Design and Analysis of Four Element MIMO Antenna for Broadband Applications

Abstract

A 2 × 2 (four-element) elliptical-shaped with hexagonal slot, self-isolated Multiple Input Multiple Output (MIMO) antenna system is proposed for the 3.43–22.7 GHz broadband application. The proposed geometry uses T-shaped stub placed diagonally on a ground plane to decouple the antenna element's radiation fields at lower frequencies. The proposed MIMO antenna size is 2.069λgx2.069λg; however, the size of the single elliptical element is 0.707λgx0.587λg. At 17.2 GHz, the maximum realized gain for the single element is 5 dBi. The MIMO antenna shows good diversity properties with isolation of more than −20 dB, envelope correlation coefficient (< 0.1), diversity gain (̴ 10 dB), mean effective gain ratio (≤ 3 dB), total active reflection coefficient (< −5 dB), and channel capacity loss (≤ 0.5 b/s/Hz) for the entire frequency bandwidth. The MIMO antenna is designed, fabricated, and experimentally verified. The measured and simulated results are in good agreement.

Keywords

elliptical antenna multiple-Input multiple-Output (MIMO) systems pattern diversity planar monopole slot ultra-wideband (UWB)super-wideband (SWB)‌

Introduction

MIMO systems mitigate multipath fading in wireless channels by transmitting the data stream through multiple antennas from the transmitter and received via multiple antennas at the receiver.¹ The MIMO system needs to place the antenna elements close enough to offer less correlation, high isolation, and hence high diversity gain. MIMO wireless communication systems using multiple antennas can increase system capacity for multipath communication channels.² Several applications require compact antenna arrays. The insufficient spacing between the antenna elements lead to increase mutual coupling, which reduces their efficiency and degrades the signal-to-noise ratio. Comparison of different compact array configurations for the MIMO system with spatial, polarization, and pattern diversity are presented in.³ The UWB spectrum is allocated the unlicensed frequency band from 3.1–10.6 GHz.⁴ Maintaining spacing and isolation between antenna elements for the ultra-wideband frequency range remains challenging. Such MIMO antenna system utilizes different decoupling structures located on the ground or in the plane of the radiator. In,⁵ pattern diversity is proposed where, to increase the isolation of two perpendicular radiating elements, two long stubs and a small strip is added to the ground plane. In,⁶ neutralization lines are connected to attain good impedance matching and less mutual coupling for the two adjacent crescent-shaped radiators. In,⁷ for good isolation, a metamaterial absorber is investigated amongst the antenna elements. In,⁸ four slots are etched in the ground to improve the isolation between antenna elements for smartphone applications. In,⁹ carbon black films enhance the isolation and absorb interference from two or more antenna elements. In,¹⁰ a common radiating element fed by four microstrip feedlines is presented in which ring-shaped ground with four slots on each corner is employed to mitigate the mutual coupling. In,¹¹ orthogonally placed dragonfly-shaped radiators with stepped ground planes are presented where cross-coupling is reduced using a circular stub in the center of the cross shaped microstrip line. In,¹² the MIMO system for ISM bands is presented in which CSRRs (complementary split ring resonator) are used in the ground plane for miniaturization of the radiating element. In,¹³ the mutual coupling is reduced by the neutralization ring structure combining rectangular ring and straight strip line for the four-port triangular radiators. In,¹⁴ three notched band MIMO antenna system is studied in which spacing and orthogonal placement of the radiators are used for isolation. In,¹⁵ the isolation of the two or four-element MIMO antenna array is enhanced using a decoupling circuit based on a second-order filter. In,¹⁶ three highly selective notch bands and a parasitic decoupler are presented. In,¹⁷ parasitic elements that increase isolation, bandwidth, and gain are presented for the MIMO antenna system with circular polarization. In,¹⁸ the mushroom EBG (Electromagnetic band gap) structure isolates and rejects multiple interferences. In,¹⁹ good isolation is achieved by polarization diversity, parasitic elements, and protruded ground.

