Multiobjective Optimization for Low SAR Antenna Design

Ibrahim Elshafiey, Abdel-Fattah Sheta, Saeed Aldosari, Majeed A. Alkanhal, and Saleh A. Alshebeili Electrical Engineering Department and Prince Sultan Advanced Technologies Research Institute (PSATRI)

King Saud University, PO Box 800, Riyadh 11421, Saudi Arabia

Abstract- With the widespread use of wireless communication

systems, efforts are directed to reduce the human exposure to RF

radiation. Multiobjective optimization is becoming essential to

achieve satisfactory antenna performance whilst minimizing the

radiation level in the human body. A technique based on the genetic

algorithm is proposed to optimize a multiobjective function

involving weighted goals related to the antenna performance and

the near-field radiation pattern inside the human body.

Electromagnetic simulation based on FDTD formulation is

performed using SEMCAD X. Dispersive material characteristic is

chosen for the human head phantom. Results illustrate the

enhancement introduced by this technique of antenna design that

could be used in multifunction communication systems.

Keywords-Antenna Design, SAR, Multiobjective Optimization,

Dispersive Material.

I. INTRODUCTION

The biological effects of RF radiation has attracted wide

interest in the research community due to the widespread use

of mobile communication systems. RF radiation was

traditionally thought to have only thermal effects in the

frequency ranges used in communication systems. Recent

studies, however, investigate other forms of effects such as

genetic changes in human cells [1].

Exposure guidelines attempt to define the level below

which health effects should not occur. Specific absorption

rate or SAR is the absorbed dose rate and it is thus the time

derivative of the incremental energy (dW) absorbed by or

dissipated in an incremental mass (dm) contained in a volume

(dV) of a given density (ρ):

𝑆𝐴𝑅 =𝒅

𝒅𝒕 𝒅𝑾

𝒅𝒎 =

𝒅

𝒅𝒕 𝒅𝑾

𝝆𝒅𝒗 (1)

It is usually straight forward to determine the field

distribution for a specific SAR value, if the exposed body is

far enough from the field source, which is the case, for

example, of the public exposure to base station fields. This

concept cannot easily be applied if the body is very close to

become in the near-field of the source, such as the case of a

user holding a mobile handset.

An obvious approach towards dosimetric analysis is to

determine the SAR in phantoms simulating human head or

body containing a tissue-equivalent material. SAR can be

measured by recording the local temperature values. SAR is

proportional to temperature increase if the effects of heat

diffusion can be neglected [2].

Another way of determining the SAR is by measuring the

electric field (E) inside the tissue-simulating material. SAR

is given in terms of conductivity and density as

𝑆𝐴𝑅 =𝜎 |𝐸|2

𝜌 (2)

where is the conductivity of the tissue.

SAR can be reduced using advanced design techniques of

antenna. Antenna design is often a complex optimization

problem involving the selection of many interrelated

parameters such as the geometric parameters of the antenna

to meet multiple design objectives such as desired bandwidth,

return loss and beamwidth. Reduction of SAR is a new

optimization objective of antenna design. The search surface

in such problems is often multimodal with many local

minima and maxima. In many cases, it could also be

discontinuous.

This study presents a design of an antenna that operates at

four frequency bands: 2.45 GHz, 3.5 GHz, 5 GHz and 5.8

GHz. This antenna could thus be operated in multifunction

systems that could operate Bluetooth, WiFi and WiMax

systems, for example.

II. ANTENNA OPTIMIZATION TECHNIQUES

Optimal antenna design for mobile communication

systems started to take into consideration the interaction of

the antenna with the human body in addition to the basic

antenna parameters. Techniques used in antenna design can

be categorized into local or global search methods. Local

search methods such as the simplex techniques and gradient-

based techniques usually fail to provide satisfactory results

since most of them are suitable only for simple optimization

problems involving smooth unimodal search surface.

Global optimization techniques can avoid being trapped in

local minima/maxima and hence they are adopted in many

complex optimization problems. Many global optimization

techniques are inspired by natural phenomena and are

becoming increasingly popular and finding growing

applications in different areas including electromagnetics

(EM). Nature inspired methods are not based on

mathematical formulation; rather, they try to mimic natural

selection and evolution processes. Unlike random-walk,

nature-inspired techniques follow a certain well-defined

procedure that help guide the search towards the optimal

parameters. Examples of these methods include simulated

annealing, particle swarm optimization, and evolutionary

algorithms.

