# Design of a Novel UWB Omnidirectional Antenna Using Particle Swarm Optimization

Authors: Chengyang Yu; Tanghong Xu; Changjun Liu
Journal: International Journal of Antennas and Propagation
 (2015)

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## Abstract

A UWB E-plane omnidirectional microwave antenna is designed and fabricated for IEEE 802.11a communication system and microwave magnetron source system as a radiation monitor. A cooptimization method based on particle swarm optimization (PSO) algorithm and FDTD software is presented. The presented PSO algorithm is useful in many industrial microwave applications, such as microwave magnetron design and other techniques with a high power level. The maximum measured relative bandwidth of 65% is achieved for the proposed antenna after a rapid and efficient optimization. Furthermore, the measured antenna polarization purity reaches about 20 dB at the communication C band. The PSO algorithm is a powerful candidate for microwave passive component design.


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## Body

## 1. Introduction

Omnidirectional antennas are widely used in wireless communication systems, especially for high-multipath communication applications based on polarization diversity technique. A typical polarization diversity system is composed of two orthogonally polarized antennas, such as a vertically polarized monopole and a horizontally polarized Alford loop antenna. As an H-plane omnidirectional antenna, monopole has been widely researched. However, in such a situation, E-plane omnidirectional antennas are also needed to investigate. Alford loop antenna, which is suitable at low frequencies with the wire type, was firstly reported in [1]. Several improved antennas based on Alford structure were also investigated to generate E-plane omnidirectional radiation patterns [2–5]. In [3], a dual-frequency Alford structure loop antenna is realized with eight T-dipoles. However, broadband omnidirectional antennas are urgently needed for modern communication systems [6, 7].In this paper, an ultrawideband (UWB) characteristic is realized on the Alford structure loop antenna with E-plane omnidirectionality. Such an antenna will be used as a radiation monitor at an actual microwave magnetron source system. Particle swarm optimization (PSO) algorithm is introduced to optimize the whole structure. The proposed antenna can be easily realized on a planar substrate while it has a far-field radiation pattern similar to that of a magnetic dipole. In addition, the optimized omnidirectional antenna has a measured impedance bandwidth from 4.6 to 9.0 GHz (relative bandwidth is about 65%), which covers the entire 5 GHz bandwidth of IEEE 802.11a (5.15 GHz–5.35 GHz and 5.725–5.875 GHz).


## 2. Antenna Design

### 2.1. Antenna Structure

The configuration of the proposed UWB omnidirectional antenna is shown in Figure1. It mainly consists of three identical pairs of printed half-wave dipole radiators. Each pair includes two dipoles which work together to generate a broadband characteristic. It is the distributed microstrip dipoles and the power combining structure that generate an omnidirectional feature for the antenna. The lengths of the two dipole radiators are 2R1×θ1 and 2R2×θ2, respectively. Combining with double-sided strip lines, two parts of a dipole radiator are fabricated on the opposite sides of one substrate. So the proposed dipole structure is equivalent to the conventional dipole. In order to form an omnidirectional radiation, according to the theory of antenna array, the excitation phase of each dipole pair should be equal. The three dipole pairs are directly fed by microstrips, while the common ground plane of microstrips is a circular patch with a constant radius Rg. The center of the ring structure is soldered with an SMA connector. It is obvious that all the dipole pairs are fed with not only an equal excitation phase, but also an equal excitation amplitude.Figure 1
The structure of the microwave antenna: (a) top plane, (b) bottom plane, and (c) side view.