In this paper, a novel four-element MIMO antenna system is presented with better port-to-port isolation due to antenna placement and excitation method. Antenna parameters like frequency bandwidth, surface current distribution, efficiency, gain, and radiation pattern characterize the performance of each antenna element. MIMO system uses multiple antennas and hence requires more parameters for investigation like envelope correlation coefficient (ECC), diversity gain (DG), multiplexing efficiency (ME), mean effective gain (MEG), total active reflection coefficient (TARC), channel capacity loss (CCL), etc. to assess the effect of adjacent elements on the MIMO system performance.

Design of Elliptical Monopole MIMO Antenna

A printed elliptical monopole antenna (PEMA) is first designed on the substrate material DiClad880 with height h = 0.508 mm, permittivity ε_r= 2.2 and loss tangent 0.009 using the CST Studio suite. The elliptical monopole antenna (EP₁) structure having dimensions W × L is illustrated in Figure 1(a) designated as Ant.1. Elliptical radiator has dimensions E_a, E_b with feedline L_f ×W_f, ground plane size is G × W. The magnitude of surface current in the case of monopole radiators is maximum at the point the feed line connects the monopole and reduces as one moves towards the center of the monopole and away from the feed. Surface current magnitude is negligibly smaller at the center of the monopole if there is no discontinuity. Therefore, the structure is modified by creating a slot at the center of the elliptical monopole. Figure 1(b) shows Ant.2, where a hexagon slot is etched on the elliptical element EP₁. The slot radius is R, equal to a regular hexagon's side length. The dimensions of the Ant.2 are the same as Ant.1 except for a hexagon slot introduced at the center of the elliptical element. A printed elliptical monopole antenna's lower band edge frequency can be determined by equation (1), as given in.²⁰

f_{l} = \frac{7.2}{(l + r + p) \times 0.1 \times k} G H z

(1)

Figure 1.

Geometry of proposed MIMO antenna (a) Ant. 1 (b) Ant. 2 (c) Ant. 3 (d) Ant. 4.

Where l = 2×E_b; r = E_a/4; p = L_f - G; k = √ε_eff, which gives a lower band edge frequency of 2.6 GHz. Further, a MIMO antenna structure is designed using four Ant.2 elements. Mutual coupling among the closely placed elements is an essential concern in MIMO antenna design. Achieving higher isolation over a broad bandwidth is a challenge. Ant.2 elements are placed orthogonal to each other so that radiated field from one element will not couple with other elements, providing high isolation. Four Ant. 2 elements are identified with equal radiator and ground plane dimensions, i.e., E_a, E_b, L_f× W_f, and this structure is designated as Ant. 3. The substrate size of this MIMO antenna is L₁×W₁, as shown in Figure 1(c). The ports are excited using a right angle, 50Ω SMA connector from the central section of A₁ × A₂. MIMO antenna structure Ant.4 is shown in Figure 1(d), where four T-shaped stubs are added in Ant.3 at four corners. T-shaped stubs are placed at each corner of the ground plane to increase the current path length so that the current flowing through a common ground plane and coupling to another element can be reduced.

The optimized dimensions of the elliptical antennas from Ant.1 to Ant.4 are listed in Table 1. The simulated reflection coefficient for the elliptical-shaped single-element EP₁ with and without the hexagonal slot is shown in Figure 2(a). Ant.1 offers |S₁₁|< -10 dB impedance bandwidth from 2.7 GHz–30 GHz. Although the reflection coefficient of Ant.1 shows an increase in value beyond 20 GHz, the standing wave ratio is nearly equal to 2. Interestingly Ant.2 has an impedance bandwidth from 2.7 GHz–20 GHz due to the hexagonal slot. The current distribution for Ant.1 and Ant.2 at 20 GHz is also shown in Figure 2(b). The magnitude of the surface current is observed to be modified due to the hexagonal slot.

Figure 2.

(a) reflection coefficient (b) Ant.1 and Ant. 2 surface current distribution at 20 GHz.

Table 1.

Dimension of the Antenna Prototype (mm).

L	W	L_f	W_f	E_a	E_b	R	G	A1
44	53	19.20	1.4	16	10.62	6	19	34
A2	L1	W1	L2	W2	S1	S2	S3	S4
34	122	122	72	72	5.5	9	3	1

A parametric study of antenna size variation for Ant.3 is shown in Figure 3(a). When the port opening area size changes from 15 to 34 mm², MIMO antenna size varies from 103 to 122 mm², respectively.

