Ann. Telecommun. DOI 10.1007/s12243-013-0395-2

A modified PSO technique using heterogeneous boundary conditions for broadband compact microstrip antenna designing S. Kibria & M. T. Islam & B. Yatim & R. Azim

Received: 2 April 2013 / Accepted: 4 September 2013 # Institut Mines-Télécom and Springer-Verlag France 2013

Abstract A modified particle swarm optimization (PSO) variant is implemented on a conventionally optimized broadband antenna. Proposed algorithm uses heterogeneous boundary conditions to particles that fly out of the search space. Search space boundary conditions were chosen depending on which bound was violated. The algorithm is executed using MATLAB for the PSO computations and IE3D. Microstrip antennae inherently suffer from low bandwidth. Thus, a broadband patch antenna is optimized to improve the antenna return loss bandwidth in order to validate the proposed algorithm. For the patch antenna, a significant 12 % bandwidth improvement and 20.84 % size reduction was achieved. It was fabricated and satisfactory conformity was found with simulated results. Keywords PSO . Microstrip antenna . Boundary condition . Search space . Optimization

1 Introduction Particle swarm optimization (PSO) is a heuristic algorithm. It is modeled on the behavior of a swarm of bees in search of nectar in a garden. PSO fairs better in most benchmark problems and requires less calibration then genetic algorithms. It S. Kibria (*) : M. T. Islam : B. Yatim : R. Azim Institute of Space Science (ANGKASA), Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Malaysia e-mail: [email protected] M. T. Islam e-mail: [email protected] B. Yatim e-mail: [email protected] R. Azim e-mail: [email protected]

was first presented by the authors in [1]. Owing to its simple nature, it became a popular way to solve complex problems. In [2], a study of PSO on various benchmark functions and problems is presented along with techniques of handling particles flying out of the search space were illustrated. PSO inherently deals with finite search spaces. Infinite search space may be traversed using PSO in theory, but it is easily understandable that its performance will suffer significantly. It shows the “invisible wall” technique to be the best of the lot but fails to explain why. In this study, some basic assumptions were made about the “walls” and their influence on the optimization problem itself. Based on the wall axioms, a hybrid implementation was perceived. Basically, different walls were used on different sides of the boundary walls. It was named as heterogeneous boundary condition PSO or HBCPSO. Wireless communication is one of the booming industries across the world [3]. Rapidly evolving industries have dynamic challenges that include the requirement of higher bandwidth and gain from smaller antennae. Microstrip antennae have a low profile and are compact enough to be placed on mobile communication devices [4–6]. The compact nature of these antennae sparked a thorough study and their use with mobile devices came intuitively. These planar structures are easy to integrate with microwave circuits and allow easier mass production owing to their simplicity of fabrication. The conventionally optimized design had an operating bandwidth from approximately 3.1–18 GHz, covering WiMAX, UWB, C-band, WLAN, X-band, Ku-band, and ITU-band [7]. From the simulation results, it may be inferred that the Ku-band may not be retained after fabrication. Microstrip antennae suffer from some intrinsic drawbacks including narrow bandwidth. This factor aggravates further for smaller designs. Hence, a typical microstrip antenna design problem looks to increase bandwidth while looking to decrease the size. It may thus be inferred as an optimization problem. Several conventional electromagnetic computational

Ann. Telecommun.

techniques have been used to optimize the antenna design. However, conventional optimization technique is tedious [8]. This paper establishes a framework for optimizing the bandwidth of a patch antenna using HBCPSO and serves as a guideline to choose algorithm parameters based on particular design requirements. It automates the development and optimization process. This drastically decreases human interaction. It makes no assumptions about the antenna or its properties [9].

2 Particle swarm optimization

Fig. 1 Illustration of different types of walls

exploration occur as the behavior of the antenna subjected to dimension change is unknown. Hence, the search may benefit from either kind of exploration and this keeps one from dominating the other.