### 2.2. Antenna Optimization and Fitness Function

Based on the proposed structure, the final goal of our work is to obtain a planar antenna with omnidirectional radiation and low return loss over WLAN operation in the 5 GHz bands. However, due to the narrow impedance bandwidth of conventional dipole, massive optimizations on radiators and connection structures among them are needed. In order to improve optimization accuracy and velocity, a cooptimization method based on PSO and FDTD simulator is introduced in this paper. The PSO algorithm and cooptimization processes will be detailed later.The omnidirectional antenna is realized on a F4B substrate with a dielectric constant of 2.65 and thickness of 1 mm. The specific optimized parameters of the proposed antenna, as shown in Figure1, are listed in Table 1. Parameters “a” and “b” are selected to match the restricted condition among kinds of radiuses of the antenna structure.Table 1
Range setup of optimized parameters.
Parameters
W
1
W
2
W
θ
1
θ
2
a
b
R
2
R
1
R
R
g
Optimization range
0.1 mm–4 mm
π/18–π/3
0.1 mm–2 mm
0.1 mm–6 mm
8 mm–14 mm
R
2
+
b
R
1
+
a
6 mm
Restricted condition
—
—
—
—
—
—
—
R
2
<
R
1
<
R
ConstantAccording to design targets of the proposed antenna, especially used on the entire 5 GHz bandwidth of IEEE 802.11a, the fitness function can be defined as(1)Fitness=0.5×BW+A+B,where BW indicates the desired antenna impedance bandwidth expressed in terms of upper frequency fU and lower frequency fL. The upper and lower frequencies are the boundary points of antenna bandwidth with dB(S11)<-10 dB. A and B represent the weight factor of reflection coefficient to optimize on the antenna at 5.2 GHz and 5.8 GHz, respectively. These factors can be expressed by(2)BW=fU-fL1GHz,fU>6GHz,fL<5GHz0,others,A=1,dBS11f=5.2GHz≤-10dB0,dBS11f=5.2GHz>-10dB,B=1,dBS11f=5.8GHz≤-10dB0,dBS11f=5.8GHz>-10dB.


### 2.3. PSO Algorithm and Cooptimization with FDTD Software

As an evolutionary computation technique based on the movement and intelligence of particle swarm, PSO is presented by Kennedy et al. [8]. Each particle in the swarm represents a possible solution to the specific optimization event. There are M particles to search an N dimensions solution space, respectively. So the velocity, position, and the personal best position are expressed by M×N matrixes. The position of particle i at a fixed iteration T is usually expressed as a vector Xi(T)=[Xi,1T,Xi,2(T),…,Xi,N(T)], where i satisfies 1≤i≤M. This particle adjusts its position with velocity Vi(T)=[Vi,1(T),Vi,2(T),…,Vi,N(T)] through the solution space. According to the fitness function calculation, the personal best particle and global best particle are involved in Pi=[Pi,1,Pi,2,…,Pi,N] and Gbest=[G1,G2,…,GN].Clerc and Kennedy have introduced a constriction factor [9], K, which is used to constrain and control velocities for PSO. In [10], Eberhart and Shi concluded that the PSO using a constriction factor K is the best approach while limiting the maximum velocity Vmax⁡ to the dynamic range of variable Xmax⁡ on each dimension compared with performance using an inertia weight. The velocity function of PSO used in this paper is(3)Vi,jT+1=K×Vi,jT+ϕ1rand×Pi,jT-Xi,jT+ϕ2rand×GjT-Xi,jT,where the constriction factor K is computed as(4)K=22-ϕ-ϕ2-4ϕϕ=ϕ1+ϕ2>4.We tested different groups of the cognitive and social component values of the PSO (ϕ1 and ϕ2) with Griewank function and Sphere function. The standard value settings in [10] (ϕ1=ϕ2=2.05) and those in [11] (ϕ1=2.8 and ϕ2=1.3) result in a better optimization accuracy and a better convergence rate, respectively. In this paper, aiming at a compromise on performances, improved cognitive and social component values are used for the PSO. Cognitive and social rates vary from 2.8 to 2.05 and from 1.3 to 2.05, synchronously. The variation is linear to iteration times. Tested results show that the proposed settings of (ϕ1 = 2.8~2.05 and ϕ2 = 1.3~2.05) result in the best performance on optimization accuracy and a good convergence rate for PSO.Reflecting boundary condition [12] is used to limit the particle velocity and position when it hits the boundary in one of the dimensions. The particle velocity and position beyond the boundary can be expressed by(5)Vi,jT+1=-mjVi,jT,(6)Xi,jT+1=Xi,jT+Vi,jT+1,where mj is determined by the distance d from particle position to the boundary:(7)mj=dXjmax⁡-Xjmin⁡,d≤Xjmax⁡-Xjmin⁡Xjmax⁡-Xjmin⁡dd>Xjmax⁡-Xjmin⁡.The steps of cooptimization with the proposed PSO and FDTD software (CST) are described in Figure2.Figure 2
Flow chart of the proposed antenna cooptimization method.Step 1.
Determine the antenna variables and ranges to be optimized. Randomly initializeM particles with velocity Vi and position Xi in the solution space.Step 2.
Write the variables into a.txt file at fixed position. Invoke the file and CST software automatically by using VBA (a macro language of Visual Basic). Use the simulatedS-parameters to calculate the fitness of each particle according to (1). Record the personal particles and global best particle according to the fitness function value.Step 3.
Update the velocity and position of each particle according to (3) and (6).Step 4.
Calculate the fitness of each particle again. Update the personal particles.Step 5.
Read the personal best particle. If its corresponding fitness function value is better than that of global best particle, update the record of the global best particle.Step 6.
Repeat Steps3, 4, and 5, until the maximum iteration number is reached.


