- Email: [email protected]
A compact modified sierpinski carpet fractal UWB MIMO antenna with square-shaped funnel-like ground stub
Journal Pre-proofs Regular paper A Compact Modified Sierpinski Carpet Fractal UWB MIMO Antenna with Square-shaped Funnel-like Ground Stub Rohit Gurjar, Dharmendra K. Upadhyay, Binod K. Kanaujia, Amit Kumar PII: DOI: Reference:
S1434-8411(19)32857-2 https://doi.org/10.1016/j.aeue.2020.153126 AEUE 153126
To appear in:
International Journal of Electronics and Communications
Received Date: Accepted Date:
15 November 2019 9 February 2020
Please cite this article as: R. Gurjar, D.K. Upadhyay, B.K. Kanaujia, A. Kumar, A Compact Modified Sierpinski Carpet Fractal UWB MIMO Antenna with Square-shaped Funnel-like Ground Stub, International Journal of Electronics and Communications (2020), doi: https://doi.org/10.1016/j.aeue.2020.153126
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier GmbH.
A Compact Modified Sierpinski Carpet Fractal UWB MIMO Antenna with Squareshaped Funnel-like Ground Stub Rohit Gurjar1*, Dharmendra K. Upadhyay2, Binod K. Kanaujia3, Amit Kumar4
1 Department
of Electronics and Communication Engineering, Faculty of Technology, University of Delhi, New Delhi, Delhi 110021, India
2 Division
of Electronics and Communication Engineering, Netaji Subhas University of Technology, New Delhi, Delhi 110078, India
3 School
of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, Delhi 110067, India
4 Department
of Electrical and Electronics Engineering, Darbhanga College of Engineering, Darbhanga, Bihar 846005, India *Email:
[email protected]
Abstract: - In this paper, a compact modified Sierpinski carpet fractal ultra-wideband (UWB) multiple-input-multiple-output (MIMO) antenna with a square-shaped funnellike ground stub is presented and experimentally investigated. Miniaturization and wideband performance are achieved by using the proposed fractal structure. Iterated function system (IFS) method is used to design the proposed fractal structure. The selfsimilarity dimension of the proposed fractal structure is 1.72. The dimension of the proposed MIMO antenna is 24×30 mm2 and consists of two novels modified Sierpinski carpet fractal monopole-antenna elements. The impedance bandwidth of the presented antenna is 9.6 GHz (S11 < ─10 dB) ranging from 3 GHz to 12.6 GHz with isolation better than 16.3 dB, which is achieved by using square-shaped funnel-like ground stub with a vertical slot. The various parameters of diversity performance are also calculated. The simulated and measured results of the presented antenna are comparable, which indicates that the presented antenna can be utilized in UWB applications.
1
Keywords: - Iterated function system, multiple-input-multiple-output antenna, Sierpinski carpet fractal antenna, ultra-wideband antenna 1. Introduction In 2002, the Federal communication commission (FCC) permitted the utilization of unlicensed frequency bandwidth ranging from 3.1 GHz to 10.6 GHz with ─41.3 dBm/MHz power limit for commercial applications [1]. The Ultra-wideband (UWB) is an interesting technology, which permits ultra-high-speed communication at low power consumption for short-range applications. But, UWB systems experience multipath fading problem and this issue can be resolved by the utilization of Multiple-input-multiple-output (MIMO) techniques in UWB systems [2]. MIMO techniques improve system reliability and channel capacity [3, 4]. But compact size MIMO antennas experience high mutual coupling, which degrades the performance of an antenna [5]. Reducing mutual coupling in a compact MIMO antenna is always challenging. While techniques like electromagnetic band-gap structures [6], metamaterials [7, 8], metasurface [9] and sometimes neutralization line [10] are more favourable for minimizing mutual coupling between elements of narrow-band MIMO antennas [11]. In the case of wideband and UWB MIMO antenna techniques like defected ground structures (DGSs) [12], protruding ground stub like radial stub loaded resonator [13] and sometimes neutralization line [14] are more useful in reducing the mutual coupling. Different patterns and polarization of the antenna elements can also minimize the mutual coupling like in [15] an isolation of more than 26 dB has been achieved in the lower UWB band ranging from 3.1–5.15 GHz with the help of pattern and polarization diversity. Fractal structures create an option to design compact antennas because of their unique properties [16–19]. In this research paper, a modified Sierpinski carpet fractal structure is designed up to the second iteration. Iterated function system (IFS) method is used to design the fractal structure. 2
Many MIMO antennas for UWB applications are designed in the past [20–33]. The Squareshaped [20–21], Octagonal-shaped fractal [22, 23], and Triangular-shaped with slot [24] MIMO antennas are reported in [20–24], which covers frequency bands 3.1-10.6 GHz, 3.1-11 GHz, 3.3-10.8 GHz, 2.0-10.6 GHz, and 3.1-10.6 GHz, respectively. A T-shaped [21], an Lshaped [22], and a Tree-like shape [24] ground stubs have been used to improve isolation. The hexagonal ring-shaped [25], rectangular-shaped with modification [26], self-similar fractal [27], hybrid Sierpinski Koch fractal [28], Sierpinski Knopp fractal [29], hexagonal molecule-shaped fractal [30], and a Triangular-shaped [31] MIMO antennas are reported in [25–31], which covers frequency bands 3.0-12 GHz, 3.08-10.98 GHz, 3.1-12.5 GHz, 2.5-11 GHz, 2.6-10.6 GHz, 3.1-10.6 GHz, and 1.9-16.7 GHz, respectively. A circular arc-shaped [25], a stepped-shape [26], and a T-shaped [27, 31] ground stubs are used for improving isolation. Some compact UWB MIMO antennas are proposed using fractal shaped defects in the ground structure with good isolation capability [32, 33]. In the above-mentioned designs, the smallest size MIMO antenna is given in [27] with a size of 24×32 = 768 mm2. A modified Sierpinski carpet fractal UWB MIMO antenna with a square-shaped funnel-like ground stub is presented in this paper. This MIMO antenna contains two modified Sierpinski carpet fractal elements. The designed MIMO antenna’s impedance bandwidth is 9.6 GHz (S11<─10 dB), which is ranging from 3.0-12.6 GHz. The square-shaped funnel-like ground stub and a vertical slot improved the isolation greater than 16.3 dB. The proposed antenna and discussed above UWB MIMO antenna systems are compared in Table 1. It is observed in Table 1 that the size of the designed antenna is the smallest in comparison with others. The dimension of this antenna is 24×30=720 mm2. The remaining paper is organized as follows: The dimension of the presented MIMO antenna, effects of fractal geometry, the effects of the square-shaped funnel-like ground stub on Sparameters, and effects of a slot on S-parameters are given in section 2. The results are 3
discussed in section 3 such as S-parameters comparison, 2-D radiation patterns at resonant frequencies, and realized gain. The various diversity parameters are shown in section 4 of this paper. The conclusion of the paper is given in section 5. Table 1. Comparison between reported UWB MIMO antennas and presented antenna S.
No. of
Frequency band
Min. Isolation
Size (mm2) No.
elements
1
2
2
Ref. No. (GHz)
(dB)
26×40=1040
3.1-10.6
15
[20]
2
22×36=792
3.1-11
15
[21]
3
2
40×25=1000
3.3-10.8
15
[22]
4
4
45×45=2025
2.0-10.6
17
[23]
5
2
35×40=1400
3.1-10.6
16
[24]
6
2
25×45=1125
3-12
15
[25]
7
2
30×30=900
3.08-10.98
20
[26]
8
2
24×32=768
3.1-12.5
16
[27]
9
2
20×40=800
2.5-11
20
[28]
10
4
40×40=1600
2.6-10.6
20
[29]
11
4
40×40=1600
3.1-10.6
20
[30]
12
2
32.6×46=1499.6
1.9-16.7
17
[31]
13
2
26.75×41.5=1110.12
3.1–11.5
19
[32]
14
2
30×41=1230
2.2-11
20
[33]
15
2
24×30=720
3.0-12.6
16.3
Proposed
2. Antenna design 4
2.1 Antenna configuration
Port 2
Port 1
Fig. 1. The geometry of the proposed antenna (light blue: bottom surface, dark blue: top surface). The geometry of a compact modified Sierpinski carpet fractal UWB MIMO antenna with a square-shaped funnel-like ground stub is shown in Fig. 1. The overall dimension of this antenna is 24×30 mm2. It has two identical modified Sierpinski carpet fractal radiating elements. A square-shaped funnel-like ground stub is used for proper matching and a vertical slot is cut to enhance isolation. This proposed antenna is simulated by utilizing the CST simulation tool. This presented antenna is fabricated on an FR4 substrate (height = 0.8 mm, dielectric constant=4.3, and loss tangent = 0.02) and its prototype photograph is shown in Fig. 8. The dimensions are listed in Table 2 of this antenna. Table 2. Dimensions of the presented MIMO antenna (Unit: mm) L
LP
LP1
LP2
LF
LG1
24
7
4.2
0.84 11.9 10.5
LG2
LG3
LS1
LS2
2
1
5
16
W WP WP1 WP2
WF
WG1 WG2 WG3 WS1
30 9.5
1.2
6.4
5.7
1.14
4.5
1
1
5
2.2 Effect of fractal geometry
Fig. 2. Fractal structure generation by IFS (A) Sierpinski carpet fractal structure (B) Proposed fractal structure Fractal means irregular or broken fragments. Benoit Mandelbrot originally devised the term Fractal to delineate structures that carry a self-affine or self-similar characteristics in their structures [34]. The desired miniaturization, wideband and multiband characteristics can be obtained by using fractal structures in antennas [19]. A Sierpinski carpet fractal structure [35] is a self-similar structure and its construction is shown in Fig. 2(A). In iteration-0, a rectangle is used as a base structure. Then this base structure is scaled by a factor of three from both directions, creating nine small rectangles, then one central rectangle is removed from nine small rectangles; this is iteration-1, the same steps of the previous iteration are repeated on remaining eight small rectangles; the iteration-2 is observed, shown in Fig. 2(A). A modified Sierpinski carpet fractal structure is shown in Fig. 2(B). This presented fractal structure is also designed by using a rectangle; which is an iteration-0. But here base structure is scaled by a factor of five from both directions, creating twenty-five small rectangles, then nine small central rectangles are removed from twenty-five small rectangles; this is the iteration-1. Then repeat the steps of the previous iteration on the remaining sixteen small 6
rectangles; the iteration-2 is observed as shown in Fig. 2(B). The iterated function system (IFS) is a fractal structure generation technique and it is described by the matrix equation [36–38]. Table 3 shows the proposed structure IFS transformation coefficients. a x W y c
(1)
b x e d y f
Table 3. The proposed fractal structure’s IFS transformation coefficients W
a
b c
d
e
f
0
0
1
1/5 0 0 1/5
2
1/5 0 0 1/5 1/5
0
3
1/5 0 0 1/5 2/5
0
4
1/5 0 0 1/5 3/5
0
5
1/5 0 0 1/5 4/5
0
6
1/5 0 0 1/5
7
1/5 0 0 1/5 4/5 1/5
8
1/5 0 0 1/5
9
1/5 0 0 1/5 4/5 2/5
10 1/5 0 0 1/5
0
0
0
1/5
2/5
3/5
11 1/5 0 0 1/5 4/5 3/5 12 1/5 0 0 1/5
0
4/5
13 1/5 0 0 1/5 1/5 4/5 14 1/5 0 0 1/5 2/5 4/5 15 1/5 0 0 1/5 3/5 4/5 16 1/5 0 0 1/5 4/5 4/5
7
There are many ways to define the dimension of any structure such as the Hausdorff dimension, Euclidean dimension, self-similarity dimension, and Topological dimension [39]. However, the self-similarity dimension is most commonly used because it is easy to understand. It is obtained using Equation (2). The calculation steps of the self-similarity dimension, D are reported in [40].