2.1 Analogy and terminology PSO was developed from the foraging behavior of bees in a garden looking for nectar and the analogy will be used in the paper for the sake of simplicity. PSO uses a population of particles, swarm of bees in our analogy, to represent candidate solutions. As the particles fly though the solution space, i.e., “the garden”, PSO updates the flight path using Eqs. (1) and (2). Search space for the algorithm needs to be finite. The update depends on three factors which are termed inertia, cognitive, and social. Inertia models the particles tendency to follow its current flight path. It is modeled by the first term in Eq. (1). Cognitive portion stores the particle’s best performance and its location. The cognitive influence drives the particle towards that very local best or personal best. This behavior is randomized by multiplying the term with a random variable. The randomness is introduced to mimic the behavior of foraging bees. The equations used to describe PSO are shown below:
viþ1 ¼ wvi þ c1 r1 ðd local best –d i Þ þ c2 r2 d global best –d i ð1Þ d iþ1 ¼ d i þ viþ1

ð2Þ

v i is the velocity of a particle at ith iteration; d i is the vector containing dimensions of a particle at ith iteration; r 1 and r 2 are the random values with uniform distribution between zero and unity; c 1, c 2, and w are the cognitive, social, and inertia coefficients, respectively. Equation (1) shows how the momentary velocity of each particle is modified and Eq. (2) shows how velocity is used to update the position of the bees. Now, the variables w, c 1, and c 2 are constants that determine the nature of the search. For instance, a large w hinders convergence [10]. Values for c 1 and c 2 should lie between 0 and 2. It is easy to see that their values determine the preference of the “bees” for local or global exploration. It determines which of the social or cognitive influence holds sway over the search. Choice of values for these constants is hotly debated and may be considered to be application specific. In antenna problems, values are chosen such that c 1 =c 2. This is done to ensure both kinds of

2.2 Heterogeneous boundary condition PSO PSO algorithm was reshaped for the problem in this paper into HBCPSO. Industry requirements push for larger operating frequencies and smaller sizes. The search space was hence designed such that overall dimensions of the antenna remain the same or decrease. Any solution presented by HBCPSO that violates that criterion was considered nonfeasible. Their performances were not evaluated and fitness was considered zero. This work deals with a maximization problem (maximum bandwidth achievable). The bandwidth has to be nonnegative. This is the invisible wall strategy as illustrated by Fig. 1. Particles fly out of the valid space as a part of the oscillating trajectory. This strategy of assigning a “bad” fitness for unfeasible solutions ensures that the particle will gravitate back into the search space as both local and global best exist inside the valid space. On the other hand, if a dimension becomes negative as allowed by Eqs. (1) and (2), it does not translate to physically meaningful antenna. Hence, another novel tactic is devised for this problem. The violating dimension is set to zero, making the design feasible. This is the absorbing wall strategy in [2]. Note the difference between the two approaches. Since the first iteration retains one antenna that was manually optimized, the global best fitness is positive and its position is within the valid search space at all times. These violation handling techniques ensure reduced computation and a more

W 1(Lp) LSUB h

4 6

5 Lf

2(Lg)

Wf

3 WSUB

Fig. 2 Antenna dimensions to be optimized showed with number

Ann. Telecommun. Fig. 3 Optimized (solid line), initial (dashed line); return loss profile of antenna before and after optimization

x - Cross-Pol _ - Co-Pol

thorough search for “better” antennae which are definitely smaller than the original design. Next comes the fitness function. As mentioned above, the invisible wall technique basically modifies the fitness function. It defines the fitness function for the region outside the wall as a constant which reflects a poor fitness. Equations (3a) and (3b) shows how the fitness function is defined within the valid region. The fitness function was simply equated to the negative 14 dB return loss bandwidth with only one penalty coefficient. Our design consideration is to keep the return loss below −10 dB in the bands of interest. Extra 4 dB is considered to improve impedance matching as lower return losses are always desirable. The −14 dB bandwidth by penalty coefficient ratio was considered the fitness function as shown in Eqs. (3a) and (3b). The fitness equation is as follows: Fitness ¼ bandwidth−14

dB =α

ð3aÞ

α ¼ f1 if lower edge < 3:15 GHz and 10 if lower edge≥ 3:15 GHz g

ð3bÞ d n ¼ ð1−arn Þd initial

ð4Þ

The population is usually generated randomly in most PSO variants including the classical variant. In this paper, a choice to deviate slightly was made but with incredible consequences. This study started with an antenna design that was