## 2.1. Antenna Structure

The configuration of the proposed UWB omnidirectional antenna is shown in Figure1. It mainly consists of three identical pairs of printed half-wave dipole radiators. Each pair includes two dipoles which work together to generate a broadband characteristic. It is the distributed microstrip dipoles and the power combining structure that generate an omnidirectional feature for the antenna. The lengths of the two dipole radiators are 2R1×θ1 and 2R2×θ2, respectively. Combining with double-sided strip lines, two parts of a dipole radiator are fabricated on the opposite sides of one substrate. So the proposed dipole structure is equivalent to the conventional dipole. In order to form an omnidirectional radiation, according to the theory of antenna array, the excitation phase of each dipole pair should be equal. The three dipole pairs are directly fed by microstrips, while the common ground plane of microstrips is a circular patch with a constant radius Rg. The center of the ring structure is soldered with an SMA connector. It is obvious that all the dipole pairs are fed with not only an equal excitation phase, but also an equal excitation amplitude.Figure 1
The structure of the microwave antenna: (a) top plane, (b) bottom plane, and (c) side view.


## 2.2. Antenna Optimization and Fitness Function

Based on the proposed structure, the final goal of our work is to obtain a planar antenna with omnidirectional radiation and low return loss over WLAN operation in the 5 GHz bands. However, due to the narrow impedance bandwidth of conventional dipole, massive optimizations on radiators and connection structures among them are needed. In order to improve optimization accuracy and velocity, a cooptimization method based on PSO and FDTD simulator is introduced in this paper. The PSO algorithm and cooptimization processes will be detailed later.The omnidirectional antenna is realized on a F4B substrate with a dielectric constant of 2.65 and thickness of 1 mm. The specific optimized parameters of the proposed antenna, as shown in Figure1, are listed in Table 1. Parameters “a” and “b” are selected to match the restricted condition among kinds of radiuses of the antenna structure.Table 1
Range setup of optimized parameters.
Parameters
W
1
W
2
W
θ
1
θ
2
a
b
R
2
R
1
R
R
g
Optimization range
0.1 mm–4 mm
π/18–π/3
0.1 mm–2 mm
0.1 mm–6 mm
8 mm–14 mm
R
2
+
b
R
1
+
a
6 mm
Restricted condition
—
—
—
—
—
—
—
R
2
<
R
1
<
R
ConstantAccording to design targets of the proposed antenna, especially used on the entire 5 GHz bandwidth of IEEE 802.11a, the fitness function can be defined as(1)Fitness=0.5×BW+A+B,where BW indicates the desired antenna impedance bandwidth expressed in terms of upper frequency fU and lower frequency fL. The upper and lower frequencies are the boundary points of antenna bandwidth with dB(S11)<-10 dB. A and B represent the weight factor of reflection coefficient to optimize on the antenna at 5.2 GHz and 5.8 GHz, respectively. These factors can be expressed by(2)BW=fU-fL1GHz,fU>6GHz,fL<5GHz0,others,A=1,dBS11f=5.2GHz≤-10dB0,dBS11f=5.2GHz>-10dB,B=1,dBS11f=5.8GHz≤-10dB0,dBS11f=5.8GHz>-10dB.