D
log( N ) log(1 S )
(2)
Here, N is the number of identical duplicate structures of scale down the original structure and S is the scaling factor. For the Sierpinski carpet fractal structure, N=8 and S= (1/3), hence, D is 1.89. Whereas, for the modified Sierpinski carpet fractal structure, N=16 and S= (1/5), hence, D is 1.72, which is also a fractional dimension. Hence, we can say the proposed structure is fractal. At iteration-0, the monopole element’s metallic area is 7×9.5 = 66.5 mm2, which is minimized to 52.54 mm2 and 27.238 mm2 at iteration-2 by cutting slots for the Sierpinski carpet fractal monopole element and proposed fractal monopole element, respectively. It is noticed that the metallic area of the Sierpinski carpet fractal monopole element and proposed fractal monopole element is reduced by 20.98 % and 59.04 % at iteration-2, respectively. The monopole element's average electrical length increases at higher-order iterations, like inductive loading and slot-loading as delineated in [41, 42]. It leads to antenna miniaturization.
8
Fig. 3. Monopole antennas (A) iteration-0, (B) Sierpinski carpet at iteration-2, (C) Proposed at iteration-2 Fig. 3 shows the different monopole antenna elements and their corresponding return loss curves are shown in Fig. 4. At iteration-0 of a monopole antenna, the impedance bandwidth is 6.74 GHz ranges from 4.75 GHz to 11.49 GHz. The lower and upper edges of the frequency band are shifted by the increase of iterations. The overall bandwidth of iteration-2 Sierpinski carpet fractal monopole antenna is 310 MHz more in comparison to iteration-0 monopole antenna bandwidth.
Fig. 4. Return loss curves of different monopole antennas.
9
Table 4. The comparison between Sierpinski carpet and proposed fractal structures at iteration-2. Fractal Structures
Self-Similarity
Frequency band
Metallic area
(Iteration-2)
dimension
(GHz)
minimized
Sierpinski Carpet structure
1.89
4.73-11.78
20.98 %
1.72
4.62-12.24
59.04 %
antenna Proposed fractal structure antenna
While the overall bandwidth of iteration-2 proposed monopole antenna is 880 MHz more in comparison to iteration-0 monopole antenna bandwidth and also getting dual-band characteristics. There is a generation of multiple resonances when fractal structures are used in antennas. These generated multiple resonances may be utilized to attain a wider bandwidth [23]. The overall comparison between the Sierpinski carpet and the proposed fractal structure at iteration-2 is given in Table 4. The parameters of the proposed modified Sierpinski carpet fractal structure antenna are better than the existing Sierpinski carpet structure antenna. The approximated primary resonant frequency of the presented planar monopole antenna at iteration-0 (Fig. 3(A)) is given below [43].
fr
14 . 4 A1 A2 l1 l 2 g 2 l1 re 2 l 2 re
re ( r 1) / 2
(3) (4)
10
Where l1 denotes the length of the ground plane, l 2 denotes the length of the radiation patch,
g denotes the gap between the radiation patch and the ground plane, A1 denotes the ground plane area; A2 denotes the radiation patch area and re is the effective dielectric constant. Fig. 3(A) shows the rectangular monopole antenna at iteration-0, its calculated resonant frequency is 6.7 GHz using the above equations. This is close to the simulated resonant frequency of rectangular monopole antenna at iteration-0 as shown in Fig. 4.
2.3 Effect of the ground plane
Fig. 5. Evolution structures of the ground plane
Fig. 6. S-parameters of MIMO antenna for the different ground configurations (A) S11 and (B) S21 11
Defected ground structures are the most popular techniques, especially when it comes to mutual coupling reduction between broadband and ultra-wideband MIMO antenna elements. Several review papers [44–47] are available on DGSs in the existing literature to showcase its importance while MIMO antenna designing. Actually, DGS is a defect in a ground plane, which intensely disturbs the surface current distribution. As a result, the impedance of the transmission line will change. It acts as a band stop filter and suppresses the coupled fields between the adjacent antenna elements of the MIMO antenna by decreasing the current on the ground plane [48]. Fig. 5 shows the evolution process of the ground plane for the proposed modified Sierpinski carpet fractal MIMO antenna. The simulated S-parameters of the MIMO antenna for different ground configurations are shown in Fig. 6. As antenna elements are symmetrical, so S22 and S12 are similar to S11 and S21 respectively. Therefore, only S21 and S11 parameters are shown in Fig. 6. For Ground 1, the lower cut-off frequency of S11 is 4.23 GHz (for S11 <-10 dB) and mutual coupling, S21 is above -15 dB. Whereas the required lower cut-off frequency of S11 is 3.1 GHz for the UWB systems [27] and mutual coupling, S21 should be less than -15 dB for the MIMO antennas [20]. However, the square-shaped funnel-like ground stub with a vertical slot (Ground 2) shifted the lower cut-off frequency of S11 from 4.23 GHz to 3.0 GHz. It has occurred because ground stub behaving as a reflector [20], the introduced vertical slot has improved the isolation S21 and now it is lower than -16.3 dB for the entire operating frequency range. MIMO antenna with Ground 2 is suitable for UWB applications as it is covering the frequency band ranging from 3.0 to 12.6 GHz.
12
(A)
(B) Fig. 7. Surface current distributions by exciting port-1 and terminating port-2 at (A) 3.2 GHz (B) 7.51 GHz Fig. 7 shows the effects of different ground planes on current distribution at 3.2 GHz and 7.51 GHz frequency. To analyze the surface current distribution, one port needs to be excited and the second port of the MIMO antenna needs to be terminated with a matched 50Ω load. Therefore, port-1 is excited and the port-2 of MIMO antenna is terminated with a 50Ω load in Fig. 7. It is clearly noticeable from Fig. 7 that large current is coupled towards the squareshaped funnel-like ground stub and a vertical ground slot. As a consequence, the surface current reduced near the next monopole element. It clearly indicates the reduction of mutual coupling between ports. 3.
Results and discussion The modified Sierpinski carpet fractal MIMO antenna is fabricated. The results of the
fabricated antenna are compared to corroborate the simulation results. The prototype image is shown in Fig. 8 and its results are measured using the Keysight vector network analyzer
13
(model N9916A). There is a slight variation in measured results when compared with the simulated results due to environmental setups, fabrication limitations, and SMA connectors.
Fig. 8. Fabricated proposed MIMO antenna (A) Top surface, (B) Bottom surface
Fig. 9. The S-parameters comparison of proposed antenna (A) S11, (B) S21 The comparison between measured and simulated S-parameters shown in Fig. 9. There is a slight mismatch between simulated and measured results due to fabrication limitations such as thickness and soldering of the connector as well as the improper copper etching. The impedance bandwidth and fractional bandwidth of the presented fractal MIMO antenna is 9.6
14
GHz and 123.07%, respectively. It can observe from Fig. 9 that the isolation, S21 is greater than 16.3 dB over the entire working frequency range. Further improvement in the fractional bandwidth can be done with the help of ground stub matching. The use of a slot antenna loaded with stubs increases the fractional bandwidth [49]. Also, slot antenna having CPW-feed will advocates higher fractional bandwidth. Some other general methods of increasing bandwidth are: using thick and low permittivity substrates; by introducing closely spaced parasitic patches on the same layer of the feed patch; using Stacked Parasitic patch; aperture Coupling; aperture- Coupled Stacked Patches and L-Probe Coupling. Also, the two-port antenna system having increased fractional bandwidth can be extended to build a larger array antenna having shaped beams approximated through maximally-sparse planar arrays [50]. The larger array has the benefits of better beam-steering and higher bit rate without sacrificing additional spectrum and transmitted power.
