Recent Advances in Array Antenna and Array Signal Processing for Radar
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Circularly Polarized Dielectric Resonator Antenna Arrays with Fractal CrossSlotCoupled DRA Elements
Abstract
In the design of circularly polarized (CP) dielectric resonator antenna (DRA) arrays, the regularshaped DRAs with simple feeding configurations are mostly used as array elements to make the design procedure more efficient. However, such array element DRA usually achieves only about 6% axial ratio (AR) bandwidth. In this paper, a CP DRA element coupled by a fractal crossslot which can radiate efficiently and excite the rectangular DRA simultaneously is considered. By adjusting the dimensions of the fractal crossslot properly, the resonances of the fractal crossslot and the dielectric resonator can be merged to obtain a wider AR bandwidth. Based on the proposed fractal crossslotcoupled CP DRA element, two different CP DRA arrays are designed: a wideband CP DRA array and a lowsidelobelevel (SLL) CP DRA array. The designed DRA arrays are fabricated and measured, and structures and performances of the arrays are presented and discussed.
1. Introduction
Over the last decades, DRAs have become more and more popular because of their high radiation efficiency due to the absence of conductor as well as surface wave loss. On the other hand, DRAs can be fed by various feeding techniques, such as the microstrip line feed, the coaxial probe feed, the coplanar waveguide feed, and the aperture coupling feed.
Initial studies of DRAs were concentrated on linearly polarized (LP) designs. In 1985, Haneishi and Takazawa [1] designed the first CP DRA by truncating two opposite corners of a rectangular DRA, and since then many designs of CP DRAs have been proposed. Nowadays, most designs of CP DRA arrays are based on the sequential feeding technique which was proposed by Huang to generate the CP array with LP elements [2]. Moreover, three different kinds of microstrip feeding network for sequential feeding technique are studied in [3], and the hybrid ring feeding network shows a better performance than the parallel feeding network and the series one.
Except for the performance of feeding network, the performance of CP DRA array will also be affected by the array element. Several techniques have been proposed to enhance the axial ratio (AR) bandwidth of the single DRA, such as multiplefeed techniques [4–6], traveling wave excitation [7, 8], and novel DRA geometries [9–11]. However, such designs are not very suitable in the design of DRA array. The multiplefeed designs are complicated to implement because they need a complex feeding network. The lumped resistance in traveling wave excitation will cause a decrease in the radiation efficiency. And compared with the novel DRA geometries, regularshaped DRAs can make the design procedure more efficient because their resonant frequencies can be predicted easily by the dielectric waveguide model (DWM) method [12].
For these reasons cited above, most designers prefer to use regularshaped DRAs (e.g., rectangular, cylindrical, and elliptical DRAs) and simple feeding configurations (e.g., single microstrip feed and slot aperture feed) in the design of DRA array. Especially, to avoid the parasitic radiation from feeding network affecting the radiation pattern of the array, the slot aperture feed is mostly widely used. In [13], a crossslotcoupled cylindrical DRA with 5.6% effective AR bandwidth (S_{11} < −10 dB and AR < 3 dB) is used as the array element in the CP DRA array. In [3], the slotcoupled elliptical DRA with 5% effective AR bandwidth is used as the array element. It can be seen that such regularshaped DRAs with simple feeding configurations usually suffer from a narrow effective AR bandwidth. To enhance the effective AR bandwidth of the array element, a structure of twolayered substrates is used in the design of a crossslotcoupled rectangular DRA, and corresponding effective AR bandwidth of the array element is enhanced to about 9% [14].
In this paper, a CP rectangular DRA element is designed using a relative permittivity ε_{r} = 8.9, which has an effective AR bandwidth of about 12% by introducing a fractal crossslot on the ground plane under the resonator. The proposed DRA element has a simple structure without dual feeds or twolayered substrates, and the mutual coupling between two elements of the proposed structure is found to be small although the distance between the elements is relatively small. Based on the fractal crossslotcoupled CP DRA element, a wideband CP DRA array and a lowsidelobelevel CP DRA array are designed and studied. The arrays are fabricated and their measured results are verified with the simulated one.
