The Design of Pixelated SIW Horn Antennas With Nearly Equal Beamwidths Using Binary Ink Stamp Optimization

Received August 12, 2021, accepted August 26, 2021, date of publication August 31, 2021, date of current version September 10, 2021. Digital Object Identifier 10.1109/ACCESS.2021.3109522 The Design of Pixelated SIW Horn Antennas With Nearly Equal Beamwidths Using Binary Ink Stamp Optimization JAROSLAV ZECHMEISTER , (Graduate Student Member, IEEE), JAROSLAV LACIK , (Member, IEEE), AND PETR KADLEC , (Member, IEEE) Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 616 00 Brno, Czech Republic Corresponding authors: Jaroslav Zechmeister (jaroslav[email protected]) and Jaroslav Lacik ([email protected]) This work was supported in part by the Internal Grant Agency of Brno University of Technology under Project FEKT-S-20-6526, and in part by Czech Science Foundation under Grant 19-06049S. ABSTRACT In this paper, linearly and circularly polarized single-layer Substrate Integrated Waveguide (SIW) horn antennas with nearly equal half power beamwidths in principal planes for the 24 GHz ISM band are designed. The uniqueness of the solution lies in the application of a pixelated structure to the design of these SIW horn antennas. For the design, a novel heuristic algorithm called Binary Ink Stamp Optimization is proposed. At first, the ability of the proposed algorithm is proved over fifteen benchmark functions and compared with the results of six state-of-the-art optimization algorithms. Then, the novel algorithm is exploited for the design of the pixelated part of the antennas. The antennas are manufactured using low-cost 3D printing technology. The experimental results prove that the linearly polarized antenna has a reflection coefficient below −18 dB in the whole 24 GHz ISM band. At the center frequency of this band, the antenna gain is 14.2 dBi, and the level of side lobes is below −15 dB in E and H-planes. In addition, E and H-plane half power beamwidths are 26.5◦and 25◦, respectively. The circularly polarized antenna radiates a right-hand circularly polarized (RHCP) wave, the reflection coefficient, and axial ratio are below −12 dB and 3 dB in the whole 24 GHz ISM band, respectively. At the center frequency of this band, the antenna gain is 8.9 dBi and the level of side lobes is below −7.4 dB in both principal planes. Further, the half power beamwidths in principal planes are 30.6◦and 33.4◦, respectively. INDEX TERMS Substrate integrated waveguide (SIW), SIW horn antenna, pixelated antenna, discrete evolutionary algorithm, binary optimization. I. INTRODUCTION Horn antennas are widely used in wireless applications due to their simple structure, high gain and efficiency, and wide bandwidth. However, since they are based on conventional waveguides, horn antennas suffer from large volume and weight, and high fabrication costs. Promising alternatives are Substrate Integrated Waveguide (SIW) horn antennas. They are electrically similar to conventional horn antennas based on the rectangular waveguide. However, they can be easily integrated with planar circuits and can be fabricated by a lowcost print circuit board process. Unfortunately, SIW horn antennas have narrow bandwidth, high levels of side and back radiation lobes, and primarily The associate editor coordinating the review of this manuscript and approving it for publication was Ladislau Matekovits . unequal radiation patterns in the E and H-plane. Several techniques can be exploited for the performance enhancement of SIW horn antennas. A higher gain and narrower beamwidth can be achieved by adding a dielectric load in front of the antenna aperture [1]. Further, a higher gain can also be achieved by adjusting the shape of the dielectric load, or by perforating the load [2], [3]. Printed metal parallel plates [4] or periodical transitions [5] on top and bottom of the load are also feasible approaches to the gain enhancement of SIW horn antennas. Although these approaches improve the radiation properties of SIW horn antennas, these antennas still provide unequal half power beamwidths (HPBW) in E and H-plane. SIW horn antennas with almost equal E and H-plane beamwidths were presented in [6] and [7]. However, the difference between both beamwidths is still more than 30%. Horn antennas based on SIW technology with equal 122216 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 9, 2021 J. Zechmeister et al.: Design of Pixelated SIW Horn Antennas With Nearly Equal Beamwidths Using BISO beamwidths in E and H-plane were presented in [8] and [9]. Unfortunately, these structures are multi-layered, therefore the main benefits of single-layered SIW horn antennas, such as ease of manufacturing and a low profile, are devalued. Circular polarization (CP) provides several advantages compared to linear polarization. CP antennas are an important technology for satellite and mobile communications, navigation systems, etc. The main advantage of CP lies in its immunity to multi-path interferences and polarization mismatch [10]. CP SIW horn antennas are mainly composed of two or more antenna elements to obtain orthogonal modes [11]–[14]. In [15] an inhomogeneous polarizer is placed in front of the antenna aperture to achieve CP. An antipodal tapered structure is presented in [16]. It describes an effective approach to designing a CP SIW horn antenna. The goal of this paper is to describe the design of linearly and circularly polarized single-layer SIW horn antennas with equal HPBW in main orthogonal radiation planes. A pixelated approach is applied to achieve desired performance. Pixelated structures provide high variability of the final shape [17]–[19]. In general, the pixelization design technique requires no a priori defined antenna template. Therefore, this approach may lead to unconventional solutions for load shapes. However, with an increasing number of pixels, the complexity of the optimization problem grows exponentially. Therefore, an efficient optimization procedure has to be adopted. Pixelated patterns are exploited in antenna applications mostly to increase bandwidth or decrease antenna dimensions. The Genetic Algorithm (GA) is used in the majority of available studies as an optimization tool. The GA updates a binary vector using selection, crossover, and mutation procedures. During the optimization process, each bit has equal significance. However, in real-world applications of binary patterns, some pixels can have a bigger influence on the structure properties. Due to this fact, we propose an evolutionary optimization algorithm named Binary Ink Stamp Optimization, reflecting the significance of the bits during the optimization process. That is the key benefit compared to the rest of the algorithms in terms of binary pattern optimization. II. BINARY INK STAMP OPTIMIZATION A. ALGORITHM DESCRIPTION Binary Ink Stamp Optimization (BISO) is a heuristic optimization algorithm for binary problems. BISO is inspired by stamps with different ink saturation. A set of stamps corresponds to a set of so far best individuals. Their ink saturation is determined by their fitness values. The next generation is determined based on a probability matrix, which can be imagined as an imprint of all stamps over each other. At darker positions, there is a higher probability of generating ‘‘1’’. On the contrary, ‘‘0’’ will be generated more often at brighter positions. General steps of BISO are depicted in the flow chart in Fig. 1. The following parameters are set at the start of the optimization run: FIGURE 1. Flow chart of the binary ink stamp optimization algorithm. •Npop – number of individuals in each iteration, •Nelit – number of selected elitist individuals, •Niter – maximal number of iterations, •probMin – the minimal probability of generating ‘‘1’’ in the next iteration, •probMinRST – the minimal probability of generating ‘‘1’’ in the next iteration when the algorithm gets stuck in local extreme, •rstCoeff – criteria for resetting the population, •sigCoeff – the steepness of the sigmoid function. At the start, an initial population is randomly generated as a binary matrix of size Npop ×Ndim, where Ndim is the number of optimized variables. Rows in this matrix correspond to the individuals of the first population. After the fitness evaluation, individuals are sorted according to their value. A set of individuals with a better rank in the ordered set are selected. At this point, Hamming distances between these elite individuals are determined and compared with Ndim ×rstCoeff. This part is designed to avoid the algorithm being stuck in a local minimum. The decreasing VOLUME 9, 2021 122217 J. Zechmeister et al.: Design of Pixelated SIW Horn Antennas With Nearly Equal Beamwidths Using BISO TABLE 1. Results for benchmark functions. Hamming distance between multiple individuals indicates that the sub-region of the domain space has been exhaustively explored and the algorithm reaches the local minimum. In the next step, the probability vector is determined. The vector is defined as a weighted sum of components according to the best individuals: probVect(i) =1 Nelit