(A)
15
(B)
(C)
(D) Fig. 10. Normalized radiation patterns at (A) 3.2 GHz, (B) 4.74 GHz, (C) 7.51 GHz and (D) 11.80 GHz in both XZ (E-plane) and YZ plane (H-plane)
16
Fig. 10 shows the normalized 2D-radiation patterns of MIMO antenna for all resonant frequencies (3.20 GHz, 4.74 GHz, 7.51 GHz, and 11.80 GHz) in E-plane (XZ-plane) and Hplane (YZ-plane). The measured and simulated co-polarization and cross-polarization radiation patterns analysis for all the four resonant frequencies also presented in Fig. 10 for both the ports by exciting one port and terminating the other port by 50 Ω load impedance. The radiation patterns are omnidirectional, except few dips, especially in the YZ planes at the higher frequency. So, we are almost getting an omnidirectional pattern, which is required and desirable for better performance of the MIMO antenna. Also, The normalized radiation pattern of Co and cross-polarization shows the isolation of almost more than 20 dB in XZ plane and 15 dB in YZ plane mainly in the main lobe direction (which is slightly varying around ±900) at all the resonant frequencies, which clearly indicates that this antenna is a linearly polarized. The pattern diversity of this antenna is improving as we move from lower to the higher resonating frequency in the XZ plane of all the four frequencies as shown in Fig. 10. The realized peak gain of this antenna is shown in Fig. 11. The radiators of the proposed MIMO antenna are symmetrical in the structure; therefore both radiators gain values are similar. Hence, the realized peak gain of one radiator is shown. The measured gain varies from 2 to 4.8 dBi throughout the working frequency band ranging from 3–12.6 GHz.
17
Fig. 11. Gain Vs Frequency 4. Diversity performance The diversity performance parameters are needed to be evaluated to corroborate the ability of the presented antenna such parameters are ECC (Envelope correlation coefficient), DG (Diversity gain), MEG (Mean effective gain), and CCL (Channel capacity loss) [51]. The correlation between one antenna radiation patterns with other adjacent antenna radiation patterns can be studied as ECC. The parameter ECC should be less than 0.05 values. In uniform domain, ECC can be determined using S-parameters [52, 53] as given in equation (5). We have calculated the ECC using the far-field radiation pattern [4, 11] also as it is considered more accurate for a wideband and low-efficiency antenna. Also, the computed ECC through equation (6) will give a better realization of pattern diversity.
e
S11 S12 S 21 S 22 2
2
2 2
2
(1 ( S11 S 21 ))(1 ( S 22 S12 ))
(5)
18
ij
XPR Ei Ej P Ei Ej P d
2
XPR Ei Ei P Ei Ei P d XPR Ej Ej P Ej Ej P d
(6)
The parameter ECC computed from far-field radiation along with DG has been shown in Fig. 12. The parameter ECC of this antenna is always under the limit of 0.05 for the entire operating bandwidth [52]. The degree of effectiveness of diversity is known by diversity gain and it can be determined by using equation (7) as given in [54, 55].
DG 10 e p 10 1 e
2
(7)
10 is the maximum diversity gain at the 1% probability level with maximum-ratio combining and ep is the diversity gain reduction factor due to correlation between the signals on the two antennas (ρe is the Envelope correlation coefficient) [56, 57]. For practical applications, the parameter DG should be more than 9.95 dB [51]. The DG of this antenna is within the limit for the entire operating bandwidth. It declares that the presented antenna has a good diversity performance.
Fig. 12. ECC computed from far-field radiation along with DG Vs Frequency 19
The diversity parameter MEG measures the power received by the antenna elements in a MIMO system as compared to an isotropic antenna in a multipath fading environment under uniform Rayleigh outdoor conditions. The ratio of MEG should follow the criteria MEGi MEG j 3dB for good diversity performance [53, 55]. The terms, i and j denote
antenna elements 1 and 2, respectively. The ratio of MEG lies within the specified limit of ±3dB for the entire operating bandwidth. The MEG has been evaluated from far-field radiation as depicted in equation (8) [4, 11] and the promising result has been shown in Fig. 13.
1 XPR MEG 02 0 G , P , G , P , sin dd 1 XPR 1 XPR
(8)
Fig. 13. Measured MEG from far-field radiation The parameter CCL defines the maximum reliable data transmission rate over the communication channel. The CCL of the presented antenna is shown in Fig. 14. The minimum acceptable limit for CCL is lower than 0.4 b/s/Hz [26]. This can be evaluated by
20
using equation (9) as given in [33, 41]. The calculated CCL for the proposed antenna is within the acceptable limit. Closs log 2 det( R )
(9)
where,
12 R 11 2 2 2 2 21 22 11 1 ( S11 S12 ) 22 1 ( S 22 S 21 ) ,
,
,
12 ( S11 S12 S 21 S12 ) , 21 ( S 22 S 21 S12 S 21 )
Fig. 14. Simulated and measured CCL
5. Conclusion A compact modified Sierpinski carpet fractal UWB MIMO antenna having dimensions 24×30×0.8 mm3 has been presented, fabricated (on FR-4 Substrate) and experimentally investigated. The two modified Sierpinski carpet fractal monopole-antenna elements are used to design this antenna, which covers the UWB operations ranging from 3 GHz to 12.6 GHz
21
with a fractional bandwidth of 123.07 %. A square-shaped funnel-like ground stub with a vertical slot is used to enhance isolation better than 16.3 dB for the entire operating range. The peak gain of the proposed fractal MIMO antenna varies from 2 to 4.8 dBi over the entire UWB range. The computed ECC and CCL are less than 0.05 and 0.2 b/s/Hz respectively for the working frequency range. The computed MIMO antenna results and diversity performances are found satisfactory, which advocates its candidature for the entire UWB applications. References [1] Federal Communications Commission, Revision of Part 15 of the Commission’s rules regarding ultra-wideband transmission system from 3.1 to 10.6 GHz, Federal Communications Commission, Washington, DC, ET Docket 98-153, 2002. [2]
T. Bolin, A. Derneryd, G. Kristensson, V. Plicanic, and Z. Ying, “Two-antenna receive diversity performance in indoor environment,” IEEE Electron. Lett., vol. 41, no. 2, pp. 1205-1206, 2005.
[3] I.B. Mabrouk, L. Talbi, M. Nedil, and K. Hettak, "MIMO-UWB channel characterization within an underground mine gallery," IEEE Trans. Antennas Propag., vol. 60, no. 10, 4866-4874, 2012. [4] A. Kumar, A.Q. Ansari, B.K. Kanaujia, and J. Kishor, “A novel ITI-shaped isolation structure placed between two-port CPW-fed dual-band MIMO antenna for high isolation,” AEU – Int. J. Electron. Commun., vol. 104, pp. 35–43, 2019. [5] A. Kumar, A.Q. Ansari, B.K. Kanaujia, J. Kishor, and N. Tewari, “Design of tripleband MIMO antenna with one band-notched characteristic,” Progr. Electromagn. Res. C., vol. 86, pp. 41–53. 2018.
22
[6] T. Jiang, T. Jiao, and Y. Li, “A Low Mutual Coupling MIMO Antenna Using Periodic Multi-Layered Electromagnetic Band Gap Structures,” Applied Computational Electromagnetics Society Journal, vol. 33, no. 03, pp. 305-311, March 2018. [7] K. Yu, Y. Li, and X. Liu, “Mutual Coupling Reduction of a MIMO Antenna Array Using
3-D
Novel
Meta-material
Structures,”
Applied
Computational
Electromagnetics Society Journal, vol. 33, no. 07, pp. 758-763, July 2018. [8] S. Luo, Y. Li, Y. Xia, G. Yang, L. Sun, and L. Zhao, “Mutual Coupling Reduction of a Dual-Band Antenna Array Using Dual-Frequency Metamaterial Structure,” Applied Computational Electromagnetics Society Journal, vol. 34, no. 03, pp. 403-410, July 2018. [9] F. Liu, J. Guo, L. Zhao, G. Huang, Y. Li, and Y. Yin, "Dual-Band Metasurface-based Decoupling Method for Two Closely Packed Dual-Band Antennas," IEEE Transactions
on
Antennas
and
Propagation,
Sept.
2019.
doi:
10.1109/TAP.2019.2940316. [10] S. Luo, Y. Li, Y. Xia, and L. Zhang, “A Low Mutual Coupling Antenna Array with Gain Enhancement Using Metamaterial Loading and Neutralization Line Structure,” Applied Computational Electromagnetics Society Journal, vol. 34, no. 03, pp. 411418, March 2019. [11] A. Kumar, A.Q. Ansari, B.K. Kanaujia, J. Kishor, and S. Kumar “An Ultra-Compact Two-Port UWB-MIMO Antenna with Dual Band-Notched Characteristics,” AEU – Int. J. Electron. Commun., vol. 114, Feb. 2020. [12] I. Gnanaharan and R. Anbazhagan, “Review on the design of the isolation techniques for UWB-MIMO antennas,” Adv. Electromagn., vol. 7, no. 4, pp. 46–70, 2018.