2. Design of the Array Element
2.1. Antenna Structure
The structure of the array element is shown in Figure 1. A Rogers RT/duroid 5880 (tm) substrate with relative permittivity ε_{r} = 2.2, dielectric loss tangent 0.0009, and thickness = 0.508 mm is used in the design, and the length and width of the substrate are both 50 mm. A ceramic cube with relative permittivity ε_{r} = 8.9, length = 9.8 mm, width = 9.8 mm, and height = 9.1 mm is mounted on the center of the ground plane, and beneath the ceramic cubic is a fractal crossslot etched on the ground plane. The 50 Ω microstrip line on the bottom side of the substrate has a length of l_{f1} + l_{f2} and a width of w_{f}. As shown in Figure 1(a), l_{f1} is the distance between the 50 Ω port and the center of the ceramic cubic, and l_{f2} is the distance between the center of the ceramic cubic and the terminal of the 50 Ω microstrip line.
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2.2. Effect of the Fractal CrossSlot
Figure 1(b) shows the structures of the fractal crossslot with iterations , 1, and 2. The fractal structure is developed from the ordinary crossslot () which has lengths of l_{s1}, l_{s2} (l_{s2} = k_{s} × l_{s1}) and a width of w_{s}. In the iterative procedure, the width of the slot is constant, and the iterative angle and iterative length coefficient are φ and 0.5, respectively.
To explain the effect of the fractal structure, simulated S_{11} and ARs of the array element with different values of and l_{s1} are presented in Figure 2. According to the DWM method, the theoretical resonant frequencies of and modes in the proposed rectangular DRA are both 6.67 GHz. To obtain the CP radiation, these two modes should be excited simultaneously in the DRA. Of course, the practical resonant frequency in the DRA will also be affected by the feeding structure. Generally speaking, practical resonant frequencies of and modes will not be identical. As long as these two modes are excited at the adjacent frequency band, the effective CP radiation can be obtained. However, the AR bandwidth due to the resonances of the dielectric resonator is usually narrow. To enhance the AR bandwidth, dimensions of the crossslot need to be adjusted suitably, so that the resonances of the crossslot and the dielectric resonator can be merged to obtain a wider AR bandwidth, and then, the corresponding DRA will be a hybridradiation CP DRA.
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However, when the ordinary crossslot () is used, such hybridradiation CP DRA is difficult to be obtained. As shown in Figure 2, when and l_{s1} = 7.9 mm, two resonant frequencies can be found in the S_{11} curve. The lower resonant frequency (about 7.2 GHz) is due to the resonance of the DRA, and the higher one (about 8.6 GHz) is due to the resonance of the slot. In fact, the and modes in the DRA are not effectively excited here. According to the DWM method, the resonant frequency at 7.2 GHz is due to the mode in the DRA (the theoretical resonant frequency of mode is about 7.4 GHz). Besides the ineffective excitation of and modes, the resonant frequency of the slot is too far away from that of the DRA.
To effectively excite the and modes and lower the resonant frequency of the slot, the simplest method is to increase the value of l_{s1}. By simulation, we found that the and modes can be most effectively excited when l_{s1} = 12 mm. At this time, the resonant frequencies of the above two modes are about 6.4 GHz and 6.8 GHz, and resonant frequencies of two orthogonal modes in the slot can be lowered to 7.2 GHz and 7.9 GHz, as shown in Figure 2(a). In this situation, the corresponding CP bands of DRA and slot are found to be around 6.5 GHz and 7.5 GHz, respectively. However, according to Figure 2(b), we can find that these two CP bands are also too far away from each other to be merged.
Compared with the ordinary crossslot, the fractal structure can lower the resonant frequency of the slot more efficiently. When the second iteration () is used, the resonant frequencies of and modes are also about 6.4 GHz and 6.8 GHz, but resonant frequencies of two orthogonal modes in the slot are further lowered to 7.0 GHz and 7.6 GHz. In this situation, CP bands of DRA and slot are found to be well merged, which can effectively enhance the AR bandwidth of the array element.
2.3. Simulated Results
In our design, the parameters of the array element are optimized by the FEMbased commercial software HFSS, and the final parameters of the array element are as follows: w_{f} = 1.52 mm, l_{f1} = 25 mm, l_{f2} = 4 mm, l_{s1} = 9.7 mm, w_{s} = 0.4 mm, k_{s} = 0.57, and φ = 50°.
Figure 3 is the simulated AR and S_{11} of the array element. The impedance bandwidth of the array element is 26.8% (from 6.12 to 8.01 GHz), and the 3 dB AR bandwidth is 11.9% (from 6.49 to 7.31 GHz). Compared with the results in [3, 13] and [14], the proposed array element coupled by the fractal crossslot can achieve the widest effective AR bandwidth (11.9%, from 6.49 to 7.31 GHz).