Nelit X k=1([1 −w(k)],if Elite(k,i)=1 w(k),if Elite(k,i)=0(1) where iis the index of the variable, Elite is the matrix of the elite individuals, kis the index of the individual in Elite and wdenotes the weight of an individual according to: w(k)=0.5−probMin 1+exp h−1 meanE f(k)−sigCoeff ×meanEi(2) where meanE is the mean fitness value of current elite individuals and fdenotes the fitness value. The range of the sigmoid function (2) is from probMin (specified by user) to 0.5 – probMin. These two values determine the minimum 122218 VOLUME 9, 2021 J. Zechmeister et al.: Design of Pixelated SIW Horn Antennas With Nearly Equal Beamwidths Using BISO TABLE 2. Parameters of conventional SIW horn antenna. and maximum probability of generating ‘‘1’’. The probMin parameter has a significant influence on the convergence rate of the algorithm. For high values of the parameter (probMin >0.1), the convergence rate is low, and achieving an optimum requires a high number of iterations. However, for low values of the parameter, the algorithm is strongly descending toward the nearest minimum. For this purpose, we have implemented the so-called ‘‘reset’’ routine. If the Hamming distance between the elite individuals of one population is below Ndim ×rstCoeff, the value of the parameter probMin is set to probMinRST. In the case that the value of probMinRST is 0.5, the next population is generated randomly. The new population is generated according to the following equation in every iteration: newPop(j,i)=(1,if rand ≤probVect(i) 0,if rand >probVect(i) j∈{1,2,...,Npop}(3) B. BENCHMARK RESULTS The proposed algorithm is tested on 15 benchmark functions with binary variables. Definitions of the benchmark functions are summarized in Appendix. Most of the benchmark functions (f1-f13) are adopted from [20]. The selected benchmark functions can be divided into two categories - unimodal (f1-f7) and multimodal (f8-f13) functions. Another two test problems (fb1,fb2) were proposed as binary test functions which behave like the real optimization of our antenna design. We have tested the BISO algorithm on these functions and compared it with six optimization algorithms, Binary Particle Swarm Optimization (BPSO) [21], Genetic Algorithm (GA) [22], Binary Covariance Matrix Adaptation Evolution Strategy (BCMAES) [23], Binary Bat Algorithm (BBA) [20], Binary Dragonfly Algorithm (BDA) [24] and Multi-Verse Optimization (MVO) [25]. The obtained values for benchmark functions with four different dimensions Ndim ={30,120, 300, 900} are shown in Table 1. Please note that the values are averaged over 100 independent optimization runs. Values in parentheses denote the standard deviation of the results. The unimodal functions are useful in terms of examining the convergence rate of optimization algorithms. The multimodal functions benchmark the ability of algorithms to avoid local minimums. BISO provides a good capability in solving unimodal as well as multimodal problems and outperforms the other algorithms in most cases. In general, BISO is a suitable alternative for optimizing binary problems, especially for those with a high number of variables. FIGURE 2. Simplified model of conventional SIW horn antenna, instead of vias, vertical solid walls are used. FIGURE 3. Normalized simulated radiation patterns of simplified SIW horn antenna at 24 GHz. HPBW is indicated by vertical dashed lines. III. DESIGN OF ANTENNAS We exploit the proposed BISO algorithm for designing linearly and circularly polarized SIW horn antennas with nearly equal beamwidths. To carry out our goal, we exploit a SIW horn antenna designed for maximal directivity depicted in Fig. 2 and defined by the parameters in Table 2. The normalized radiation patterns of the simplified SIW horn antenna are shown in Fig 3. The E and H-plane beamwidths of the conventional antenna are 138.6◦and 25.6◦, respectively. The conventional antenna provides a gain of 8.2 dBi (please note that the losses of the substrate were not considered in this case). The performance enhancement of such an antenna is achieved by extending the antenna aperture and its pixelization. This step depends on the antenna polarization. Therefore, it will be described in the following sections individually. The parameters of the BISO algorithm during the optimization were set as shown in Table 3. Both antennas are designed for a substrate with a thickness of 3.3 mm and a relative permittivity of 2.75. The substrate is made of an XT co-polyester 3D printed filament from Colorfabb [26]. The relative permittivity for this