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Simulated annealing (SA) is an optimization technique

that tries to simulate the physical process of annealing,

through which a material is made less brittle by gradual

heating and cooling cycles. Simulated annealing methods

have been applied in various antenna optimization problems

as in [3].

Particle Swarm Optimization (PSO) has been introduced

into EM applications recently [4]. It is a stochastic nature-

inspired computation technique based on the concept of

emulating the intelligent movement of swarms of bees

looking for feeding locations. In contrast to techniques that

rely on a competitive model (survival of the fittest), PSO is

based on a cooperative model. Relying on the social

behavior of a swarm of bees, fish and other animals, the

concept of PSO has proved to be useful in solving

unconstrained global optimization problems.

Evolutionary techniques are increasingly being

implemented in electromagnetic design tools because of their

flexibility, versatility and ability to handle complex

multimodal search spaces [5]. These techniques are

discussed next.

III. EVOLUTIONARY ALGORITHMS

The search process in evolutionary algorithms (EA)

usually starts with a random initial guess, and then the

parameters are evolved using an evolutionary process. This

evolutionary process is guided by a fitness function, which

quantifies the goodness of the current solution and helps

direct the search towards the optimal solution.

Three main categories of EAs can be identified in the

literature: genetic algorithm (GA), evolution strategies (ES),

and evolutionary programming (EP) [6]. In terms of the

evolution level, GA operates at the genetic level, ES at the

individual level, while EP operates at the species level. In

addition, one of the most important differences between these

algorithms is the choice of the variation operator, which

directly affects the evolution process. For instance, since GA

operate at the genetic level, evolution is carried out using a

mix of crossover and mutation of genes, where the former is

the dominant operator. It requires two parents to produce an

evolved offspring. In contrast, EP operating at the species

level is entirely based on mutation, where one parent is used

to produce evolved species.

Of the three EA multiagent stochastic search methods, GA

is the most popular within the electromagnetic community.

Results have shown that ES and EP can be more efficient in

problems involving multimodal optimization problems

especially when the optimization parameters are highly

correlated [6]. Since its introduction in 1975 by John

Holland the genetic algorithms (GA) has found a wide spread

use in many fields including communications and

electromagnetics. An example of the use of GA in antenna

design is found in [7], where GA optimization resulted in

excellent bandwidth and gain properties with good

impedance characteristics that outperformed conventional

designs. The GA was also applied successfully in the design

of the microstrip patch antenna as in [8].

The genetic algorithm is based on the concept of survival

of the fittest outlined in Fig. 1. The process starts with a

random population corresponding to an initial guess. The

population comprises a group of chromosomes from which

candidate solutions are selected. Each chromosome in the

population represents a candidate solution. The chromosomes

are represented by strings of binary bits (genes), which

represent the value of the optimization parameters. The

goodness of all chromosomes in the population is assessed by

evaluating the fitness function then a group of chromosomes

is selected from the population. These parent chromosomes

are used to generate the offspring after which their fitness is

evaluated similarly. A replacement strategy is then followed

to replace chromosomes in the current population with their

offspring. This process is repeated until a desired criterion is

achieved.

GA-based algorithms usually suffer from the high

computational complexity. This is because the GA performs

its searching process via a population-to-population instead

of point-to-point search. Therefore, at each optimization

(evolution) step, the fitness function is evaluated for all

members of the population instead of just one.

IV. MULTIOBJECTIVE OPTIMIZATION

Multiobjective optimization is becoming essential in the

antenna design of modern communication systems. Various

commercial packages are becoming equipped with

optimization tools such as SEMCAD-X, which we adopt to

conduct the optimization analysis and electromagnetic

modeling simulation [9].

Recombination

END

Initial Population

Mutation

Reproduction

Fitness Evaluation

Fitness Evaluation

STOP?

yes

no

For Each

Cromosome

Fig. 1. Outline of the Genetic Algorithm

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SEMCAD-X is based on the FDTD method and is

specialized in the computation of SAR. One of the most

attractive features of SEMCAD-X is the ability to conduct

multiobjective optimization. This environment is used to

develop muli-frequency band antennas which minimize SAR

value in the tissues of the head of the system operator.