Figure 4 is the simulated radiation patterns across the effective AR bandwidth. It can be seen that the radiation patterns are stable across the effective AR bandwidth. Moreover, the radiation pattern has no sidelobe in the upper half space at every frequency, and the maximum radiation happens at θ = 0° and φ = 0°, which can ensure the design of a lowsidelobelevel array. The lefthand circular polarization (LHCP) gain at 6.5 GHz, 6.75 GHz, 7.0 GHz, and 7.25 GHz are 7.16 dBi, 7.02 dBi, 6.61 dBi, and 6.33 dBi, respectively.
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Since we are proposing the proposed fractal crossslot coupled DRA for array applications, the mutual coupling between two array elements is studied. The positions of two DRAs in Figures 5(a) and 5(b)are roughly equal to that in a sequential feeding network and a series feeding network which will be used in our design, respectively. The simulated port mutual coupling is shown in Figure 6. The maximum mutual coupling between two elements is lower than −20 dB, which shows a good isolation between array elements.
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(b)
3. Design of the Wideband CP DRA Array
3.1. Antenna Structure
The structure of the proposed 2 × 2 wideband CP DRA array is shown in Figure 7. The length l and width w of the substrate are 100 mm and 84 mm, respectively. In our design, the hybrid ring feeding network for sequential feeding technique is used, and details of the feeding network designs and analyses can be found in [3].
To get the best performance of the DRA array, parameters of the array are optimized by HFSS. In the design of the array element, the distance between the center of the DRA and the 50 Ω port is l_{f1} = 25 mm. In fact, the value of l_{f1} in the array element is decided by dimensions of the substrate. For the array element, a large enough substrate is needed to guarantee the performance of the DRA (mainly the radiation pattern and AR), which means that the value of l_{f1} cannot be too small. But in the design of the array, the substrate is much larger than that in the array element, which can ensure the performance of the DRA array. In this situation, a smaller value of l_{f1} can be selected to accelerate the simulation without degenerating the performance of the array.
Besides the value of l_{f1}, dimensions of the fractal crossslot are also optimized in the design, and we find that value of w_{s} can affect the array more than other parameters.
3.2. Discussion of the Effect of w_{s}
Figure 8 shows the effect of w_{s} on AR of the DRA array. When w_{s} increases, the curve of AR is found to move to the higher frequency band, and the 3 dB AR bandwidth is enhanced due to a lower AR over the frequency band above 8 GHz. When w_{s} = 1.2 mm, the widest 3 dB AR bandwidth can be obtained. This is an interesting conclusion, which means that the value of w_{s}, which can lead the widest 3 dB AR bandwidth in the array, is very different from that in the array element.
To explain this problem more clearly, the effect of w_{s} on the AR of the array element is presented in Figure 9. It is true that the widest 3 dB AR bandwidth can be obtained when w_{s} = 0.4 mm. However, when w_{s} = 0.4 mm is used, AR of the array element will increase quickly with the increase of frequency. In this situation, the AR of the array element over the frequency band above 8 GHz is higher than 9 dB. When a larger value of w_{s} is used, the 3 dB AR bandwidth will deteriorate, but a lower AR can be found in the higher frequency band. When the value of w_{s} is larger than 1.0 mm, AR of the array element is basically lower than 9 dB from 6.0 to 8.5 GHz.
Through analyzing, we think that the above interesting phenomenon is due to the intrinsic characteristic of the sequential feeding network. As mentioned before, the sequential feeding technique can be used to generate CP array with LP elements, which means that the sequential feeding network can be used to lower the AR of the array element. For example, assume that AR of an array element at frequency f_{0} is AR_{0}, if we use the sequential feeding technique to structure an array, the corresponding AR of the array at the same frequency f_{0} should be lower than AR_{0}. So, if we want to obtain the widest 3 dB AR bandwidth in the DRA array, we can use another value of AR (AR′) as the design objective in the design of the array element, and AR′ should be higher than 3 dB.
Comparing the results in Figures 8 and 9, we can find that, considering the frequency band from 6.0 to 8.5 GHz, once the AR of the array element at a particular frequency (f_{0}) is not higher than 9 dB, the corresponding AR of the DRA array at the same frequency f_{0} can be lowered to below 3 dB by the sequential feeding network. So, even though w_{s} = 0.4 mm can lead the widest 3 dB AR bandwidth in the array element, the larger value of w_{s} can lead a wider 9 dB AR bandwidth in the array element, which can finally lead a wider 3 dB AR bandwidth in the DRA array. Finally, we select w_{s} = 1.2 mm in our design, because in this situation, the widest 3 dB AR bandwidth can be obtained in the DRA array.