material is published in [27]. VOLUME 9, 2021 122219 J. Zechmeister et al.: Design of Pixelated SIW Horn Antennas With Nearly Equal Beamwidths Using BISO TABLE 3. Parameters setting for BISO algorithm during antenna optimization. FIGURE 4. Simplified model of the proposed linearly polarized pixelated SIW horn antenna. The electromagnetic simulations were performed by CST Studio Suite, whereas the process of optimization was controlled by an in-house MATLAB code. For the sake of the speed of the design process, a simplified model of the SIW horn antenna with vertical solid walls was exploited. A. LINEARLY POLARIZED ANTENNA The linearly polarized (LP) antenna is designed to achieve equal HPBW in the E and H-plane of the radiation pattern with emphasis on SLL reduction. The antenna is axially symmetrical as shown in Fig. 4. The pixelization is applied over a grid intersected with the body of the antenna. Cells assigned FIGURE 5. Optimized binary pattern for the linearly polarized antenna. FIGURE 6. Optimized linearly polarized antenna with SIW structure and coaxial-SIW transition. with ‘‘1’’ are filled by a substrate material and cells with ‘‘0’’ are filled by air. The pixel grid geometry is controlled using parameters lc1-lc6, which are integer multiples of the side length of the pixels and therefore refer to the number of pixels in the columns. Bits of the optimized pattern which are outside the grid become so-called dummy pixels because these positions are defined as filled by the substrate material and covered by a metal layer. After a few trials, we observed that the shape of the grid can be roughly approximated with a parabolic shape, therefore some of the pixels are allocated to determine the parameters lc1-lc7. This approach helps to reduce the number of variables (these pixels are highlighted with blue color in Fig. 5). The variable lc7 is used to determine the length of the edge metallization. The total number of pixels of the optimized pattern is 6×28. The fitness function fis specified as follows: f=qfS112+fHPBW2+fSLL2+fG2(4) 122220 VOLUME 9, 2021 J. Zechmeister et al.: Design of Pixelated SIW Horn Antennas With Nearly Equal Beamwidths Using BISO TABLE 4. Parameters of the proposed linearly polarized antenna. FIGURE 7. Normalized E-field distribution of the linearly polarized antenna at 24.125 GHz in a) H-plane and b) E-plane. where parameters fS11,fHPBW,fSLL, and fGare defined by the following equations: fS11 =(S11/15 +1,if S11 ≥ −15 0,if S11 <−15 (5) fHPBW =1HPBW 10 (6) fSLL =     1,if SLL <8 −SLL/12 +5/3,if 8 ≤SLL ≤20 0,if SLL >20 (7) FIGURE 8. Manufactured prototype of the linearly polarized antenna. FIGURE 9. Measured and simulated reflection coefficient of the linearly polarized antenna. and fG=     1,if G<8 −G/12 +5/3,if 8 ≤G≤15 0,if G>15 (8) where S11 is the reflection coefficient at 24 GHz in dB, 1HPBW is the difference between HPBW in the E and H-plane, SLL is the side lobe level at 24 GHz, and Gis the gain in the main direction at 24 GHz, respectively. The optimized pixelated pattern is shown in Fig. 5. The simplified model is transformed to the SIW structure and the coaxial-SIW transition is added (see Fig. 6). Dimensions of the optimized model are listed in Table 4. Note that the coaxial feed probe length in the substrate lin is 1.8 mm. Values in parentheses are the found optimal lengths for lc1-lc7. The E-field distributions at the center frequency of the 24 GHz ISM band are shown in Fig. 7. Obviously, the E-field is focused by the pixelated part. The dielectric part of the proposed antenna is made of an XT co-polyester from Colofabb [26] using a fused deposition VOLUME 9, 2021 122221 J. Zechmeister et al.: Design of Pixelated SIW Horn Antennas With Nearly Equal Beamwidths Using BISO TABLE 5. Comparison of the linearly polarized antenna with state-of-the-art works. FIGURE 10. Normalized measured and simulated radiation patterns of the linearly polarized antenna at 24.125 GHz a) E-plane and b) H-plane. Measured HPBW is indicated by vertical dashed lines. modeling 3D printer Prusa i3 MK3S with a 0.25 mm nozzle. The substrate is fully printed without any post-processing steps, such as drilling, grinding, etc. The metal layer is made of copper foil and its optimized shape is cut. The vertical walls of the SIW structure are created by a copper wire of diameter 0.8 mm. The individual vias are soldered to the top and bottom side of the antenna and the SMA connector is soldered. The manufactured LP antenna (see Fig. 8) was measured in an anechoic chamber to experimentally verify its