� Abstract—In this study we propose an optimized Sierpinski

gasket fractal antenna for Long Term Evolution (LTE) standard. The existing mathematical models of the Sierpinski gasket monopole are also investigated and compared to our optimized model. It is observed that the designed antenna can be utilized for seven different LTE sub-bands.

Keywords—Antenna optimization, Method of Moments, Particle swarm optimization, Sierpinski gasket fractal antennas.

I. INTRODUCTION HE increases of the need of high capacity and quality of the existing wireless communication systems make researchers and engineers find optimum solutions by

switching their abilities to the maximum level. One of the solutions is to maximize the throughput by rearranging the used frequency spectrum. In this manner Cognitive Radio and LTE are proposed as promising future wireless communication standards [1], [2]. There are a lot of studies and projects to move these standards to the next level [3]-[5]. On the other hand antennas are the indispensable part of the communication systems and need to be evolved to meet the new communication standard requirements. For this reason a reconfigurable antenna is a good idea to propose for the incoming communication standards such as Cognitive Radio [6], [7]. Furthermore, due to the less computational complexity and power consuming properties, multiband antennas may be the best solution for the multiband communication standards such as LTE. In this manner, one of the most studied fractal antennas for multiband applications is the Sierpinski gasket monopole. As an antenna this fractal structure was first proposed by Puente et al. [8]-[10]. Sierpinski gasket fractal antennas are well known multiband antennas with space filling property to make the antennas more compact and smaller size. However some properties of this antenna need to be optimized to obtain the desired radiation parameters. For this purpose, in order to meet the communication standard requirements, perturbed fractal antennas were investigated [11]. In this direction, most of the studies on the Sierpinski gasket monopole antenna focused on the band spacing and controlling by modifying the flare angle or scale factor of the antenna [12], [13]. Genetic algorithm and Particle Swarm optimization (PSO) were combined to

Manuscript received February 26, 2012. This work was supported partly

by EMCoS Antenna virtual LAB and Karadeniz Technical University OSA Student Chapter.

A. Yazgan, I. Hakki Cavdar, and H. Kaya are with the Electrical Electronics Engineering Department, Karadeniz Technical University, 61080, Trabzon, Turkey (phone:+904623774164; fax:+904623257405; e-mails:{ ayhanyazgan, cavdar, hkaya}@ktu.edu.tr).

optimize the multiband antenna operating at 0.9 GHz, 1.8 GHz (both GSM) and 2.4 GHz (Bluetooth) [14]. Especially for LTE-700 and LTE-2600 which are the most flexible bands covering different countries, the Sierpinski gasket fractal may be a good candidate with two iterations. In this manner, authors used the perturbed Sierpinski gasket to design an LTE antenna covering these frequency bands. Their optimized antenna exhibits a 24% size reduction with respect to a standard quarter-wave resonant monopole [15]. Our optimized antenna also gives good impedance matching properties within the LTE bands at 700 MHz and 2600 MHz range to obtain the geographical flexibility too. Furthermore our design reaches 26.3% size reduction considering the antenna height compared to a standard quarter wave monopole antenna. From the point of view of the wide band concept, different antenna types were also designed [16], [17]. But, according to the authors who are dealing with the Sierpinski gasket fractal antennas, the first band is not too easy to control [13]. For this reason, we propose a different perspective to the mathematical model of the Sierpinski gasket fractal antenna especially for the first band which we call the fzeroband. As an optimization algorithm, we selected the PSO which is presented in Section II with details [18]-[20].

The rest of this paper is organized as following; In Section II the optimization method is detailed. Section III describes how to control the frequency bands of the Sierpinski gasket fractal antennas. In Section IV we introduce the simulation results based on the Method of Moments (MoM) and Section V concludes the paper.

II. PARTICLE SWARM OPTIMIZATION PSO is a robust stochastic optimization method introduced

first by J. Kennedy and R.C Eberhart in 1995. This algorithm is inspired by social behavior of bird flocking or fish schooling. Fast convergence property is the most important advantage of PSO algorithm [18]-[20]. PSO includes particles which are determined according to the problem complexity. The number of the particle is selected between 10 and 50 for the simulation but this range may be increased according to the complexity of the design. Iteration number can be either predefined or adaptively changed according to the defined cost function’s convergence value. Once the optimization is completed, the optimized parameters become the input of another simulation tool based on MoM. Since the algorithm runs only one time for each design it is wise to choose the particle number of the PSO as high as possible. The velocity and position of the particle are updated using the equations given in (1) and (2) where v is the velocity vector, x is the position vector, i is the particle index and k is the iteration number. In (1) rand1 and rand2 are uniformly distributed

An Optimized LTE Antenna Implementation Using Sierpinski Gasket Fractal Structure

Ayhan Yazgan, I. Hakki Cavdar, and Haydar Kaya

T

367978-1-4799-0404-4/13/$31.00 ©2013 IEEE TSP 2013

random numbers and provide the free moving ability to the particle in the problem space. In this robust algorithm pbest is the best position value for a particle that has been achieved so far and gbest is the best position value that has been o needed. There are four basic principles on the basis of this new model:btained so far for the whole swarm. c1 and c2 are learning factors selected between 0 and 4 to define movement procedure of the particle whether it is determined by its own or swarm’s experience. When the stopping criterion is satisfied, gbest stores the solution of the problem. For this optimization simulation, gbest is a vector restoring the scale factor and flare angle.