V. MULTIFUNCTION SYSTEM ANTENNA

We consider the design of an antenna that can be used in

multifunction mobile communication systems. A suitable

prototype is presented in [10] where an ultra-wide band UWB

antenna was used in microwave imaging. As shown in Fig. 2,

the antenna consists of a slotted patch implemented on one

side of the dielectric substrate and a partial ground in the

form of L-shaped on the other side. The antenna is based on

a prototype UWB antenna presented in [11] which is a planar

antenna manufactured over a single PCB of size 25 mm x 25

mm x 1.5 mm, which achieves operation in the range 2.9-11.6

GHz.

The L-shaped ground of the proposed antenna structure

consists of two perpendicular rectangular structures.

Analysis of antenna structure revealed that changes in main

shape of antenna deteriorate performance while the L-shaped

ground is easy to optimize.

Optimization is performed to adapt the antenna structure

to achieve a set of requirements. Tree algorithm is used to

avoid the destruction of good schemata during the

optimization process by estimating the chromosome

probability density and giving more chances to those

chromosome distributions whose fitness is higher through the

use of dependency trees,. Optimization parameters are chosen

such that elitism (percentage of samples copied) is 30% and

mutation probability is 1%. Population size is 30.

Five parameters are chosen for optimization including the

length (L1) and width (W1) of the horizontal arm in addition

to the length and width L2 and W2 of the small vertical arm

shown in Fig. 3. The center (C1) of the horizontal arm along

the horizontal axis is also set for optimization. Table 1

presents the range of the chosen parameters. Number of bits

is chosen to be 8 for all optimization parameters, which

indicates the resolution of values given in the table.

Fig. 2. UWB planar structure. Grid divisions are 1x1 cm2.

Fig. 3. L-shaped ground structure implemented in the optimization.

The optimization goal is set so that the S11 parameter in

the input port is less than -10 dB in the frequency ranges [2.3-

2.7], [3.3-3.7] and [5.0-6.0] GHz.

Best five chromosomes and their fitness values are given

in Table 2. The S11 value corresponding to the best-obtained

chromosome is presented in Fig. 4 along with the goal values.

Fig. 4. S11 corresponding to the best chromosome

Table 1. Optimization parameters

Parameter Minimum value

Maximum value Resolution

C1 22.5 27.5 0.0195313

L1 45 55 0.0390625

W1 8.1 9.9 0.00703125

L2 11.7 14.3 0.0101562

W2 2.7 3.3 0.00234375

Table 2. Best five chromosomes for antenna in free space.

C1 L1 W1 L2 W2 Fitness

26.559 54.490 8.135 14.157 2.940 91.320

27.343 54.529 8.142 13.566 2.825 87.549

26.088 54.804 8.121 12.944 3.274 87.349

26.931 53.784 8.185 14.188 3.274 83.802

27.480 54.569 8.255 14.096 2.754 81.703

L1

W1

L2

W2

C1

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VI. OPTIMIZATION OF SAR

Multiobjective optimization is performed to enhance the

antenna characteristics while minimizing the RF deposition in

human head. A model is built in which the antenna is set

close to SAM phantom of human head as shown in Fig. 5.

Same optimization parameters presented in Table 1 are

used. The optimization goal is set so that the S11 parameter in

the input port is less than -15 dB in the frequency ranges [2.3-

2.6], [3.3-3.6] and [4.9-6.0] GHz. SAR is set to be minimized

below 1.5 W/kg at frequencies 2.5, 3.5, 5.0 and 5.8 GHz.

Fig. 5. Antenna close to human head phantom.

Since the human tissue parameters are frequency

dependent, dispersive material characteristic is chosen for

human head phantom. Debye model with single pole is

chosen such that the complex permittivity 𝜀 is given as

𝜀 𝜔 = 𝜀∞ +(𝜀0−𝜀∞ )𝐴

1+𝑗𝜔𝜏 (3)

where 0 is the static permittivity and is the permittivity at

infinity. A and are the magnitude and relaxation time

corresponding to the pole. The parameters given in Table 3

are fitted to Equation 3 to obtain the various parameters.

VII. RESULTS AND DISCUSSIONS

Best five chromosomes and their fitness values are given

in Table 4. The SAR values corresponding to the best

chromosome are given in Table 5 averaged on 1 gram and 5

gram of the tissue. The S11 values are presented in Fig. 6.

