowing factors will be

considered to be independent lognormal random

variables with mean equals to 0-dB and 2-dB

variance. Moreover, a constant transmit power

level of 10-dB is assigned to all PUs. The rest of

simulation parameters are set as shown in Table

2.

The average minimal throughput (in bps/Hz)

against the number of SUs, the number of PUs,

PSO MMTPA EPA

Addition K-1 K-1 K-1

Multiplication VK 2K-2

Division V(K-1) K-1+L L

Simulation

parameter

Value Simulation

parameter

Value

No. of PUs (L) 2 Swarm size 100

No. of SUs (K) 4 Max. Iterations 100

No. of antennas

(N)

4 No. of

dimensions

1

Noise power

(Į)

-10-dB C1, C2 2

Threshold level

(Ȳ)

1-dB Inertia weight

(߱)

0.8

Path-loss

exponent Ȝ

4 Stopping

criteriaߝ ͳͲ

ି

Figure 5. The average minimal throughput (in bps/Hz)

versus noise power (dB).

Figure 6. The average minimal throughput (in bps/Hz)

versus interference threshold

(

dB

)

.

Figure 3. The average minimal throughput (in bps/Hz)

versus the number of PUs.

Figure 4. The average minimal throughput (in bps/Hz)

versus the number of number of receivin

g

antennas.

the number of receiving antennas, the noise power

(in decibel), and threshold interference level (in

decibel) is plotted in figures 2-6, respectively. In

addition, the proposed PSO scheme gives higher

performance compared to MMTPA and EPA in

the minimal throughput (among all SUs) and

outperforms them. In Figure 2, as the number of

SUs increases, the minimal throughput decreases.

This coincides with the results presented in

Equation (10). As the number of SUs increases,

the aggregated co-channel interference from other

SUs increases yielding less throughput. The

results in Figure 3 show that the increment in the

number of PUs has a relatively slight decrease in

the achieved minimal throughput.

This is because of the fixed relatively large

threshold level of 1-dB for all PUs. Therefore, the

assigned transmit power for each SUs is relatively

high which produces interference from all SUs

larger than that of PUs interference. For a MIMO

system, the more usage of receive antennas, the

more throughput will be achieved. That is what

Figure 4 proves as the number of receiving

antennas increases, the average minimal

throughput increases. The effect of a noise power

level (in dB) is shown in Figure 5 where noise

power level does not make a significant effect on

the average minimal throughput.

This is because of the small number of SUs and

PUs used in our simulation and in this case the

interference dominates the average minimal

throughput.

In addition, Figure 6 presents the impact of

interference threshold level on the average

minimal throughput where the increase in

threshold level leads to an increase in the average

minimal throughput until it reaches a saturation

level. As the threshold level increases, the

influence of PUs noise-interference will be

negligible compared to SUs noise-interference

influence that makes the average minimal

throughput reaches saturation.

VI. CONCLUSION

In this paper, a proposed power assignment

scheme based on the PSO algorithm was used to

maximize the minimal throughput among all SUs

in CRNs. In particular, in the uplink

infrastructure-based MIMO CRN where underlay

spectrum sharing paradigm is applied for

spectrum sharing between SUs and PUs. Where

the usage of a MIMO system ensures a high

system capacity and reliability. The proposed

scheme aims to optimize the transmit power of

SUs while assuring the QoS of PUs. It was

compared with two other power assignment

schemes named MMTPA and EPA using the

average minimal throughput among all SUs as

performance measurement parameter. Simulation

results showed that the proposed scheme gives

higher performance compared to MMTPA and

EPA in minimal throughput. Moreover, it

increases the total SUs throughput than other

schemes. The issue of complexity was considered

where EPA results in the least complexity and the

least average minimal throughput and PSO yields

the best average minimal throughput than

MMTPA and EPA however, with more

complexity.

REFERENCE

[1] J. Mitola and G. Q. Maguire. Cognitive radios: Making

software radios more personal. IEEE Pers. Commune.,

1999. 6(4), 13–18.

[2] S. Haykin. Cognitive radio: Brain-empowered wireless

communications. IEEE J. Sel. Areas Commun., 2005.