� �

� �1 1

2 2

( 1) ( ) . ( ) ( ) ( )

. ( ) ( ) ( )i i i i

i i

v k v k c rand k pbest k x k

c rand k gbest k x k

� � � �

� � (1)

( 1) ( ) ( 1)i i ix k x k v k� � � � (2)

III. SIERPINSKI GASKET FRACTAL ANTENNAS Mathematical background of the fractal antennas were

investigated by different researches. Most of the studies were focused on the Weierstrass functions [21]. The space filling ability and the quality factor properties of the fractal antennas were also investigated [22]. Atomic-fractal Kravchenko functions as a generator function was examined to estimate the radiation pattern of a fractal antenna. They also utilized the generalized Weierstrass functions [22]-[24].

There are different kinds of fractal structures that can be found in literature that were applied to the antenna geometries. But generally fractal antennas can be classified in two categories such as random and deterministic. Deterministic fractal antennas which are the most suitable for antennas to analyze are generated from several rotated copies or scaled down of themselves [25]. For the random categories any design can be used as a radiating element. Among these different type antennas the most famous one is the Sierpinski gasket fractal [8]-[10].

According to the (3) resonance frequencies of the Sierpinski gasket fractal antenna can be computed as given below [3].

� �0.152 cos2

nr

cfh

� � � �� � � � � � � �� �

(3)

In this equation fr is the resonance frequency (Hz), c is the

speed of the light (m/s) in free space, h is the height of the Sierpinski gasket monopole antenna (m), � is the flare angle � is the log period or scale factor and n is the band number starts from 2. This formula may show little differences according to the substrate thickness, permittivity and the dimension of the ground plane.

One of the most significant information that needs to be detailed here is the equation does not valid for the first band of the Sierpinski gasket fractal antenna. Therefore especially for the first band which we call it fzeroband, a contribution to this mathematical explanation is needed. There are four basic principles on the basis of this new model:

1. The scale factor does not affect the zeroth band (fzeroband) of the antenna directly.

2. The fzeroband is the fundamental band of the Sierpinski gasket fractal antenna which can be used to determine the overall antenna height as calculated in (4).

3. The first band (fdeadband) is never observed.

4. Once the fzeroband is determined then the upper bands, except for the fdeadband, may be calculated using (5) and (6).

According to the four sections described above, it is clear that, to design a dual band antenna with minimum size, we need to utilize the fzeroband and the second band of the gasket. The related mathematical explanation is given below.

cos2zerobandf a � � �� � �

� �� � (4)

� � � �, 2,3, 4...nnf a n� � (5)

� � 10.152 opt

ca ch

� �� � � �

(6)

Where fzeroband is the fundamental frequency (Hz) as

depicted above, fn is the upper band which depends upon the band number n and copt is the correction factor that needs to be optimized using the previous results. At the end of the optimization, copt was determined as 0.86 for this design. To allocate the considered LTE sub-bands given in Table I, the second frequency, f2, is assigned as 2600 MHz.

These values become the inputs of the PSO algorithm and determine the fitness function as shown in (7).

� � 2cos2

nfitness abs a f� � � �� �� � �

� �� �� � (7)

The output of this algorithm is a vector named gbest which

is detailed in Section III. This register stores the optimized scale factor and flare angle at the end of the iteration. According to this scenario PSO may finds infinite results which satisfy the condition of the stopping criterion. All are

TABLE I SUITABLE LTE BANDS FOR THE OPTIMIZED ANTENNA

LTE Band Low (MHz) High (MHz)

7 2500 2690

12 699 746

13 746 787

14 758 798

17 704 746

38 2570 2620

41 2496 2690

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suitable vectors but only one of them includes the 30 degree as a flare angle. We select this vector whose second parameter is the desired scale factor.

IV. RESULTS Using EMCoS Antenna Virtual Lab simulation tool, the

geometry of the optimized antenna on the 50 mm X 50 mm ground plane is given in Fig.1. Antenna is fed by a coaxial cable with 50 ohm characteristic impedance. A good impedance matching is achieved for the considered sub-bands given in Table I. The condition to be able to have suitable impedance matching is given in (8).

11 10s dB� (8)

As it can be seen in Fig. 2, the S11 values of both LTE-700

and LTE-2600 bands are below the condition given in (8). Since the center frequency of the LTE-700 band is around 750 MHz, center frequency of the lower band of the designed antenna is optimized to 750 MHz. The same process is applied for the second band of the antenna by switching the frequency to 2600 MHz. Another important parameter which we emphasized in our previous work is the distance between the triangles [26]. In our design we kept this distance constant as 0.25 mm. Its dimension needs to be well configured especially for the upper bands. Other sizes are given in Fig.1. All dimensions in the figure are the unit of mm.

The radiated power spectrum of the designed antenna is given in Fig.3 assuming 1 V source voltage and 1 m distance from the antenna. In this figure dual band specifications can be observed clearly. In addition antenna patterns for �=90 and �=90 within the LTE-750 and LTE-2600 bands are given in Fig.4 and Fig.5 respectively.

Fig.1. The geometry of the optimized fractal antenna (dimensions in mm)

Fig.2. S11 magnitude of the optimized fractal antenna

Fig.3. The radiated power of the optimized fractal antenna

Fig.4. Antenna patterns for 750 MHz, �=90 (left) and �=90(right)

Fig.5. Antenna patterns for 2600 MHz, �=90 (left) and �=90(right)

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V. CONCLUSION An optimized Sierpinski gasket fractal LTE antenna for 7

different sub-bands (LTE-700 and LTE-2600) was designed and simulated. From the point of view of mathematical improvement a correction factor named copt was proposed to achieve the good impedance matching for all resonant bands. This different approach brings good frequency control ability especially for the first band of the Sierpinski gasket fractal antennas. Furthermore our design reaches 26.3% size reduction considering the antenna height compared to a standard quarter wave monopole antenna.

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