Figure 3.

(a) antenna size optimization for Ant.3 (b) s parameters plot of Ant.3 and Ant.4.

A comparison of the S parameters for Ant.3 and Ant.4 is shown in Figure 3(b). It can be seen that Ant.3 offers an impedance bandwidth from 2.7 GHz to 22.5 GHz, but due to the T-shaped stub, the |S₁₁| < -10 dB impedance bandwidth changes from 3.43 GHz to 22.7 GHz for Ant.4. Isolation between port 1 to port 4 is more than 20 dB for the entire bandwidth as both are more than half wavelength apart. Port 1 to port 2 and port 1 to port 3 are equidistant and have similar isolation characteristics. Ant.3 and Ant.4 have more than 15 dB and 20 dB isolation (|S₂₁|) at frequencies 3.84 GHz and 2.7 GHz onwards, respectively. It is due to the T-shaped stub resonating at 3.38 GHz, which provides further isolation for Ant.4 at lower frequencies. It can be further understood using surface current distribution. At the resonant frequency of 3.38 GHz, the current distribution for the MIMO Ant.3 and Ant.4 is depicted in Figure 4. The T-shaped stub resonates at this frequency & thus, no current is coupled to the other elements. This improves the isolation among the ports to 20 dB. Hence Ant.4 is a more suitable MIMO antenna design having −20 dB isolation for the whole frequency range. The comparison of the characteristics of the elliptical monopole MIMO antenna is summarized in Table 2.

Figure 4.

Current distribution of the MIMO antenna design at 3.38 GHz; (a) Ant.3 (b) Ant.4.

Table 2.

Summary of the Evolution of Elliptical Monopole MIMO Antenna.

Antenna	Size(mm³)	Impedance Bandwidth	Isolation\|S₂₁\| or \|S₃₁\|
Ant.1	44 × 53	2.7 GHz to 30 GHz	-
Ant.2	44 × 53	2.7 GHz to 20 GHz	-
Ant.3	122 × 122	2.7 GHz to 22.5 GHz.	< -15 dB, 3.84 GHz onwards
Ant.4	122 × 122	3.43 GHz to 22.7GHz	< -20 dB, 2.7 GHz onwards

MIMO Antenna Parameters

Simulation results are taken to calculate the MIMO antenna parameters discussed below.

Envelope Correlation Coefficient: ECC is determined from the far field pattern according to formulas given in equation (2) as referred from.^21,22

ρ_{e n v} = \frac{{| \oint {X P R . E_{θ 1} (Ω) E_{θ 2} * P_{θ} (Ω) + E_{ϕ 1} (Ω) E_{ϕ 2} * P_{ϕ} (Ω)} d Ω |}^{2}}{\begin{matrix} (\oint {X P R . E_{θ 1} (Ω) E_{θ 1} * P_{θ} (Ω) + E_{ϕ 1} (Ω) E_{ϕ 1} * P_{ϕ} (Ω)} d Ω) \times \\ (\oint {X P R . E_{θ 2} (Ω) E_{θ 2} * P_{θ} (Ω) + E_{ϕ 2} (Ω) E_{ϕ 2} * P_{ϕ} (Ω)} d Ω) \end{matrix}}

(2)

where XPR is the cross-polarization ratio of vertical and horizontal components,

P_{θ} (Ω)

and

P_{ϕ} (Ω)

are Gaussian distributions,

E_{θ i} (Ω)

and

E_{ϕ i} (Ω)

are field radiation patterns of the antenna where the i^th port excited and other ports are kept terminated to a matched load. Calculation of these parameters included elevation Gaussian and azimuthal uniform distribution as per the condition described in²⁵ for isotropic, indoor, and outdoor environments. The ECC for the different elements in the proposed structure is plotted as shown in Figure 5(a). The correlation coefficient value should be less than 0.5 for good diversity performance of the MIMO antenna system & the proposed design has ECC < 0.1 for the entire frequency band.

Figure 5.

Plot of (a) ECC and DG (b) ME (c) TARC (d) CCL for the MIMO antenna.