## 2.3. PSO Algorithm and Cooptimization with FDTD Software

As an evolutionary computation technique based on the movement and intelligence of particle swarm, PSO is presented by Kennedy et al. [8]. Each particle in the swarm represents a possible solution to the specific optimization event. There are M particles to search an N dimensions solution space, respectively. So the velocity, position, and the personal best position are expressed by M×N matrixes. The position of particle i at a fixed iteration T is usually expressed as a vector Xi(T)=[Xi,1T,Xi,2(T),…,Xi,N(T)], where i satisfies 1≤i≤M. This particle adjusts its position with velocity Vi(T)=[Vi,1(T),Vi,2(T),…,Vi,N(T)] through the solution space. According to the fitness function calculation, the personal best particle and global best particle are involved in Pi=[Pi,1,Pi,2,…,Pi,N] and Gbest=[G1,G2,…,GN].Clerc and Kennedy have introduced a constriction factor [9], K, which is used to constrain and control velocities for PSO. In [10], Eberhart and Shi concluded that the PSO using a constriction factor K is the best approach while limiting the maximum velocity Vmax⁡ to the dynamic range of variable Xmax⁡ on each dimension compared with performance using an inertia weight. The velocity function of PSO used in this paper is(3)Vi,jT+1=K×Vi,jT+ϕ1rand×Pi,jT-Xi,jT+ϕ2rand×GjT-Xi,jT,where the constriction factor K is computed as(4)K=22-ϕ-ϕ2-4ϕϕ=ϕ1+ϕ2>4.We tested different groups of the cognitive and social component values of the PSO (ϕ1 and ϕ2) with Griewank function and Sphere function. The standard value settings in [10] (ϕ1=ϕ2=2.05) and those in [11] (ϕ1=2.8 and ϕ2=1.3) result in a better optimization accuracy and a better convergence rate, respectively. In this paper, aiming at a compromise on performances, improved cognitive and social component values are used for the PSO. Cognitive and social rates vary from 2.8 to 2.05 and from 1.3 to 2.05, synchronously. The variation is linear to iteration times. Tested results show that the proposed settings of (ϕ1 = 2.8~2.05 and ϕ2 = 1.3~2.05) result in the best performance on optimization accuracy and a good convergence rate for PSO.Reflecting boundary condition [12] is used to limit the particle velocity and position when it hits the boundary in one of the dimensions. The particle velocity and position beyond the boundary can be expressed by(5)Vi,jT+1=-mjVi,jT,(6)Xi,jT+1=Xi,jT+Vi,jT+1,where mj is determined by the distance d from particle position to the boundary:(7)mj=dXjmax⁡-Xjmin⁡,d≤Xjmax⁡-Xjmin⁡Xjmax⁡-Xjmin⁡dd>Xjmax⁡-Xjmin⁡.The steps of cooptimization with the proposed PSO and FDTD software (CST) are described in Figure2.Figure 2
Flow chart of the proposed antenna cooptimization method.Step 1.
Determine the antenna variables and ranges to be optimized. Randomly initializeM particles with velocity Vi and position Xi in the solution space.Step 2.
Write the variables into a.txt file at fixed position. Invoke the file and CST software automatically by using VBA (a macro language of Visual Basic). Use the simulatedS-parameters to calculate the fitness of each particle according to (1). Record the personal particles and global best particle according to the fitness function value.Step 3.
Update the velocity and position of each particle according to (3) and (6).Step 4.
Calculate the fitness of each particle again. Update the personal particles.Step 5.
Read the personal best particle. If its corresponding fitness function value is better than that of global best particle, update the record of the global best particle.Step 6.
Repeat Steps3, 4, and 5, until the maximum iteration number is reached.