23
[13] Y. Li, W. Li, and W. Yu, “A Multi-Band/UWB MIMO/Diversity Antenna with an Enhanced Isolation Using Radial Stub Loaded Resonator,” Applied Computational Electromagnetics Society Journal, vol. 28, no. 01, pp. 08-20, Jan. 2013. [14] S. Zhang and G. F. Pedersen, "Mutual Coupling Reduction for UWB MIMO Antennas With a Wideband Neutralization Line," IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 166-169, May 2015. [15] S. Zhang, B. K. Lau, A. Sunesson and S. He, "Closely-Packed UWB MIMO/Diversity Antenna With Different Patterns and Polarizations for USB Dongle Applications," IEEE Transactions on Antennas and Propagation, vol. 60, no. 9, pp. 4372-4380, Sept. 2012. [16] Y. Li, X. Yang, C. Liu, and T. Jiang “Miniaturization Cantor Set Fractal Ultrawideband Antenna With A Notch Band Characteristic,” Microw. Opt. Technol. Lett., vol. 54, no. 05, pp. 1227-1230, May 2012. [17] D.H. Werner, R.L. Haupt,
and P.L. Werner, “Fractal antenna engineering: The
Theory and Design of Fractal antenna Arrays,” IEEE Antennas and Propag. Mag., vol. 41, no. 5, pp. 37-58, 1999. [18] J. Anguera, C. Puente, V. Borja, and J. Soler, “Fractal-shaped antennas: A review, Encyclopaedia of RF and microwave engineering,” Wiley. Hoboken, NJ, vol. 2, pp. 1620–1635, 2005. [19] M.R. Haji-Hashemi, H. Mir-Mohammad Sadeghi, and V.M. Moghtadai, “Spacefilling patch antennas with CPW feed,” Progr Electromagn Res., vol. 2, no. 1, pp. 69– 73, 2006. [20] L. Liu, S.W. Cheung, and T.I. Yuk, “Compact MIMO antenna for portable devices in UWB applications,” IEEE Trans Antennas Propag., vol. 61, no. 8, pp. 4257–4264, 2013.
24
[21] L. Liu, S.W. Cheung, and T.I. Yuk, “Compact MIMO antenna for portable UWB applications with band-notched characteristic,” IEEE Trans. Antennas Propag., vol. 63, no. 5, pp. 1917-1924, 2015. [22] S. Tripathi, A. Mohan, and S. Yadav, “A compact octagonal fractal UWB MIMO antenna with WLAN band rejection,” Microw Opt Technol Lett., vol. 57, pp. 1919– 1925, 2015. [23] S. Tripathi, A. Mohan, and S. Yadav, “A Compact Koch Fractal UWB MIMO Antenna with WLAN Band-Rejection,” IEEE Antennas and Wireless Propagation Letters, vol. 14, pp. 1565–1568, 2015. [24] S. Zhang, Z. Ying, J. Xiong, and S. He, “Ultrawideband MIMO/Diversity antennas with a tree-like structure to enhance wideband isolation,” IEEE Ant. Wireless Propag. Letters, vol. 8, pp. 1279-1282, 2009. [25] R. Mathur, and S. Dwari, “Compact CPW‐fed ultrawideband MIMO antenna using hexagonal ring monopole antenna elements,” AEU ‐ Int J Electron Commun, vol. 93, pp. 1‐6b, 2018. [26] S.P. Biswal, and S. Das S, “A low‐profile dual port UWB‐MIMO/diversity antenna with band rejection ability,” Int. J. RF Microw Comput Aided Eng., vol. 28, no. 1, e21159, 2017. [27] R. Gurjar R, D.K. Upadhyay, B.K. Kanaujia, and K. Sharma, “A Novel Compact Self-Similar Fractal UWB MIMO Antenna,” Int. J. RF Microw Comput Aided Eng., e21632, 2018. [28] R. Sampath, and K.T. Selvan, “Compact hybrid Sierpinski Koch fractal UWB MIMO antenna with pattern diversity,” Int. J. RF Microw Comput Aided Eng, e22017, 2019.
25
[29] S. Rajkumar, K.T. Selvan, and P.H. Rao, “Compact 4 element Sierpinski Knopp fractal UWB MIMO antenna with dual band notch,” Microw Opt Technol Lett, vol. 60, pp. 1023-1030, 2018. [30] S. Rajkumar, A. Anto Amala, and K.T. Selvan, “Isolation improvement of UWB MIMO antenna utilising molecule fractal structure,” Electronics letters, vol. 55, no. 10, pp. 576-579, 2019. [31] R. Kumar, and G. Surushe, “Design of microstrip-fed printed UWB diversity antenna with tee crossed shaped structure,” Eng. Sci. Technol. Int. J. (JESTECH). Vol. 19, no. 2, pp. 946–955, 2016. [32] J. Banerjee, A. Karmakar, R. Ghatak, and D.R. Poddar, “Compact CPW-fed UWB MIMO antenna with a novel modified Minkowski fractal defected ground structure (DGS) for high isolation and triple band-notch characteristic,” Journal of Electromagnetic Waves and Applications, vol. 31, no. 15, pp. 1550-1565, 2017. [33] A. Gorai, A. Dasgupta, and R. Ghatak, “A Compact quasi-self-complementary Dual Band Notched UWB MIMO Antenna with enhanced isolation using Hilbert fractal slot,” AEU-Int. J. Electron Comm., vol. 94, pp. 36-41, 2018. [34] B.B. Mandelbrot, “The fractal geometry of nature,” W. H. Freeman New York. 1983. [35] H.O. Peitgen, H. Jurgens, and D. Saupe, “Chaos and fractals: New frontiers in science,” Springer-Verlag New York. 1992. [36] S.N. Sinha, and M. Jain, “A self-affine fractal multiband antenna,” IEEE Antennas and Wireless Propag. Lett., vol. 6, pp. 110-112, 2007. [37] R. Gurjar, R. Singh, and S. Kumar, “Elliptically slotted self-affine 8-shaped fractal multiband antenna,” Proceedings of the Int. Conf. on Recent Cognizance in Wireless Comm. & Image Processing Springer, Jaipur, India, pp. 783-78, 2016.
26
[38] R. Gurjar, D.K. Upadhyay, and B.K. Kanaujia, “Compact four-element 8-shaped selfaffine fractal UWB MIMO antenna,” IEEE International Microwave and Photonics Conference Preceedings, Dhanbad, India, pp. 1-2, 2018. [39] K.J. Vinoy, J.K. Abraham, and V.K. Varadan, “On the relationship between fractal dimension and the performance of multi-resonant dipole antennas using Koch curves,” IEEE Trans Antenna Propag., vol. 51, no. 9, pp. 2296-2303, 2003. [40] Y.K. Choukiker, S.K. Sharma, and S.K. Behera, “Hybrid fractal shape planer monopole antenna covering multiband wireless communications with MIMO implementation for handheld mobile devices,” IEEE Trans Antenna Propag., vol. 62, pp. 1483-1488, 2014. [41] S. Reed, L. Desclos, C. Terret, and S. Toutain, “Patch antenna size reduction of a patch antenna by means of inductive loads,” Microw. Opt. Technol. Lett., vol. 29, no. 2, pp. 79–81, 2001. [42] L. Desclos, “Size reduction of patch by means of slots insertion,” Microw. Opt. Technol. Lett., vol. 25, no. 2, pp. 111–113, 2000. [43] K.G. Thomas, M. Sreenivasan, “A simple ultrawideband planar rectangular printed antenna with band dispensation,” IEEE Trans Antennas Propag., vol. 58, no. 1, pp. 27-34, 2010. [44] M. K. Khandelwal, B. K. Kanaujia and S. Kumar, “Defected Ground Structure: Fundamentals, Analysis, and Applications in Modern Wireless Trends,” Int. J. Antennas Propag., vol. 2017, Article ID 2018527, 22 pages, 2017. [45] J. G. Webster, M. S. Bhuiyan and N. C. Karmakar, “Defected Ground Structures for Microwave Applications,” In Wiley Encyclopedia of Electrical and Electronics Engineering, J. G. Webster (Ed.), Jan. 2014.
27
[46] L. H. Weng, Y.-C. Guo, X.-W. Shi, and X.-Q. Chen, "An Overview on Defected Ground Structure," Progr. Electromagn. Res. B, vol. 7, pp. 173-189, 2008. [47] G. Breed, “An Introduction to Defected Ground Structures in Microstrip Circuits,” High Frequency Electronics, Summit Technical Media, pp. 50-54, 2008. [48] M.S. Sharawi, “Printed MIMO antenna engineering,” Artech House, Norwood, MA, USA, 2014. [49] J. Lin and Q. Chu, "Increasing Bandwidth of Slot Antennas With Combined Characteristic Modes," IEEE Transactions on Antennas and Propagation, vol. 66, no. 6, pp. 3148-3153, June 2018. [50] A. F. Morabito, "Power synthesis of mask-constrained shaped beams through maximally-sparse planar arrays," Telkomnika (Telecommunication Computing Electronics and Control), vol. 14, no. 4, pp. 1217-1219, 2016. [51] G. Das, A. Sharma, and R.K. Gangwar, “Dual port aperture coupled MIMO cylindrical dielectric resonator antenna with high isolation for WiMax application,” Int. J. RF Microw., vol. 27, no. 7, pp. 1-10, 2017. [52] H.S. Singh, G.K. Pandey, P.K. Bharti, and M.K. Meshram, “Design and performance investigation
of
a
low
profile
MIMO/Diversity
antenna
for
WLAN/WiMAX/HIPERLAN applications with high isolation,” Int. J. RF Microw., vol. 25, pp. 510–521, 2015. [53] A. Kumar, A.Q. Ansari, B.K. Kanaujia, and J. Kishor, “High isolation compact fourport MIMO antenna loaded with CSRR for multiband applications,” Frequenz, vol. 72, pp. 415–427, 2018. [54] J. Nasir, M.H. Jamaluddin, M. Khalily, M.R. Kamarudin, I. Ullah, and R. Selvaraju, “A reduced size dual port MIMO DRA with high isolation for 4 G applications,” Int. J. RF Microwave Comp Aid. Eng., vol. 25, no. 6, pp. 495–501, 2014.
28
[55] R. Chandel, A.K. Gautam, and K. Rambabu, “Tapered fed compact UWB MIMOdiversity antenna with dual band-notched characteristics,” IEEE Trans. Antennas Propag, vol. 66, no. 4, pp. 1677–1684, 2018. [56] S. Singh, B. Meruva, G.K. Pandey, P.K. Bharti, and M.K. Meshram, “Low mutual coupling between MIMO antennas by using two folded shorting strips,” Prog Electromagn Res B, vol. 53, pp. 205-221, 2013. [57] J.N. Pierce, and S. Stein, “Multiple diversity with non-independent fading," IRE Proc., vol. 48, pp. 89-104, Jan. 1960.