SAR map inside human head phantom at 2.5 GHz is shown in

Fig. 7.

Figure 8 illustrates the field sensor region that includes the

antenna and part of the human head phantom. Results of the

electric field maps within the field sensor region

corresponding to best obtained chromosome are shown in

Fig. 9, where the input power is set to 1 W. 0-dB

corresponds to 8029 V/m for 2.5 Ghz, 6473 V/m for 3.5 Ghz

and 8175 V/m for 5 GHz. The figure reveals the increase of

attenuation of the field in the human head with increase of

frequency.

Figure 10 presents the current density at different

frequency values. 0-dB corresponds to 94792.6A/m2 for the

antenna structure and 59219.7A/m2

for the ground at 2.5

GHz, 68408.9A/m2 (antenna) and 63140.6A/m

2 (ground) at

3.5 GHz, and 51735.8A/m2 and 40167.4A/m

2 at 5 GHz. The

figure reveals the role of different arms of the slotted patch

and in different frequencies. It also illustrate the role of each

of the two arms of the L-shaped ground in different

frequencies.

Table 3. Human head material parameters

Frequency

(GHz)

Relative Permittivity Conductivity

(S/m)

0.15 42.1883 0.816924

0.3 42.1702 0.828701

0.45 42.1399 0.848304

0.83 42.0096 0.932686

0.9 41.9773 0.953601

0.91 41.9725 0.956724

1.45 41.6362 1.17454

1.61 41.5087 1.25715

1.8 41.3413 1.36557

2.0 41.1469 1.49147

2.45 40.6448 1.81674

3.0 39.9192 2.28677

5.8 34.9284 5.51948

Table 4. Best five chromosomes for antenna close to human phantom.

C1 L1 W1 L2 W2 Fitness

27.422 53.078 8.34 13.484 2.778 91.08

27.069 54.804 8.884 12.322 2.879 90.77

27.186 52.961 8.926 13.882 3.173 90.446

27.304 51.51 8.538 13.637 2.9 90.356

27.245 49.039 8.919 14.106 2.825 89.751

Table 5. SAR values in the human phantom.

Freuqency Mean SAR

(W/kg)

Minimum SAR

(W/kg)

Maximum SAR in

(W/kg)

Maximum SAR

averaged

on 1g (W/kg)

Max SAR

averaged

on 5g (W/kg)

2.5 GHz 1.92391 0.157442 10.4047 5.59799 3.78053

3.5 GHz 0.561778 0.0146166 4.057678 2.11378 1.416

5 GHz 0.655285 0.030957 3.20819 1.67999 1.12386

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Fig. 6. S11 corresponding to the best chromosome when antenna is close to

the human head phantom.

Fig. 7. Map of SAR inside human head phantom at 2.5 GHz. 0-db

corresponds to 10.4 W/kg.

Fig. 8. Field sensor including the antenna and part of the phantom

Fig. 9. Electric field map at 2.5 GHz (top), 3.5 GHz (middle) and 5 GHz (bottom).

2 3 4 5 6 7 8 9 10 11 12 13 14-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

Frequency (GHz)

S11

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Fig. 10. Current density maps at 2.5 GHz (top), 3.5 GHz (middle) and 5

GHz (bottom

VIII. CONCLUSIONS

Multiobjective optimization is becoming essential to

achieve satisfactory antenna performance, particularly in

minimizing the radiation level in the human body. A

technique based on genetic algorithms is presented, where a

multiobjective function is formed by weighted goals related

to the antenna performance and the near-field radiation

pattern inside the human body. This function is minimized

using the genetic algorithm. The inherent parallel nature of

the genetic algorithms can help eliminate the required high

computational complexity through parallel processing.

Electromagnetic simulation is performed under SEMCAD-

X environment. Since the human tissue parameters are

frequency dependent, dispersive material characteristic is

chosen for simulating head tissue. Debye model with a single

pole is assumed. Presented results illustrate the power of the

developed techniques in optimizing antenna design,

particularly for challenging problems requiring the reduction

of SAR of an antenna of a multifunction communication

system operating at various frequency bands, close to

dispersive biological material.

ACKNOWLEDGEMENT

This research is funded by King Abdulaziz City for

Science and Technology (KACST), Research Grant: MT-2-5.

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