performance. The comparison of the measured and simulated reflection coefficient over the frequency band 22-26 GHz is shown in Fig. 9. The measured reflection coefficient of the proposed antenna is below -18 dB in the whole 24 GHz ISM band. The measured radiation patterns (see Fig. 10) show good agreement with the simulated ones. A small discrepancy between the measured and simulated results is caused by the inaccuracy of the fabrication technology, and further by the fact that losses of the substrate were not considered during the design process of the antenna. The measured gain of the antenna is 14.2 dBi at the central frequency of the 24 GHz ISM band, the SLL is below -15 dB, E and H-plane beamwidths are 26.5◦and 25◦, respectively. The nearly equal TABLE 6. Parameters of the optimized circularly polarized antenna. HPBW in the E and H-plane is achieved for the single-layer configuration of the antenna. In this scope, the proposed antenna outperforms the state-of-the-art works (see Table 5). Please note that the SMA connectors used for the antennas feeding are rated up to 26.5 GHz which is sufficient considering the fact that the antennas are designed for the 24 GHz ISM band. The measured −10 dB S11 bandwidths (BW) cannot 122222 VOLUME 9, 2021 J. Zechmeister et al.: Design of Pixelated SIW Horn Antennas With Nearly Equal Beamwidths Using BISO FIGURE 11. Simplified model of the proposed circularly polarized SIW horn antenna. be considered valid, because they are beyond the connectors operating range. Consequently, the presented values of -10 dB S11 BW are according to the simulated data. B. CIRCULARLY POLARIZED ANTENNA The approach to generate the dielectric part of the CP antenna is similar to the LP one. The pixelated grid of the CP antenna is also axially symmetrical. However, the top and bottom metal layers are antipodal (see Fig. 11). We were inspired by the configuration presented in [16] where the ability of antipodal structure generating CP is presented. The pixel grid geometry is also controlled using parameters lc1-lc6, which refer to the number of pixels in the columns, plus additional parameters lc7-lc13 that determine the rest of FIGURE 12. Optimized binary pattern for the circularly polarized antenna. FIGURE 13. Optimized circularly polarized antenna with SIW structure and coaxial-SIW transition. the adjusted part of the metal layer. Pixels allocated for determining parameters lc1-lc13 are highlighted with blue color in Fig. 12. The total number of pixels for the optimized pattern is 6×28. The fitness function fis specified as follows: f=qfS112+fHPBW2+fAR2+fG2(9) where fS11 and fHPBW are defined as (5) and (6), respectively. The fitness parameter for axial ratio fAR is defined as: fAR =     1,if AR >10 −AR/7−3/7,if 3 ≤AR ≤10 0,if AR <3 (10) VOLUME 9, 2021 122223 J. Zechmeister et al.: Design of Pixelated SIW Horn Antennas With Nearly Equal Beamwidths Using BISO FIGURE 14. Normalized E-field distribution of the circularly polarized antenna at 24.125 GHz in a) xy plane and b) yz plane. FIGURE 15. Manufactured prototype of the circularly polarized antenna. where AR is the axial ratio in the main direction at 24 GHz. The desired value of gain is set as 13 dBi and fGis defined as: fG=     1,if G<8 −G/5+13/5,if 8 ≤G≤13 0,if G>13 (11) where Gis gain in the main direction at 24 GHz. FIGURE 16. Measured and simulated reflection coefficient of the circularly polarized antenna. FIGURE 17. Measured and simulated axial ratio of the circularly polarized antenna. The optimized pattern is shown in Fig. 12. and the dimensions of the proposed CP antenna are listed in Table 6. Values in parentheses denote the found optimal lengths for the parameters lc1-lc13. The simplified model of the CP antenna is also transformed to the SIW structure and the coaxial-SIW transition is added (see Fig. 13). The length of the feeding coaxial probe in the substrate lin is 1.8 mm. The E-field distribution of the proposed CP antenna is shown in Fig. 14. The CP antenna provides a less uniform E-field at the aperture compared to the LP antenna. The antenna is manufactured in the same way as for the LP antenna presented in the previous section. The fabricated sample of the antenna is shown in Fig. 15. The measured and simulated reflection coefficient over the frequency band 22-26 GHz is shown in Fig. 16. It remains below -12 dB for the whole 24 GHz ISM band. The measured and simulated axial ratio (see Fig. 17) is below 3 dB over the operating band. The measured radiation patterns (see Fig. 18) in the 122224 VOLUME 9, 2021