Current mobile communication users prefer multi-band portable devices that can access various wireless network services. This accessibility is enabled by the multi-band antenna. The structure usually becomes larger to create multiple resonances and acquire several bands. A mobile device should be small and light, and the multi-band in one compact antenna is preferred.
Creating many bands in a small antenna involves a complex layout with numerous geometrical parameters. With this layout, design optimization requires numerous iterations before the target value is reached. Therefore, an efficient optimization process with a reduced number of design parameters must be developed.
In this study, we investigate the characteristics of the antenna through current distribution to find dominant design parameters. Then, we use the Taguchi method to identify the critical parameters. Adaptive particle swarm optimization (APSO), which has faster convergence than particle swarm optimization (PSO), is adopted to optimize the antenna design with only the critical parameters. This method allows rapid computation.
To validate the proposed scheme, we apply it to a planar-type multi-band antenna that is small enough to fit the USB dongle. The necessary geometrical parameters from the complicated structure are considered in the APSO to optimize the antenna. The APSO is compared with the other algorithm. An optimized antenna is fabricated to confirm the results of full-wave simulation. Results show that the antenna produces two target bands that range from 2.3GHz to 2.7GHz and from 5.1 GHz to 5.9 GHz.
2. Steps to Reduce the Number of Design Parameters
The following are the steps to select the critical parameters:
1) After the surface current on the structure is observed and the resonance characteristics are analyzed, dominant parameters are selected using the Taguchi method.2) A suitable orthogonal array is selected to save experimental efforts. Applying the Taguchi method, we conduct a sensitivity analysis on the design parameters and estimate the effect of each parameter on the performance. Based on the result, only the critical parameters are selected.3) Defining the objective function and setting the constraint, we perform an optimization process with the selected parameters. An appropriate antenna is designed through this process.
To verify the proposed procedure, we apply it to a planar-type antenna with a complicated structure. The reference antenna has a compact multi-band characteristic for USB dongle application, and its structure is shown in Fig. 1. The antenna, which is 10 × 50 × 1 mm3 in size, uses the FR-4 substrate. By coupling a loop and spiral patch, the antenna has a dual-band characteristic from 2.3 GHz to 2.7 GHz and from 5.1 GHz to 5.9 GHz. The antenna is suitable for use as a compact, multi-band USB dongle antenna capable of accessing various wireless network services that cover WiBro (2.3-2.4 GHz), Bluetooth (2.4-2.484 GHz), WiMAX (2.5-2.7 GHz), satellite DMB (2.605-2.655 GHz), and 802.11 b/g/n WLAN (2.4-2.485 GHz and 5.15-5.825 GHz) .
Fig. 1.Structure of the reference antenna
However, the antenna has 20 design parameters, which cause an excessive computational burden to reach an acceptable performance, and 300 iterations are required. The overall process takes long to finish because one iteration requires many evaluations. We apply the proposed procedure to the antenna design and analyze the results to solve this problem.
2.1.1 Electromagnetic field simulation
The initial structure of the antenna is a loop-coupled spiral patch similar to that of the reference antenna, but has no slit to reduce the number of design parameters. Fig. 2 shows the 18 design parameters of the antenna.
Fig. 2.Initial structure of the antenna for USB dongle
Through an electromagnetic field simulation based on the finite element method, the surface current is obtained and the resonance effect is analyzed by observing the surface current. The surface current at 2.5 and 5.5 GHz is plotted in Fig. 3.
Fig. 3.Current distribution: (a) 2.5 GHz; (b) 5.5 GHz
The spiral has a low resonant frequency of 2.5 GHz, whereas the loop has a high resonant frequency of 5.5 GHz. Considering that the current on the strip line near the feed point is strong, we can choose line widths W3 and W4 as the dominant parameters. In addition, the current near the edge is strong, which shows that the coupling between the strip lines significantly affects the performance.
2.1.2 Sensitivity analysis
The sensitivity analysis of the design parameters is conducted by the Taguchi method. As the main parameters, line widths W3 and W4 are considered as the noise parameters in the Taguchi method. Sixteen test parameters are set as control factors. Basing on the settings considered in Table 1, we select orthogonal array L36 (29 × 37) for the control factors.
Table 1.Control and noise parameters selected for sensitivity analysis
A 4 × 36 matrix is set up for the numerical experiments, where the parameters are assumed to be mutually independent. The performance for each 4 × 36 = 144 combination of the control and noise factors is calculated by
where Ni is the number of sampling points, S11( f ) means the return loss at a sampling frequency f, and the target return loss is defined as 10dB Sobj = −10dB at band1 (2.3–2.7 GHz) and band2 (5.1–5.9 GHz). For the smaller-the-better characteristics case, which resembles performance minimization, the SN ratio is calculated by 
where MSD is the mean squared deviation from the performance, n is the total experimental number, and yi is the performance of the i th experiment.