Table 1 Dimensions before and after optimization Dimension

Initial value (mm)

Optimized value (mm)

1 2 3 4 5 6

14.5 5.5 8.125 2.62 19.875 6.37

12.018 5.024 7.104 2.267 19.448 5.921

optimized using conventional means. A population of 80 antennae was generated from the original design by making random modifications to their dimensions as per the equations below. Higher populations result in better fitness and thorough search [10]. It does however also lead to higher number of fitness evaluations to get there. Also, in most cases including this paper, the updating of local and global best positions becomes less frequent. How this effects the search is not completely understood but intuitively it can be said that the effect is detrimental. In Eq. 4, d n is a column vector containing dimensions of the nth element, “a” is a constant between (0,1), and r n is a column vector of same size as d n and random elements between (−1,1). This is basically taking a leaf out of simulated annealing algorithm. These random modifications, or mutations, are limited to a maximum 20 % of the original antenna dimension. This corresponds to a =0.2 in Eq. 4. One antenna in the population is left unaltered from the original design as there is no sense in “reinventing the wheel.” Finally, the HBCPSO process applies a process of varying the acceleration coefficients, namely the inertia coefficient. Study show that decreasing inertia results in faster convergence [11]. The author of [11] shared various strategy for coefficient variation. This study uses a simple technique for the modification. Initially, w =0.9 is considered. After a nondefinite number of iterations when the performance of the antenna is deemed to have improved sufficiently, w is reduced to 0.2, hence allowing quick convergence. Allowing a final rapid convergence, rather than using a termination criterion, allows a final bout of local exploration around the best result. This ensures that local optima are reached. 2.3 Initial design and search space Broadband antennae are designed as compact and simple antennae that introduce low distortion with large. Figure 2 illustrates the configuration of the proposed antenna. It consists of a rectangular patch and a partial ground plane. The radiating patch, which has a compact size of W p ×L p , is

Ann. Telecommun. Fig. 4 Fabricated antenna front (left) and back (right) o - Initial _ - Optimized

printed on one side of a FR4 PCB substrate of 1.6 mm thickness. The FR4 substrates have a relative permittivity of 4.6 and loss tangent of 0.02. A microstrip feed line of width w f and length l f is printed on the same side of the FR4 substrate as the radiator. The partial ground plane with side length L g and width W g =W SUB is printed on the other side of the substrate. The lower edge of the 50-Ω microstrip feed line is attached to a SMA connector. The parameters of the conventionally optimized antenna are as follows: W SUB =29 mm, L SUB =20.5 mm, L g =5.5 mm, W g =29 mm, L p =14.5 mm, W p =13.5 mm, L f =6 mm, W f =2.75 mm, h =0.5 mm, dim6= 6.375 mm, dim4=2.62 mm. The parameters were broken down to new parameters as shown in Fig. 2. The reason for the different parameterization was to properly study the effect of the feed-line position with respect to the radiating and ground plains. The geometric parameters of the proposed antenna structure were adjusted to tune the return loss as well as the bandwidth over a wide range of frequencies. The rectangular patch is capable of supporting multiple resonant modes, hence providing a wider impedance bandwidth [12].

3 Discussion The return loss profile comparison is shown in Fig. 3. It shows a 12 % rise in the −10 dB bandwidth for the HBCPSO optimization over the conventionally optimized antenna. Here, we can see that the −14 dB bandwidth has increased significantly more than 12 %. For certain design considerations, including the one presented here, this may be seen as a fallacy of the algorithm. As mentioned before, this just ensures a greater likelihood than the bandwidth achieved in simulation