23(2), 201–220.

[3] Hrishikesh Venkataraman, Gabriel-Miro Muntean.

Cognitive radio and its application for next generation

cellular and wireless networks. In Lecture Notes in

Electrical Engineering, 116. Springer, Netherlands,

2012.

[4] Akyildiz IF, Lee W-Y, Vuran MC, Mohanty S. Next

generation/dynamic spectrum access/cognitive radio

wireless networks: a survey. Computer Networks, 2006,

50(13), 2127–2159.

[5] L. Zhang, Y.-C. Liang, and Y. Xin. Joint beam forming

and power allocation for multiple access channels in

cognitive radio networks. IEEE J.Sel. Areas Commun.

2008, 26(1), 38–51.

[6] Y. C. Liang, Y. H. Zeng, E. Peh, and A. T. Hoang.

Sensing-throughput tradeoff for cognitive radio

networks. IEEE Trans. Wireless Commun., 2008, 7(4),

1326–1337.

[7] T. Hoang, Y.-C. Liang, and M. H. Islam. Power control

and channel allocation in cognitive radio networks with

primary users’ cooperation. IEEE Trans. Mobile

Comput., 2010, 9(3), 348–360.

[8] J. T.Wang. Rate adaptation with joint receive diversity

and power control for cognitive radio networks.

Computer Networks, 2011, 55(8), 1711–1718.

[9] Sakran, H., Shokair, M., Nasr, O., El-Rabaie, E.-S., and

El-Azm, A. A. Proposed relay selection scheme for

physical layer security in cognitive radio networks. IET

Communications. 2012, 6(16), 2676–2687.

[10] Yang, Li and Nosratinia, A. Spectrum sharing with

distributed relay selection and clustering. IEEE

Transactions on, Communications. 2013, 61(1), 53–62.

[11] Sakran, H., Shokair, M., El-Rabaie, E.-S., and El-Azm,

A.A. Three bits softened decision scheme in cooperative

spectrum sensing among cognitive radio networks. 28th

National, Radio Science Conference (NRSC),2011, 1–9.

[12] Sakran, H. and Shokair, M. Hard and softened

combination for cooperative spectrum sensing over

imperfect channels in cognitive radio networks.

Telecomm. System, 2011, 52(1), 61–71.

[13] Xin, Kang, Ying-Chang, Liang, Garg, H. K., and Lan,

Zhang. Sensing-based spectrum sharing in cognitive

radio networks. IEEE Transactions on, Vehicular

Technology, 2009, 58(8), 4649–4654.

[14] Wang, Jui Teng. Maximum–minimum throughput for

MIMO systems in cognitive radio networks. IEEE

Transactions on, Vehicular Technology. 2014, 63(1),

217–224.

[15] Tsoulos, George. MIMO System Technology for

Wireless Communications. Electrical Engineering and

Applied Signal Processing Series, CRC Press, 2006.

[16] Farrokhi, F. R., Foschini, G. J., Lozano, A., and

Valenzuela, R. A. Link–optimal space–time processing

with multiple transmit and receive antennas. IEEE

Commun. Lett., 2001, 5(3), 85–87.

[17] Y. Song and S. D. Blostein. MIMO channel capacity in

co-channel interference, in Proc. 21st Biennial Symp.

Commun, Kingston, ON, Canada, 2002, 220–224.

[18] M.Webb, M. Beach, and A. Nix. Capacity limits of

MIMO channels with co-channel interference. in Proc.

IEEE VTC-Spring, 2004, 703–707.

[19] Jindal, N. and Goldsmith, A. Dirty-paper coding versus

TDMA for MIMO broadcast channels. IEEE Trans.

Inf. Theory, 2005, 51(5), 1783–1794.

[20] R. C. Eberhart and J. Kennedy. Particle swarm

optimization. Proc. IEEE ICNN 1995, Perth, Australia,

1995, 1942-1948.

[21] R. C. Eberhart and J. Kennedy. A new optimizer using

particle swarm theory. Proc. MHS 1995, Nagoya, Japan.

1995, 39-43.