The SN ratios are computed to evaluate the effects of the seven parameters and determine the relative importance of each design parameter . Table 2 shows the average SN ratios for all levels of parameters.
Table 2.Average SN ratios for all levels of parameters
Based on these results, the sum of squares resulting from control factor (SSF) is computed to evaluate the effects. SSF can be calculated by 
Table 3 and Fig. 4 show the calculated results for the SSF and effects of all parameters.
Table 3.SSF and effect for all parameters
Fig. 4.Effects for all levels of parameters
Based on sensitivity analysis, the smallest number of design parameters is obtained as W3, W4, G2, G4, and G6. We use the uniform line width for each band and redefine the parameter to apply the optimization as shown in Fig. 5.
Fig. 5.Structure of the antenna with the fewest parameters
2.1.3 Optimization algorithm
In this paper, the antenna with a reduced number of design parameters is applied to the APSO. The APSO is an improved version of the PSO in terms of fast convergence. It uses a simple mechanism that mimics swarm behavior in bird flocking and fish schooling to guide the particles to search for global optimal solutions. Given its easy implementation, the APSO has rapidly progressed in recent years and has been employed in many successful applications to solve optimization problems .
Its basic algorithm is the same as that of the PSO, but it has a four-evolutionary-state estimation procedure, including exploration, exploitation, convergence, and jumping out in each generation. Based on these states, acceleration coefficients c1 and c2 are controlled, and the APSO updates the particle velocity for fast convergence. Fig. 6 presents the APSO flow chart .
Fig. 6.Flow chart of the APSO
In this paper, the APSO is compared with the genetic algorithm (GA), which is the evolutionary algorithm to show the fast convergence rate. The GA is a search algorithm based on the mechanism of natural evolution. To solve optimization problems, the GA maintains a population of individuals and probabilistically modifies the population by some genetic operators, such as selection, crossover, and mutation . To evaluate the objective function, a gene is decoded by the following formula :
where is the binary representation of parameter X. Xmin, Xmax are the minimum and maximum of the parameter, respectively, and NX is the number of bits that determines the degree of resolution in its representation. The GA flow chart is shown in Fig. 7 .
Fig. 7.Flow chart of the GA
The APSO and GA are developed using the visual basic for applications in Excel and then linked with the script interface of analysis program to optimize the antenna for comparison. The initial antenna structure with five design parameters is applied to the APSO and GA. The objective function is defined as
where N1 and N2 are the numbers of sampling points, S11( f ) means the return loss at a sampling frequency f, and the target return loss value is Sobj = −10 dB. We set the forcing region 1 from f1 = 2.3 GHz to f2 = 2.7 GHz and the forcing region 2 from f3 = 5.1 GHz to f4 = 5.9 GHz.
The APSO has five particles, and the GA has five individuals. Under the same initial conditions, the result of the optimal design is shown in Fig. 8.
Table 4.Initial and optimal design parameters
Fig. 8.Simulated results of return loss and radiation pattern
After the optimization, the return loss below −10 dB is satisfied in band1 and band2. According to the radiated patterns, the peak gains of the reference, GA, and APSO are 2.26, 2.24, and 2.18 dB at 2.5 GHz, respectively, and 3.16, 3.2, and 3.27 dB at 5.5 GHz, respectively. This result means that the proposed scheme that uses only a small number of parameters produces frequency responses that are almost the same as those of the reference.
The optimization algorithms are conducted iteratively until the objective function converges to zero. Although the APSO and GA achieve similar results that meet the objective, the APSO with the convergence from the 9th iteration is superior to the GA with the slower convergence from the 75th (Fig. 9).
Fig. 9.Convergence rate of optimal design
2.1.4 Measured results
The antenna designed by the proposed scheme with the reduced number of parameters is fabricated as follows. Its return loss and far-field patterns are measured and compared with those of the reference in Fig. 11.
Fig. 10.Photograph of the fabricated antenna
Fig. 11.Measured results of return loss and radiation pattern
The frequency responses of the proposed and reference antennas are in good agreement. The slight discrepancy may be attributed to the attached cable and fabrication error.
This paper presents an optimization process with a reduced number of parameters and APSO for faster convergence. This process is applied to the design of a planar-type antenna for validity check. The Taguchi method is adopted to use fewer parameters and find the critical geometrical parameters based on the sensitivity analysis. The selected parameters enter the APSO with faster convergence rate than the GA. The optimization of a dual-band dongle antenna as a complicated structure can also be accelerated through this process. The target performance is achieved with the reduced number of parameters, such as the dual bands from 2.3 GHz to 2.7 GHz and from 5.1 GHz to 5.9 GHz.