29
S1434-8411(19)32857-2 https://doi.org/10.1016/j.aeue.2020.153126 AEUE 153126
To appear in:
International Journal of Electronics and Communications
Received Date: Accepted Date:
15 November 2019 9 February 2020
Please cite this article as: R. Gurjar, D.K. Upadhyay, B.K. Kanaujia, A. Kumar, A Compact Modified Sierpinski Carpet Fractal UWB MIMO Antenna with Square-shaped Funnel-like Ground Stub, International Journal of Electronics and Communications (2020), doi: https://doi.org/10.1016/j.aeue.2020.153126
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier GmbH.
A Compact Modified Sierpinski Carpet Fractal UWB MIMO Antenna with Squareshaped Funnel-like Ground Stub Rohit Gurjar1*, Dharmendra K. Upadhyay2, Binod K. Kanaujia3, Amit Kumar4
1 Department
of Electronics and Communication Engineering, Faculty of Technology, University of Delhi, New Delhi, Delhi 110021, India
2 Division
of Electronics and Communication Engineering, Netaji Subhas University of Technology, New Delhi, Delhi 110078, India
3 School
of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, Delhi 110067, India
4 Department
of Electrical and Electronics Engineering, Darbhanga College of Engineering, Darbhanga, Bihar 846005, India *Email:
[email protected]
Abstract: - In this paper, a compact modified Sierpinski carpet fractal ultra-wideband (UWB) multiple-input-multiple-output (MIMO) antenna with a square-shaped funnellike ground stub is presented and experimentally investigated. Miniaturization and wideband performance are achieved by using the proposed fractal structure. Iterated function system (IFS) method is used to design the proposed fractal structure. The selfsimilarity dimension of the proposed fractal structure is 1.72. The dimension of the proposed MIMO antenna is 24×30 mm2 and consists of two novels modified Sierpinski carpet fractal monopole-antenna elements. The impedance bandwidth of the presented antenna is 9.6 GHz (S11 < ─10 dB) ranging from 3 GHz to 12.6 GHz with isolation better than 16.3 dB, which is achieved by using square-shaped funnel-like ground stub with a vertical slot. The various parameters of diversity performance are also calculated. The simulated and measured results of the presented antenna are comparable, which indicates that the presented antenna can be utilized in UWB applications.
1
Keywords: - Iterated function system, multiple-input-multiple-output antenna, Sierpinski carpet fractal antenna, ultra-wideband antenna 1. Introduction In 2002, the Federal communication commission (FCC) permitted the utilization of unlicensed frequency bandwidth ranging from 3.1 GHz to 10.6 GHz with ─41.3 dBm/MHz power limit for commercial applications [1]. The Ultra-wideband (UWB) is an interesting technology, which permits ultra-high-speed communication at low power consumption for short-range applications. But, UWB systems experience multipath fading problem and this issue can be resolved by the utilization of Multiple-input-multiple-output (MIMO) techniques in UWB systems [2]. MIMO techniques improve system reliability and channel capacity [3, 4]. But compact size MIMO antennas experience high mutual coupling, which degrades the performance of an antenna [5]. Reducing mutual coupling in a compact MIMO antenna is always challenging. While techniques like electromagnetic band-gap structures [6], metamaterials [7, 8], metasurface [9] and sometimes neutralization line [10] are more favourable for minimizing mutual coupling between elements of narrow-band MIMO antennas [11]. In the case of wideband and UWB MIMO antenna techniques like defected ground structures (DGSs) [12], protruding ground stub like radial stub loaded resonator [13] and sometimes neutralization line [14] are more useful in reducing the mutual coupling. Different patterns and polarization of the antenna elements can also minimize the mutual coupling like in [15] an isolation of more than 26 dB has been achieved in the lower UWB band ranging from 3.1–5.15 GHz with the help of pattern and polarization diversity. Fractal structures create an option to design compact antennas because of their unique properties [16–19]. In this research paper, a modified Sierpinski carpet fractal structure is designed up to the second iteration. Iterated function system (IFS) method is used to design the fractal structure. 2
Many MIMO antennas for UWB applications are designed in the past [20–33]. The Squareshaped [20–21], Octagonal-shaped fractal [22, 23], and Triangular-shaped with slot [24] MIMO antennas are reported in [20–24], which covers frequency bands 3.1-10.6 GHz, 3.1-11 GHz, 3.3-10.8 GHz, 2.0-10.6 GHz, and 3.1-10.6 GHz, respectively. A T-shaped [21], an Lshaped [22], and a Tree-like shape [24] ground stubs have been used to improve isolation. The hexagonal ring-shaped [25], rectangular-shaped with modification [26], self-similar fractal [27], hybrid Sierpinski Koch fractal [28], Sierpinski Knopp fractal [29], hexagonal molecule-shaped fractal [30], and a Triangular-shaped [31] MIMO antennas are reported in [25–31], which covers frequency bands 3.0-12 GHz, 3.08-10.98 GHz, 3.1-12.5 GHz, 2.5-11 GHz, 2.6-10.6 GHz, 3.1-10.6 GHz, and 1.9-16.7 GHz, respectively. A circular arc-shaped [25], a stepped-shape [26], and a T-shaped [27, 31] ground stubs are used for improving isolation. Some compact UWB MIMO antennas are proposed using fractal shaped defects in the ground structure with good isolation capability [32, 33]. In the above-mentioned designs, the smallest size MIMO antenna is given in [27] with a size of 24×32 = 768 mm2. A modified Sierpinski carpet fractal UWB MIMO antenna with a square-shaped funnel-like ground stub is presented in this paper. This MIMO antenna contains two modified Sierpinski carpet fractal elements. The designed MIMO antenna’s impedance bandwidth is 9.6 GHz (S11<─10 dB), which is ranging from 3.0-12.6 GHz. The square-shaped funnel-like ground stub and a vertical slot improved the isolation greater than 16.3 dB. The proposed antenna and discussed above UWB MIMO antenna systems are compared in Table 1. It is observed in Table 1 that the size of the designed antenna is the smallest in comparison with others. The dimension of this antenna is 24×30=720 mm2. The remaining paper is organized as follows: The dimension of the presented MIMO antenna, effects of fractal geometry, the effects of the square-shaped funnel-like ground stub on Sparameters, and effects of a slot on S-parameters are given in section 2. The results are 3
discussed in section 3 such as S-parameters comparison, 2-D radiation patterns at resonant frequencies, and realized gain. The various diversity parameters are shown in section 4 of this paper. The conclusion of the paper is given in section 5. Table 1. Comparison between reported UWB MIMO antennas and presented antenna S.
No. of
Frequency band
Min. Isolation
Size (mm2) No.
elements
1
2
2
Ref. No. (GHz)
(dB)
26×40=1040
3.1-10.6
15
[20]
2
22×36=792
3.1-11
15
[21]
3
2
40×25=1000
3.3-10.8
15
[22]
4
4
45×45=2025
2.0-10.6
17
[23]
5
2
35×40=1400
3.1-10.6
16
[24]
6
2
25×45=1125
3-12
15
[25]
7
2
30×30=900
3.08-10.98
20
[26]
8
2
24×32=768
3.1-12.5
16
[27]
9
2
20×40=800
2.5-11
20
[28]
10
4
40×40=1600
2.6-10.6
20
[29]
11
4
40×40=1600
3.1-10.6
20
[30]
12
2
32.6×46=1499.6
1.9-16.7
17
[31]
13
2
26.75×41.5=1110.12
3.1–11.5
19
[32]
14
2
30×41=1230
2.2-11
20
[33]
15
2
24×30=720
3.0-12.6
16.3
Proposed
2. Antenna design 4
2.1 Antenna configuration
Port 2
Port 1
Fig. 1. The geometry of the proposed antenna (light blue: bottom surface, dark blue: top surface). The geometry of a compact modified Sierpinski carpet fractal UWB MIMO antenna with a square-shaped funnel-like ground stub is shown in Fig. 1. The overall dimension of this antenna is 24×30 mm2. It has two identical modified Sierpinski carpet fractal radiating elements. A square-shaped funnel-like ground stub is used for proper matching and a vertical slot is cut to enhance isolation. This proposed antenna is simulated by utilizing the CST simulation tool. This presented antenna is fabricated on an FR4 substrate (height = 0.8 mm, dielectric constant=4.3, and loss tangent = 0.02) and its prototype photograph is shown in Fig. 8. The dimensions are listed in Table 2 of this antenna. Table 2. Dimensions of the presented MIMO antenna (Unit: mm) L
LP
LP1
LP2
LF
LG1
24
7
4.2
0.84 11.9 10.5
LG2
LG3
LS1
LS2
2
1
5
16
W WP WP1 WP2
WF
WG1 WG2 WG3 WS1
30 9.5
1.2
6.4
5.7
1.14
4.5
1
1
5
2.2 Effect of fractal geometry
Fig. 2. Fractal structure generation by IFS (A) Sierpinski carpet fractal structure (B) Proposed fractal structure Fractal means irregular or broken fragments. Benoit Mandelbrot originally devised the term Fractal to delineate structures that carry a self-affine or self-similar characteristics in their structures [34]. The desired miniaturization, wideband and multiband characteristics can be obtained by using fractal structures in antennas [19]. A Sierpinski carpet fractal structure [35] is a self-similar structure and its construction is shown in Fig. 2(A). In iteration-0, a rectangle is used as a base structure. Then this base structure is scaled by a factor of three from both directions, creating nine small rectangles, then one central rectangle is removed from nine small rectangles; this is iteration-1, the same steps of the previous iteration are repeated on remaining eight small rectangles; the iteration-2 is observed, shown in Fig. 2(A). A modified Sierpinski carpet fractal structure is shown in Fig. 2(B). This presented fractal structure is also designed by using a rectangle; which is an iteration-0. But here base structure is scaled by a factor of five from both directions, creating twenty-five small rectangles, then nine small central rectangles are removed from twenty-five small rectangles; this is the iteration-1. Then repeat the steps of the previous iteration on the remaining sixteen small 6
rectangles; the iteration-2 is observed as shown in Fig. 2(B). The iterated function system (IFS) is a fractal structure generation technique and it is described by the matrix equation [36–38]. Table 3 shows the proposed structure IFS transformation coefficients. a x W y c
(1)
b x e d y f
Table 3. The proposed fractal structure’s IFS transformation coefficients W
a
b c
d
e
f
0
0
1
1/5 0 0 1/5
2
1/5 0 0 1/5 1/5
0
3
1/5 0 0 1/5 2/5
0
4
1/5 0 0 1/5 3/5
0
5
1/5 0 0 1/5 4/5
0
6
1/5 0 0 1/5
7
1/5 0 0 1/5 4/5 1/5
8
1/5 0 0 1/5
9
1/5 0 0 1/5 4/5 2/5
10 1/5 0 0 1/5
0
0
0
1/5
2/5
3/5
11 1/5 0 0 1/5 4/5 3/5 12 1/5 0 0 1/5
0
4/5
13 1/5 0 0 1/5 1/5 4/5 14 1/5 0 0 1/5 2/5 4/5 15 1/5 0 0 1/5 3/5 4/5 16 1/5 0 0 1/5 4/5 4/5
7
There are many ways to define the dimension of any structure such as the Hausdorff dimension, Euclidean dimension, self-similarity dimension, and Topological dimension [39]. However, the self-similarity dimension is most commonly used because it is easy to understand. It is obtained using Equation (2). The calculation steps of the self-similarity dimension, D are reported in [40].