## 3. Fabrication and Measurements

The omnidirectional antenna mentioned above is optimized with the proposed optimization method based on PSO and FDTD software. The operation frequency of this antenna is the entire 5 GHz wideband of IEEE 802.11a, especially for frequency bands of 5.2 GHz and 5.8 GHz. For obtaining a fine UWB characteristic, 20 particles and 150 iteration times are employed. The final optimized geometric parameters area=0.88 mm, b=3.90 mm, R2=9.65 mm, θ1=0.30, θ2=0.74, W=0.30 mm, W1=2.39 mm, and W2=1.75 mm. Figure 3 shows the fabricated UWB omnidirectional antenna. The diameter of this antenna is 36 mm.Figure 3
The fabricated UWB omnidirectional microwave antenna (top view and bottom view).The reflection coefficient was measured using an Agilent N5230A vector network analyzer. As shown in Figure4, the simulated results matched well with the measured results. This indicates that the cooptimization method based on PSO and FDTD software is effective for antenna design. Furthermore, the improved Alford structure antenna, without any additional matching circuits, definitely has an UWB characteristic from 4.6 GHz to 9.0 GHz.Figure 4
Simulated and measured results of reflection coefficient.The radiation patterns of the proposed antenna are measured and simulated at 4.8 GHz, 5.2 GHz, 5.8 GHz, and 6.5 GHz. Figure5 shows the comparison of simulated and measured patterns which include the coplanar polarization (E and H) and cross polarization (Ex and Hx) of the antenna. It is obvious that the proposed antenna has an excellent omnidirectional radiation in the entire 5 GHz band of IEEE 802.11a. The measured polarization purity in the E-plane reaches about 20 dB. The data differences between measured and simulated polarization purity parameters are mainly caused by the noise background of power receiver in the antenna measurement system. However, 20 dB polarization purity is good enough to be an E-plane omnidirectional antenna of polarization diversity system.Figure 5
Simulated and measured microwave radiation patterns at (a) 4.8 GHz, (b) 5.2 GHz, (c) 5.8 GHz, and (d) 6.5 GHz.
(a)
At 4.8 GHz
(b)
At 5.2 GHz
(c)
At 5.8 GHz
(d)
At 6.5 GHzThe simulated and measured antenna gains are shown in Figure6. The maximum measured antenna gains are 1.3 and 1.0 dBi at 5.2 and 5.8 GHz, respectively.Figure 6
Simulated and measured results of the microwave antenna gain.


## 4. Conclusion

A novel UWB E-plane omnidirectional antenna has been proposed for polarization diversity of IEEE 802.11a communication system and some industrial applications. Power combining construction with three microstrip dipoles is investigated to form the omnidirectional radiation feature. The PSO algorithm is a powerful candidate for the design and optimization on the proposed UWB antenna. The measured results show that the antenna has a relative bandwidth of 65% (4.6 to 9.0 GHz). The good measured omnidirectional radiation feature in the 5 GHz band enables the antenna to operate at IEEE 802.11a system and monitor the radiation level in microwave magnetron source effectively. Furthermore, it is experimentally demonstrated that the proposed E-plane omnidirectional antenna is suitable for realizing polarization diversity technique associated with an H-plane omnidirectional antenna.



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*Source: 303195-2015-04-07.xml*