Diversity Gain: DG is related to the correlation coefficient, calculated according to the formula given in equation (3) as referred from.²¹

D G = 10. \sqrt{(1 - ρ_{e n v})}

(3)

The plot of diversity gain vs. frequency is depicted in Figure 5(a). The diversity gain value should be equal to 10 dB for a good diversity performance of the MIMO antenna system, which is achieved for the proposed design.

Multiplexing Efficiency: It is related to envelope correlation and the total efficiencies of the two antennas according to equation (4), as referred from.²³

M E = \sqrt{η_{1} η_{2} (1 - ρ_{e n v})}

(4)

The plot of multiplexing efficiency is shown in Figure 5(b). It can be inferred that multiplexing efficiency is more than 95 percent for the entire bandwidth.

Mean Effective Gain: The mean received power to mean incident power ratio (MEG) of the MIMO antenna is described using equation (5) as given in.^12,21,24

M E G_{i} = \int_{0}^{2 π} \int_{0}^{π} {\begin{matrix} \frac{X P R}{1 + X P R} G_{θ} (θ, ϕ) P_{θ} (θ, ϕ) + \\ \frac{1}{1 + X P R} G_{ϕ} (θ, ϕ) P_{ϕ} (θ, ϕ) \sin θ d θ d ϕ \end{matrix}}

(5)

XPR denotes cross-polarization power ratio, G_θ(θ, ∅) and G_∅(θ,∅) the antenna power gain pattern, P_θ(θ,∅) and P_∅(θ,∅) are angular density functions of the incoming plane waves. The MIMO antenna system's MEG for each element is tabulated in Table 3. MIMO system performs well when the condition is fulfilled, i.e.,

| M E G_{i} / M E G_{j} | \leq 3 d B

. MEG values for different ports of the MIMO system are tabulated for the isotropic (XPR = 0 dB) and indoor (XPR = 5 dB) environments. It can be noted from the table that the ratio of MEG between two different ports is almost unity.

Table 3.

MEG of the MIMO Antenna Design.

Center Frequency (GHz)	Mean Effective Gain in dB, XPR = 0dB				Mean Effective Gain in dB, XPR = 5dB
Center Frequency (GHz)	EP₁	EP₂	EP₃	EP₄	EP₁	EP₂	EP₃	EP₄
4.45	−5.75	−5.75	−5.75	−5.78	−6.89	−6.87	−6.89	−6.94
8.54	−2.92	−2.92	−2.92	−2.91	−5.30	−5.30	−5.30	−5.29
10.64	−3.11	−3.10	−3.11	−3.09	−4.85	−4.85	−4.85	−4.83
14.32	−2.50	−2.50	−2.50	−2.49	−4.12	−4.11	−4.12	−4.12

Total Active Reflection Coefficient: It is a ratio of square root of total reflected power to square root of the total incident power of multi-port MIMO antenna system. S parameters for the MIMO antenna system are used to calculate it. TARC for N-element MIMO antenna is given by equation (6), as referred from.^12,21,26

Γ_{a}^{t} = \sqrt{{Σ {| b_{i} |}^{2}}_{i = 1}^{N}} / \sqrt{{Σ {| a_{i} |}^{2}}_{i = 1}^{N}}

(6)

Where

a_{i}

is incident signals and

b_{i}

is reflected signals. The incident and reflected waves in a multi-port network with comparable characteristic impedances at all ports are related as given in equation (7)

b = S a

(7)

where S represents S parameter matrix of N × N for the N port MIMO antenna. b, a, and S are vector quantities having magnitude and phase value. Figure 5(c) shows the condition when port 1 is excited with phase θ = 0^o, but other ports have different phases.