D
log( N ) log(1 S )
(2)
Here, N is the number of identical duplicate structures of scale down the original structure and S is the scaling factor. For the Sierpinski carpet fractal structure, N=8 and S= (1/3), hence, D is 1.89. Whereas, for the modified Sierpinski carpet fractal structure, N=16 and S= (1/5), hence, D is 1.72, which is also a fractional dimension. Hence, we can say the proposed structure is fractal. At iteration-0, the monopole element’s metallic area is 7×9.5 = 66.5 mm2, which is minimized to 52.54 mm2 and 27.238 mm2 at iteration-2 by cutting slots for the Sierpinski carpet fractal monopole element and proposed fractal monopole element, respectively. It is noticed that the metallic area of the Sierpinski carpet fractal monopole element and proposed fractal monopole element is reduced by 20.98 % and 59.04 % at iteration-2, respectively. The monopole element's average electrical length increases at higher-order iterations, like inductive loading and slot-loading as delineated in [41, 42]. It leads to antenna miniaturization.
8
Fig. 3. Monopole antennas (A) iteration-0, (B) Sierpinski carpet at iteration-2, (C) Proposed at iteration-2 Fig. 3 shows the different monopole antenna elements and their corresponding return loss curves are shown in Fig. 4. At iteration-0 of a monopole antenna, the impedance bandwidth is 6.74 GHz ranges from 4.75 GHz to 11.49 GHz. The lower and upper edges of the frequency band are shifted by the increase of iterations. The overall bandwidth of iteration-2 Sierpinski carpet fractal monopole antenna is 310 MHz more in comparison to iteration-0 monopole antenna bandwidth.
Fig. 4. Return loss curves of different monopole antennas.
9
Table 4. The comparison between Sierpinski carpet and proposed fractal structures at iteration-2. Fractal Structures
Self-Similarity
Frequency band
Metallic area
(Iteration-2)
dimension
(GHz)
minimized
Sierpinski Carpet structure
1.89
4.73-11.78
20.98 %
1.72
4.62-12.24
59.04 %
antenna Proposed fractal structure antenna
While the overall bandwidth of iteration-2 proposed monopole antenna is 880 MHz more in comparison to iteration-0 monopole antenna bandwidth and also getting dual-band characteristics. There is a generation of multiple resonances when fractal structures are used in antennas. These generated multiple resonances may be utilized to attain a wider bandwidth [23]. The overall comparison between the Sierpinski carpet and the proposed fractal structure at iteration-2 is given in Table 4. The parameters of the proposed modified Sierpinski carpet fractal structure antenna are better than the existing Sierpinski carpet structure antenna. The approximated primary resonant frequency of the presented planar monopole antenna at iteration-0 (Fig. 3(A)) is given below [43].
fr
14 . 4 A1 A2 l1 l 2 g 2 l1 re 2 l 2 re
re ( r 1) / 2
(3) (4)
10
Where l1 denotes the length of the ground plane, l 2 denotes the length of the radiation patch,
g denotes the gap between the radiation patch and the ground plane, A1 denotes the ground plane area; A2 denotes the radiation patch area and re is the effective dielectric constant. Fig. 3(A) shows the rectangular monopole antenna at iteration-0, its calculated resonant frequency is 6.7 GHz using the above equations. This is close to the simulated resonant frequency of rectangular monopole antenna at iteration-0 as shown in Fig. 4.
2.3 Effect of the ground plane
Fig. 5. Evolution structures of the ground plane
Fig. 6. S-parameters of MIMO antenna for the different ground configurations (A) S11 and (B) S21 11
Defected ground structures are the most popular techniques, especially when it comes to mutual coupling reduction between broadband and ultra-wideband MIMO antenna elements. Several review papers [44–47] are available on DGSs in the existing literature to showcase its importance while MIMO antenna designing. Actually, DGS is a defect in a ground plane, which intensely disturbs the surface current distribution. As a result, the impedance of the transmission line will change. It acts as a band stop filter and suppresses the coupled fields between the adjacent antenna elements of the MIMO antenna by decreasing the current on the ground plane [48]. Fig. 5 shows the evolution process of the ground plane for the proposed modified Sierpinski carpet fractal MIMO antenna. The simulated S-parameters of the MIMO antenna for different ground configurations are shown in Fig. 6. As antenna elements are symmetrical, so S22 and S12 are similar to S11 and S21 respectively. Therefore, only S21 and S11 parameters are shown in Fig. 6. For Ground 1, the lower cut-off frequency of S11 is 4.23 GHz (for S11 <-10 dB) and mutual coupling, S21 is above -15 dB. Whereas the required lower cut-off frequency of S11 is 3.1 GHz for the UWB systems [27] and mutual coupling, S21 should be less than -15 dB for the MIMO antennas [20]. However, the square-shaped funnel-like ground stub with a vertical slot (Ground 2) shifted the lower cut-off frequency of S11 from 4.23 GHz to 3.0 GHz. It has occurred because ground stub behaving as a reflector [20], the introduced vertical slot has improved the isolation S21 and now it is lower than -16.3 dB for the entire operating frequency range. MIMO antenna with Ground 2 is suitable for UWB applications as it is covering the frequency band ranging from 3.0 to 12.6 GHz.
12
(A)
(B) Fig. 7. Surface current distributions by exciting port-1 and terminating port-2 at (A) 3.2 GHz (B) 7.51 GHz Fig. 7 shows the effects of different ground planes on current distribution at 3.2 GHz and 7.51 GHz frequency. To analyze the surface current distribution, one port needs to be excited and the second port of the MIMO antenna needs to be terminated with a matched 50Ω load. Therefore, port-1 is excited and the port-2 of MIMO antenna is terminated with a 50Ω load in Fig. 7. It is clearly noticeable from Fig. 7 that large current is coupled towards the squareshaped funnel-like ground stub and a vertical ground slot. As a consequence, the surface current reduced near the next monopole element. It clearly indicates the reduction of mutual coupling between ports. 3.
Results and discussion The modified Sierpinski carpet fractal MIMO antenna is fabricated. The results of the
fabricated antenna are compared to corroborate the simulation results. The prototype image is shown in Fig. 8 and its results are measured using the Keysight vector network analyzer
13
(model N9916A). There is a slight variation in measured results when compared with the simulated results due to environmental setups, fabrication limitations, and SMA connectors.
Fig. 8. Fabricated proposed MIMO antenna (A) Top surface, (B) Bottom surface
Fig. 9. The S-parameters comparison of proposed antenna (A) S11, (B) S21 The comparison between measured and simulated S-parameters shown in Fig. 9. There is a slight mismatch between simulated and measured results due to fabrication limitations such as thickness and soldering of the connector as well as the improper copper etching. The impedance bandwidth and fractional bandwidth of the presented fractal MIMO antenna is 9.6
14
GHz and 123.07%, respectively. It can observe from Fig. 9 that the isolation, S21 is greater than 16.3 dB over the entire working frequency range. Further improvement in the fractional bandwidth can be done with the help of ground stub matching. The use of a slot antenna loaded with stubs increases the fractional bandwidth [49]. Also, slot antenna having CPW-feed will advocates higher fractional bandwidth. Some other general methods of increasing bandwidth are: using thick and low permittivity substrates; by introducing closely spaced parasitic patches on the same layer of the feed patch; using Stacked Parasitic patch; aperture Coupling; aperture- Coupled Stacked Patches and L-Probe Coupling. Also, the two-port antenna system having increased fractional bandwidth can be extended to build a larger array antenna having shaped beams approximated through maximally-sparse planar arrays [50]. The larger array has the benefits of better beam-steering and higher bit rate without sacrificing additional spectrum and transmitted power.