would still be below −10 dB once fabricated. In some rare cases, this might even result in the optimized design having a smaller −10 dB bandwidth that the original design. For this application, the −14 dB strategy is applicable. The rationale behind settling for a smaller −10 dB bandwidth from the algorithm is that the initial design, after fabrication is less likely to maintain its large −10 dB bandwidth. Figure 3 shows that the initial design has poor performance around 14 GHz. It is barely below the industry required −10 dB. Thus, we can use this band to validate our −14 dB strategy. Further, the region between 18 and 20 GHz is not covered by the initial design. The optimized design, using the precisely calibrated dimensions, has overcome both these problems of the initial design. The choice of wall type at the boundaries of the search space needs to be considered carefully. The absorbing wall ensures a thorough search along the wall. The invisible wall technique decreases computational complexity by decreasing the number of simulations that need to be run. Though this does not guarantee the finding of a smaller design, it does increase the likelihood of doing so. All the dimensions were reduced after optimization, as can be seen in Table 1, even the ones that do not cause the overall antenna dimensions to increase. The simulated results for the characteristic input impedance show that the optimized design has better matching to 50Ω over the spectrum under consideration. The optimization process succeeded in reducing the reactive impedance also. 3.1 Experimental validation The optimized antenna was fabricated for experimental verification as shown in Fig. 4. A SMA connector is soldered to

-- - Simulated _ - Measured

Fig. 5 Measured (solid line), simulated (dashed line); measured and simulated (HBCPSO optimized) return loss

Fig. 6 Copolarized (solid line) and cross-polarized (x line) Radiation pattern at 3.6 GHz

Ann. Telecommun. Fig. 7 Dim2=3.024 mm (green dotted line), Dim2=4.024 mm (orange dotted line), Dim2= 5.024 mm (solid black line), Dim2=6.024 mm (magenta dashed line); simulated parametric study on dimension 2. The optimized design clearly achieves highest −10 dB bandwidth

the feed-line and ground plane as illustrated in the figure. An Agilent E8362C vector network analyzer was employed to measure the input impedance characteristics. A 0.5–20 GHz anechoic chamber was used for the radiation pattern measurements [13]. Figure 5 shows good agreement between the HBCPSO optimized and measured results. The antenna’s measured impedance bandwidth extends from 3.05 to 20 GHz (147 %) for which its return-loss characteristic is better than −10 dB. Despite very compact size, the performance of the proposed antenna is sufficient to cover WiMAX, WLAN, UWB, C-band, X-band, and Ku band. The disparity between the measured and simulated results is attributed to manufacturing tolerance and imperfect soldering effect of the SMA connector. It also may be due to the effect of the feeding cable, which is used in measurements but not considered in simulation as the antenna is small. Figure 6 exhibits the measured 2D radiation patterns of the copolarized field and cross-polarized field in the two principle planes, namely E and H plane at different frequencies. As the frequency increases, higher-order current modes are excited and the radiation patterns become more directional with slight deformations. As illustrated in Fig. 6, the structure acts like an omnidirectional antenna at 3.6 GHz. The radiation pattern shows that the copolarized radiation pattern is significantly greater than cross-polarized radiation in the E-plane and has a nearly uniform strength in all directions. Thus, this antenna may be used for applications requiring omnidirectional radiation feature. Figure 7 shows the return loss profile of the optimized antenna when dimension 2 is varied. It can be seen clearly that the antenna design performance hinges significantly on this dimension. Further, it serves to prove that the optimized value is quite sensitive and caution had to be taken when fabricating. When dimension 2 is increased to 6.024 mm, the upper band suffered performance degradation. The return loss for dimension 2= 4.024 and dimension 2=3.024, the performance degrades from about 9 GHz onwards. Lower edge of the band was mostly unaffected by it, and may be assumed to be independent. According to theory, the lower band is dependent on L SUB, hence it is unaffected.

.. - dim2=3.024 .. - dim2=4.024 _ - dim2=5.024 -- - dim2=6.024

4 Conclusion PSO is quite simple and versatile tool for antenna design and optimization. HBCPSO, though a bit more complicated than PSO itself, has a more organic nature when applied to realworld problems. This study illustrates how conceptual design considerations can be incorporated into a HBCPSO algorithm. When compared to conventional optimization, which would warrant manually redesigning and analyzing multiple antennae, HBCPSO is far less tedious. It needs only recalibration for new antennae and its dimensions. The cost of processing power is ever decreasing. Hence, HBCPSO may be used in better and bolder ways to optimize antenna design in the future. This paper showed the design process of starting out with an antenna design and modifying it to our desired goals. The bandwidth was increased significantly along with slight improvement in omnidirectionality. Application-specific antennae can be designed from a generic initial design.

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