Of course, it must be point out that the above conclusion “once the AR of the array element at a particular frequency (f_{0}) is not higher than 9 dB, the corresponding AR of the DRA array at the same frequency f_{0} can be lowered to below 3 dB” is not obtained by theoretical analysis or computation, but by the comparison of results in Figures 8 and 9. However, even though it is not a quantitative conclusion, we think that it is a correct qualitative conclusion, which can have a guiding significance in the design of antenna arrays.
3.3. Simulated and Measured Results
In our design, parameters of the DRA array are optimized by HFSS, and all optimized parameters of the array are shown in Table 1.

The proposed wideband CP DRA array is fabricated and measured, and the photo of the fabricated array is shown in Figure 10. To mount the dielectric resonator properly, two extra Lshaped slots are etched around the fractal crossslot which can show an accurate position of the rectangular dielectric resonator, and by simulation, we ensure that such extra structure will not affect the performance of the array.
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Figure 11 is the S_{11} of the proposed DRA array. The simulated impedance bandwidth is 46.5% (from 5.54 to 8.90 GHz), and the measured one is 51.5% (from 5.52 to 9.35 GHz). According to Figure 11, the measured result has a wider impedance bandwidth than the simulated one due to a better impedance matching over the frequency band above 9.0 GHz.
The standard linearly polarized horn antennas are employed for radiation measurements. The simulated and measured boresight ARs of the array are shown in Figure 12. The simulated 3 dB AR bandwidth is 37.7% (from 5.84 to 8.55 GHz), and the measured one is 38.3% (from 6.06 to 8.93 GHz). A good agreement is obtained between the simulated and measured ARs, except for about 300 MHz shift between the simulated and measured results. The measured boresight LHCP gain of the array is also shown in Figure 12. Across most of the 3 dB AR bandwidth, the measured boresight LHCP gain is higher than 10 dBi (from 6.06 to 8.51 GHz), and a highest 12.17 dBi gain is found at 7.9 GHz.
The simulated and measured radiation patterns with vertical and horizontal polarization at 6.5 GHz, 7.5 GHz, and 8.5 GHz in xz plane are shown in Figure 13. Over the lower frequency band, the patterns are stable, and symmetric radiation can be found in the broadside directions. Moreover, good agreements are obtained between the simulated and measured results at 6.5 GHz and 7.5 GHz. When frequency increases to 8.5 GHz, about 5° beam tilt can be found in the measured pattern. Compared with the simulated result, a higher gain can also be found at 8.5 GHz, as well as a higher backlobe level.
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3.4. Comparisons
Table 2 gives the comparisons of the proposed DRA array to other reported wideband CP DRA arrays. It can be seen that the proposed DRA array in this paper can provide a wider effective AR bandwidth than others. It is necessary to point out that the sequential feeding technique and the corresponding hybrid ring feeding network are all used in [3, 14], and this design. So, we can ensure that it is the structure of fractal crossslot and the careful parameter optimization that provide a wider effective AR bandwidth in our design.

4. Design of the LowSidelobeLevel CP DRA Array
In recent years, more and more attentions have been paid to the design of lowsidelobelevel DRA arrays. In [15], lowsidelobelevel DRA array fed by dielectric insular image guide (DIIG) is investigated. In [16], slot windows and reflector are used in the design of DRA array. In [17], DRA array with parasitic DRA elements is proposed. However, it seems that most of the designs mentioned in this paper are either on generating circular polarization or suppressing the SLL of DRA array, but not both.
In this paper, a lowsidelobelevel CP DRA array is also designed based on the proposed fractal crossslotcoupled array element, which can be another verification of the proposed DRA element.
4.1. Antenna Structure
Figure 14 shows the structure of the designed 1 × 6 lowsidelobelevel CP DRA array. In this design, we rotate all slots to 90° to generate the righthanded circularly polarized (RHCP) radiation. Six ceramic cubes are mounted on a substrate with length L = 206 mm and width W = 59 mm. The proposed DRA array is designed to operate at 7.0 GHz with a −20 dB SLL. To achieve such goal, a Chebyshev amplitude distribution and the corresponding series feeding network are used. To achieve a −20 dB SLL, the current ratios of the 6element Chebyshev array is I_{1} : I_{2} : I_{3} = 1 : 0.777 : 0.551. Details of series feeding network designs and analyses can be found in [18].
When the series feeding network is used, we need to adjust the input impedance of the array element to get 50 Ω input impedance in the sum port of the DRA array. In our design, the required input impedance of the array element is 190 Ω. To reduce the discontinuity of the width of the microstrip line in the feeding network, two λ/4 lines are used for impedance conversion in our design. Firstly, the 70 Ω microstrip line is used between the array element and series feeding network, which can convert the input impedance of the array element to 98 Ω. Thus, the input impedance in the sum port becomes 25.85 Ω. So, another 36 Ω microstrip line is used to get the 50 Ω input impedance in the sum port.