(A)
15
(B)
(C)
(D) Fig. 10. Normalized radiation patterns at (A) 3.2 GHz, (B) 4.74 GHz, (C) 7.51 GHz and (D) 11.80 GHz in both XZ (E-plane) and YZ plane (H-plane)
16
Fig. 10 shows the normalized 2D-radiation patterns of MIMO antenna for all resonant frequencies (3.20 GHz, 4.74 GHz, 7.51 GHz, and 11.80 GHz) in E-plane (XZ-plane) and Hplane (YZ-plane). The measured and simulated co-polarization and cross-polarization radiation patterns analysis for all the four resonant frequencies also presented in Fig. 10 for both the ports by exciting one port and terminating the other port by 50 Ω load impedance. The radiation patterns are omnidirectional, except few dips, especially in the YZ planes at the higher frequency. So, we are almost getting an omnidirectional pattern, which is required and desirable for better performance of the MIMO antenna. Also, The normalized radiation pattern of Co and cross-polarization shows the isolation of almost more than 20 dB in XZ plane and 15 dB in YZ plane mainly in the main lobe direction (which is slightly varying around ±900) at all the resonant frequencies, which clearly indicates that this antenna is a linearly polarized. The pattern diversity of this antenna is improving as we move from lower to the higher resonating frequency in the XZ plane of all the four frequencies as shown in Fig. 10. The realized peak gain of this antenna is shown in Fig. 11. The radiators of the proposed MIMO antenna are symmetrical in the structure; therefore both radiators gain values are similar. Hence, the realized peak gain of one radiator is shown. The measured gain varies from 2 to 4.8 dBi throughout the working frequency band ranging from 3–12.6 GHz.
17
Fig. 11. Gain Vs Frequency 4. Diversity performance The diversity performance parameters are needed to be evaluated to corroborate the ability of the presented antenna such parameters are ECC (Envelope correlation coefficient), DG (Diversity gain), MEG (Mean effective gain), and CCL (Channel capacity loss) [51]. The correlation between one antenna radiation patterns with other adjacent antenna radiation patterns can be studied as ECC. The parameter ECC should be less than 0.05 values. In uniform domain, ECC can be determined using S-parameters [52, 53] as given in equation (5). We have calculated the ECC using the far-field radiation pattern [4, 11] also as it is considered more accurate for a wideband and low-efficiency antenna. Also, the computed ECC through equation (6) will give a better realization of pattern diversity.
e
S11 S12 S 21 S 22 2
2
2 2
2
(1 ( S11 S 21 ))(1 ( S 22 S12 ))
(5)
18
ij
XPR Ei Ej P Ei Ej P d
2
XPR Ei Ei P Ei Ei P d XPR Ej Ej P Ej Ej P d
(6)
The parameter ECC computed from far-field radiation along with DG has been shown in Fig. 12. The parameter ECC of this antenna is always under the limit of 0.05 for the entire operating bandwidth [52]. The degree of effectiveness of diversity is known by diversity gain and it can be determined by using equation (7) as given in [54, 55].
DG 10 e p 10 1 e
2
(7)
10 is the maximum diversity gain at the 1% probability level with maximum-ratio combining and ep is the diversity gain reduction factor due to correlation between the signals on the two antennas (ρe is the Envelope correlation coefficient) [56, 57]. For practical applications, the parameter DG should be more than 9.95 dB [51]. The DG of this antenna is within the limit for the entire operating bandwidth. It declares that the presented antenna has a good diversity performance.
Fig. 12. ECC computed from far-field radiation along with DG Vs Frequency 19
The diversity parameter MEG measures the power received by the antenna elements in a MIMO system as compared to an isotropic antenna in a multipath fading environment under uniform Rayleigh outdoor conditions. The ratio of MEG should follow the criteria MEGi MEG j 3dB for good diversity performance [53, 55]. The terms, i and j denote
antenna elements 1 and 2, respectively. The ratio of MEG lies within the specified limit of ±3dB for the entire operating bandwidth. The MEG has been evaluated from far-field radiation as depicted in equation (8) [4, 11] and the promising result has been shown in Fig. 13.
1 XPR MEG 02 0 G , P , G , P , sin dd 1 XPR 1 XPR
(8)
Fig. 13. Measured MEG from far-field radiation The parameter CCL defines the maximum reliable data transmission rate over the communication channel. The CCL of the presented antenna is shown in Fig. 14. The minimum acceptable limit for CCL is lower than 0.4 b/s/Hz [26]. This can be evaluated by
20
using equation (9) as given in [33, 41]. The calculated CCL for the proposed antenna is within the acceptable limit. Closs log 2 det( R )
(9)
where,
12 R 11 2 2 2 2 21 22 11 1 ( S11 S12 ) 22 1 ( S 22 S 21 ) ,
,
,
12 ( S11 S12 S 21 S12 ) , 21 ( S 22 S 21 S12 S 21 )
Fig. 14. Simulated and measured CCL
5. Conclusion A compact modified Sierpinski carpet fractal UWB MIMO antenna having dimensions 24×30×0.8 mm3 has been presented, fabricated (on FR-4 Substrate) and experimentally investigated. The two modified Sierpinski carpet fractal monopole-antenna elements are used to design this antenna, which covers the UWB operations ranging from 3 GHz to 12.6 GHz
21
with a fractional bandwidth of 123.07 %. A square-shaped funnel-like ground stub with a vertical slot is used to enhance isolation better than 16.3 dB for the entire operating range. The peak gain of the proposed fractal MIMO antenna varies from 2 to 4.8 dBi over the entire UWB range. The computed ECC and CCL are less than 0.05 and 0.2 b/s/Hz respectively for the working frequency range. The computed MIMO antenna results and diversity performances are found satisfactory, which advocates its candidature for the entire UWB applications. References [1] Federal Communications Commission, Revision of Part 15 of the Commission’s rules regarding ultra-wideband transmission system from 3.1 to 10.6 GHz, Federal Communications Commission, Washington, DC, ET Docket 98-153, 2002. [2]
T. Bolin, A. Derneryd, G. Kristensson, V. Plicanic, and Z. Ying, “Two-antenna receive diversity performance in indoor environment,” IEEE Electron. Lett., vol. 41, no. 2, pp. 1205-1206, 2005.
[3] I.B. Mabrouk, L. Talbi, M. Nedil, and K. Hettak, "MIMO-UWB channel characterization within an underground mine gallery," IEEE Trans. Antennas Propag., vol. 60, no. 10, 4866-4874, 2012. [4] A. Kumar, A.Q. Ansari, B.K. Kanaujia, and J. Kishor, “A novel ITI-shaped isolation structure placed between two-port CPW-fed dual-band MIMO antenna for high isolation,” AEU – Int. J. Electron. Commun., vol. 104, pp. 35–43, 2019. [5] A. Kumar, A.Q. Ansari, B.K. Kanaujia, J. Kishor, and N. Tewari, “Design of tripleband MIMO antenna with one band-notched characteristic,” Progr. Electromagn. Res. C., vol. 86, pp. 41–53. 2018.
22
[6] T. Jiang, T. Jiao, and Y. Li, “A Low Mutual Coupling MIMO Antenna Using Periodic Multi-Layered Electromagnetic Band Gap Structures,” Applied Computational Electromagnetics Society Journal, vol. 33, no. 03, pp. 305-311, March 2018. [7] K. Yu, Y. Li, and X. Liu, “Mutual Coupling Reduction of a MIMO Antenna Array Using
3-D
Novel
Meta-material
Structures,”
Applied
Computational
Electromagnetics Society Journal, vol. 33, no. 07, pp. 758-763, July 2018. [8] S. Luo, Y. Li, Y. Xia, G. Yang, L. Sun, and L. Zhao, “Mutual Coupling Reduction of a Dual-Band Antenna Array Using Dual-Frequency Metamaterial Structure,” Applied Computational Electromagnetics Society Journal, vol. 34, no. 03, pp. 403-410, July 2018. [9] F. Liu, J. Guo, L. Zhao, G. Huang, Y. Li, and Y. Yin, "Dual-Band Metasurface-based Decoupling Method for Two Closely Packed Dual-Band Antennas," IEEE Transactions
on
Antennas
and
Propagation,
Sept.
2019.
doi:
10.1109/TAP.2019.2940316. [10] S. Luo, Y. Li, Y. Xia, and L. Zhang, “A Low Mutual Coupling Antenna Array with Gain Enhancement Using Metamaterial Loading and Neutralization Line Structure,” Applied Computational Electromagnetics Society Journal, vol. 34, no. 03, pp. 411418, March 2019. [11] A. Kumar, A.Q. Ansari, B.K. Kanaujia, J. Kishor, and S. Kumar “An Ultra-Compact Two-Port UWB-MIMO Antenna with Dual Band-Notched Characteristics,” AEU – Int. J. Electron. Commun., vol. 114, Feb. 2020. [12] I. Gnanaharan and R. Anbazhagan, “Review on the design of the isolation techniques for UWB-MIMO antennas,” Adv. Electromagn., vol. 7, no. 4, pp. 46–70, 2018.
23
[13] Y. Li, W. Li, and W. Yu, “A Multi-Band/UWB MIMO/Diversity Antenna with an Enhanced Isolation Using Radial Stub Loaded Resonator,” Applied Computational Electromagnetics Society Journal, vol. 28, no. 01, pp. 08-20, Jan. 2013. [14] S. Zhang and G. F. Pedersen, "Mutual Coupling Reduction for UWB MIMO Antennas With a Wideband Neutralization Line," IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 166-169, May 2015. [15] S. Zhang, B. K. Lau, A. Sunesson and S. He, "Closely-Packed UWB MIMO/Diversity Antenna With Different Patterns and Polarizations for USB Dongle Applications," IEEE Transactions on Antennas and Propagation, vol. 60, no. 9, pp. 4372-4380, Sept. 2012. [16] Y. Li, X. Yang, C. Liu, and T. Jiang “Miniaturization Cantor Set Fractal Ultrawideband Antenna With A Notch Band Characteristic,” Microw. Opt. Technol. Lett., vol. 54, no. 05, pp. 1227-1230, May 2012. [17] D.H. Werner, R.L. Haupt,
and P.L. Werner, “Fractal antenna engineering: The
Theory and Design of Fractal antenna Arrays,” IEEE Antennas and Propag. Mag., vol. 41, no. 5, pp. 37-58, 1999. [18] J. Anguera, C. Puente, V. Borja, and J. Soler, “Fractal-shaped antennas: A review, Encyclopaedia of RF and microwave engineering,” Wiley. Hoboken, NJ, vol. 2, pp. 1620–1635, 2005. [19] M.R. Haji-Hashemi, H. Mir-Mohammad Sadeghi, and V.M. Moghtadai, “Spacefilling patch antennas with CPW feed,” Progr Electromagn Res., vol. 2, no. 1, pp. 69– 73, 2006. [20] L. Liu, S.W. Cheung, and T.I. Yuk, “Compact MIMO antenna for portable devices in UWB applications,” IEEE Trans Antennas Propag., vol. 61, no. 8, pp. 4257–4264, 2013.
24
[21] L. Liu, S.W. Cheung, and T.I. Yuk, “Compact MIMO antenna for portable UWB applications with band-notched characteristic,” IEEE Trans. Antennas Propag., vol. 63, no. 5, pp. 1917-1924, 2015. [22] S. Tripathi, A. Mohan, and S. Yadav, “A compact octagonal fractal UWB MIMO antenna with WLAN band rejection,” Microw Opt Technol Lett., vol. 57, pp. 1919– 1925, 2015. [23] S. Tripathi, A. Mohan, and S. Yadav, “A Compact Koch Fractal UWB MIMO Antenna with WLAN Band-Rejection,” IEEE Antennas and Wireless Propagation Letters, vol. 14, pp. 1565–1568, 2015. [24] S. Zhang, Z. Ying, J. Xiong, and S. He, “Ultrawideband MIMO/Diversity antennas with a tree-like structure to enhance wideband isolation,” IEEE Ant. Wireless Propag. Letters, vol. 8, pp. 1279-1282, 2009. [25] R. Mathur, and S. Dwari, “Compact CPW‐fed ultrawideband MIMO antenna using hexagonal ring monopole antenna elements,” AEU ‐ Int J Electron Commun, vol. 93, pp. 1‐6b, 2018. [26] S.P. Biswal, and S. Das S, “A low‐profile dual port UWB‐MIMO/diversity antenna with band rejection ability,” Int. J. RF Microw Comput Aided Eng., vol. 28, no. 1, e21159, 2017. [27] R. Gurjar R, D.K. Upadhyay, B.K. Kanaujia, and K. Sharma, “A Novel Compact Self-Similar Fractal UWB MIMO Antenna,” Int. J. RF Microw Comput Aided Eng., e21632, 2018. [28] R. Sampath, and K.T. Selvan, “Compact hybrid Sierpinski Koch fractal UWB MIMO antenna with pattern diversity,” Int. J. RF Microw Comput Aided Eng, e22017, 2019.
25
[29] S. Rajkumar, K.T. Selvan, and P.H. Rao, “Compact 4 element Sierpinski Knopp fractal UWB MIMO antenna with dual band notch,” Microw Opt Technol Lett, vol. 60, pp. 1023-1030, 2018. [30] S. Rajkumar, A. Anto Amala, and K.T. Selvan, “Isolation improvement of UWB MIMO antenna utilising molecule fractal structure,” Electronics letters, vol. 55, no. 10, pp. 576-579, 2019. [31] R. Kumar, and G. Surushe, “Design of microstrip-fed printed UWB diversity antenna with tee crossed shaped structure,” Eng. Sci. Technol. Int. J. (JESTECH). Vol. 19, no. 2, pp. 946–955, 2016. [32] J. Banerjee, A. Karmakar, R. Ghatak, and D.R. Poddar, “Compact CPW-fed UWB MIMO antenna with a novel modified Minkowski fractal defected ground structure (DGS) for high isolation and triple band-notch characteristic,” Journal of Electromagnetic Waves and Applications, vol. 31, no. 15, pp. 1550-1565, 2017. [33] A. Gorai, A. Dasgupta, and R. Ghatak, “A Compact quasi-self-complementary Dual Band Notched UWB MIMO Antenna with enhanced isolation using Hilbert fractal slot,” AEU-Int. J. Electron Comm., vol. 94, pp. 36-41, 2018. [34] B.B. Mandelbrot, “The fractal geometry of nature,” W. H. Freeman New York. 1983. [35] H.O. Peitgen, H. Jurgens, and D. Saupe, “Chaos and fractals: New frontiers in science,” Springer-Verlag New York. 1992. [36] S.N. Sinha, and M. Jain, “A self-affine fractal multiband antenna,” IEEE Antennas and Wireless Propag. Lett., vol. 6, pp. 110-112, 2007. [37] R. Gurjar, R. Singh, and S. Kumar, “Elliptically slotted self-affine 8-shaped fractal multiband antenna,” Proceedings of the Int. Conf. on Recent Cognizance in Wireless Comm. & Image Processing Springer, Jaipur, India, pp. 783-78, 2016.
26
[38] R. Gurjar, D.K. Upadhyay, and B.K. Kanaujia, “Compact four-element 8-shaped selfaffine fractal UWB MIMO antenna,” IEEE International Microwave and Photonics Conference Preceedings, Dhanbad, India, pp. 1-2, 2018. [39] K.J. Vinoy, J.K. Abraham, and V.K. Varadan, “On the relationship between fractal dimension and the performance of multi-resonant dipole antennas using Koch curves,” IEEE Trans Antenna Propag., vol. 51, no. 9, pp. 2296-2303, 2003. [40] Y.K. Choukiker, S.K. Sharma, and S.K. Behera, “Hybrid fractal shape planer monopole antenna covering multiband wireless communications with MIMO implementation for handheld mobile devices,” IEEE Trans Antenna Propag., vol. 62, pp. 1483-1488, 2014. [41] S. Reed, L. Desclos, C. Terret, and S. Toutain, “Patch antenna size reduction of a patch antenna by means of inductive loads,” Microw. Opt. Technol. Lett., vol. 29, no. 2, pp. 79–81, 2001. [42] L. Desclos, “Size reduction of patch by means of slots insertion,” Microw. Opt. Technol. Lett., vol. 25, no. 2, pp. 111–113, 2000. [43] K.G. Thomas, M. Sreenivasan, “A simple ultrawideband planar rectangular printed antenna with band dispensation,” IEEE Trans Antennas Propag., vol. 58, no. 1, pp. 27-34, 2010. [44] M. K. Khandelwal, B. K. Kanaujia and S. Kumar, “Defected Ground Structure: Fundamentals, Analysis, and Applications in Modern Wireless Trends,” Int. J. Antennas Propag., vol. 2017, Article ID 2018527, 22 pages, 2017. [45] J. G. Webster, M. S. Bhuiyan and N. C. Karmakar, “Defected Ground Structures for Microwave Applications,” In Wiley Encyclopedia of Electrical and Electronics Engineering, J. G. Webster (Ed.), Jan. 2014.
27
[46] L. H. Weng, Y.-C. Guo, X.-W. Shi, and X.-Q. Chen, "An Overview on Defected Ground Structure," Progr. Electromagn. Res. B, vol. 7, pp. 173-189, 2008. [47] G. Breed, “An Introduction to Defected Ground Structures in Microstrip Circuits,” High Frequency Electronics, Summit Technical Media, pp. 50-54, 2008. [48] M.S. Sharawi, “Printed MIMO antenna engineering,” Artech House, Norwood, MA, USA, 2014. [49] J. Lin and Q. Chu, "Increasing Bandwidth of Slot Antennas With Combined Characteristic Modes," IEEE Transactions on Antennas and Propagation, vol. 66, no. 6, pp. 3148-3153, June 2018. [50] A. F. Morabito, "Power synthesis of mask-constrained shaped beams through maximally-sparse planar arrays," Telkomnika (Telecommunication Computing Electronics and Control), vol. 14, no. 4, pp. 1217-1219, 2016. [51] G. Das, A. Sharma, and R.K. Gangwar, “Dual port aperture coupled MIMO cylindrical dielectric resonator antenna with high isolation for WiMax application,” Int. J. RF Microw., vol. 27, no. 7, pp. 1-10, 2017. [52] H.S. Singh, G.K. Pandey, P.K. Bharti, and M.K. Meshram, “Design and performance investigation
of
a
low
profile
MIMO/Diversity
antenna
for
WLAN/WiMAX/HIPERLAN applications with high isolation,” Int. J. RF Microw., vol. 25, pp. 510–521, 2015. [53] A. Kumar, A.Q. Ansari, B.K. Kanaujia, and J. Kishor, “High isolation compact fourport MIMO antenna loaded with CSRR for multiband applications,” Frequenz, vol. 72, pp. 415–427, 2018. [54] J. Nasir, M.H. Jamaluddin, M. Khalily, M.R. Kamarudin, I. Ullah, and R. Selvaraju, “A reduced size dual port MIMO DRA with high isolation for 4 G applications,” Int. J. RF Microwave Comp Aid. Eng., vol. 25, no. 6, pp. 495–501, 2014.
28
[55] R. Chandel, A.K. Gautam, and K. Rambabu, “Tapered fed compact UWB MIMOdiversity antenna with dual band-notched characteristics,” IEEE Trans. Antennas Propag, vol. 66, no. 4, pp. 1677–1684, 2018. [56] S. Singh, B. Meruva, G.K. Pandey, P.K. Bharti, and M.K. Meshram, “Low mutual coupling between MIMO antennas by using two folded shorting strips,” Prog Electromagn Res B, vol. 53, pp. 205-221, 2013. [57] J.N. Pierce, and S. Stein, “Multiple diversity with non-independent fading," IRE Proc., vol. 48, pp. 89-104, Jan. 1960.
29