The parameters of the DRA array are optimized by HFSS, and the final results are shown in Table 3. Different from the sequential feeding network, the series feeding network has no effect on AR, so it can be found that the optimized value of w_{s} in Table 3 is close to the optimized value in array element.

4.2. Simulated and Measured Results
The proposed DRA array is fabricated and measured, and a photo of the array is shown in Figure 15.
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Figures 16 and 17 show the S_{11}, AR, and boresight RHCP gain of the array. The simulated and measured impedance bandwidths of the array are 18.1% (from 6.38 to 7.65 GHz) and 33.1% (from 6.07 to 8.48 GHz), respectively. The simulated 3 dB AR bandwidth is 13.9% (from 6.51 to 7.48 GHz), and the measured one is 12.4% (from 6.58 to 7.45 GHz). Due to a better impedance matching over the frequency band from 7.8 to 8.5 GHz, the measured impedance is much wider than the simulated one. However, it is obvious that the real performance of DRA array will be subject to the measured 3 dB AR bandwidth, which is 1.5% narrower than the simulated AR bandwidth. Across the measured 3 dB AR bandwidth, the boresight RHCP gain of the array is about 12.5 dBi, except a lowest measured RHCP gain around 7.1 GHz (about 10.0 dBi), and the highest measured RHCP gain is 13.43 dBi at 7.4 GHz.
Figures 18 and 19 are the normalized radiation patterns of the array. It is necessary to point out that all data in Figures 18 and 19 are based on the total gain of the DRA array. As mentioned above, two standard linearly polarized horn antennas are employed for radiation measurements, so the measured results of radiation pattern consist of two parts: the vertical polarized gain G_{V} and the horizontal polarized gain G_{H}, and the corresponding total gain can be computed by
Figure 18 shows the normalized radiation patterns of the array at 7.0 GHz. The simulated SLL in xz plane (φ = 0°) is about −21 dB, which is lower than our design target. Of course, we think that such result is derived from the errors in simulation. The measured SLL at 7.0 GHz is −18.72 dB, which is very close to the design target.
As shown in Figure 19, the frequency band over which SLL < −15 dB is found to be from 6.67 to 7.37 GHz, which is 9.97%. As mentioned above, over such frequency band (SLL < −15 dB), S_{11} < −10 dB and AR < 3 dB can also be satisfied. The lowest measured SLL of −19.23 dB happens at 6.94 GHz.
4.3. Comparisons
Because no reported results of lowsidelobelevel CP DRA arrays are found, we present the comparisons of the proposed array to other reported lowsidelobelevel and wideband DRA arrays (LP arrays) in recent years in Table 4. The proposed lowsidelobelevel CP DRA array shows a wider impedance bandwidth than other designs (except [16], in which the slot windows and reflector are used), and the minor difference between the expected SLL and the obtained SLL can show a successful suppression of sidelobe. Of course, compared to our design, higher antenna gain can be found in others. We think the cause of that is the difference in element number. Through the abovementioned comparisons, we believe that our design can be considered as a good design of lowsidelobelevel and wideband DRA array. On this basis, an extra 3 dB AR bandwidth of 12.4% can be obtained in our design. Compared with the purely LP arrays, we think that the proposed lowsidelobelevel DRA array with CP characteristic is more attractive and valuable.

5. Conclusion
Based on the proposed fractal crossslotcoupled CP DRA, designs of a wideband CP DRA array and a lowsidelobelevel DRA array are proposed in this paper. Effective AR bandwidth of the proposed wideband CP DRA array is 38.3% (from 6.06 to 8.93 GHz), and 12.17 dBi peak gain is obtained. The proposed lowsidelobelevel CP DRA array has an effective AR bandwidth of 12.4% (from 6.58 to 7.45 GHz), and a 9.97% (from 6.67 to 7.37 GHz) for −15 dB SLL bandwidth is obtained. The results of our work show that the proposed fractal crossslotcoupled DRA element, which has a simple structure without dual feeds or twolayered substrates, is quite suitable for the design of DRA arrays.
Conflicts of Interest
The authors declare that there are no competing interests regarding the publication of this paper.
Acknowledgments
This work was supported by the Natural Science Foundation of China under Grant no. 61171031.
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Copyright
Copyright © 2017 JiaHong Lin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.