Channel Capacity Loss: MIMO antenna systems are assumed to provide good channel capacity, but due to correlation in MIMO channels increases capacity loss. It can be inferred as channel capacity for the multi-port system increases for lower values of correlation coefficient.^21,27 Channel capacity loss for the four-element MIMO is given by equation (8)

C C L = - \log_{2} det (Ψ^{R})

(8)

where

Ψ^{R} = [\begin{matrix} ρ_{11} & ρ_{12} & ρ_{13} & ρ_{14} \\ ρ_{21} & ρ_{22} & ρ_{23} & ρ_{24} \\ ρ_{31} & ρ_{32} & ρ_{33} & ρ_{34} \\ ρ_{41} & ρ_{42} & ρ_{43} & ρ_{44} \end{matrix}], ρ_{i i} = 1 - | \sum_{n = 1}^{N} s_{i, n}^{*} s_{n, i} | & ρ_{i j} = - | \sum_{n = 1}^{N} s_{i, n}^{*} s_{n, j} |

where i,j = 1,2,3,4, N = No of antenna element, Ψ^R is N × N Matrix. CCL (b/s/Hz) against the frequency plot is depicted in Figure 5(d). It can be verified from the plot that CCL is ≤ 0.4 b/s/Hz for the frequency range 3.7 – 21.6 GHz. The TARC and CCL parameters are computed and plotted using MATLAB software.

Results and Discussions

MIMO antenna system is designed and simulated using CST Microwave Studio suite. It is then fabricated using printing and chemical etching processes. S parameter measurement is accomplished using Agilent E5071C Network Analyzer, ENA series. The fabricated MIMO antenna prototype side view and bottom view are shown in Figure 6(a). S parameter comparison for the proposed MIMO antenna system is depicted in Figure 6(b). Adding T-shaped stub in the ground plane enhances isolation at the 3.38 GHz resonance frequency. The measured impedance bandwidth is observed from the 3.43–20 GHz frequency range.

Figure 6.

(a) fabricated prototype (b) s parameters of the MIMO antenna (c) realized gain and radiation efficiency of the MIMO antenna.

Antenna Radiation pattern measurement is carried out in the Anechoic chamber. Simulated gain is compared with measured gain and plotted as shown in Figure 6(c). The maximum realized gain is 5 dBi at frequency 17.2 GHz. Radiation efficiency is more than 95% for the whole bandwidth. Simulated and measured radiation patterns at ∅ = 0⁰ and ∅ = 90⁰ planes are drawn for the resonant frequencies of 4.45 GHz, 8.54 GHz, 10.64 GHz, and 14.32 GHz, respectively, illustrated in Figure 7. Port 1 is excited for the radiation pattern measurement and other ports are terminated to a matched load. It can be inferred from the plot that the MIMO antenna is linearly polarized with low cross-polarization levels. Performance of the proposed structure with other references is tabulated in Table 4. The proposed structure offers comparable results compared to other state of the art references.

Figure 7.

Simulated and measured radiation characteristics of the MIMO antenna at frequency. (a) 4.45 GHz (b) 8.54 GHz (c) 10.64 GHz (d) 14.32 GHz

Table 4.

Performance Comparison of the Proposed MIMO Antenna with the Previous Reported Works.

Ref.	$f_{l} - f_{h}$ (GHz)	Size (λg³)	Isolation Method	Isolation	Gain
¹³	3.1–17.3	1.630 × 1.630 × 0.035 Four Element	Neutralization ring structure	S₂₁<-15.9 dB, S₃₁<-13.5dB	1–5 dBi
¹⁴	2.6–12.2	0.654 × 0.636 × 0.029 Four Element	Orthogonal placement and spacing	<-17dB	3.1 dBi
¹⁶	3.1–11.8	0.827 × 0.827 × 0.023 Four Element	Parasitic decoupling structure	<-20dB	6.35 dBi
¹⁹	3.1–13.1	0.975 × 0.975 × 0.035 Four Element	Protruded ground, parasitic elements	<-17dB	4 dBi
This work	3.43–22.7	2.069 × 2.069 × 0.009 Four Element	Port to port isolation & T-shaped stubs at ground	<-20dB	3–5 dBi

Conclusion

A MIMO antenna with a self-isolated structure is presented for broadband application. The prototype consists of four antenna elements placed opposite & perpendicular to each other to achieve good isolation. Four T-shaped stubs are placed in the corners at the ground plane to further isolate antenna elements in the lower frequency. Simulation and measured results show that the proposed configuration operates for a frequency range from 3.43 GHz-22.7 GHz with more than 20 dB isolation. The proposed MIMO antenna has a 19.27 GHz impedance bandwidth and fractional bandwidth of 147.49%, which comes under Ultra-Wide bandwidth. It has good diversity properties with isolation < -20 dB, ECC < 0.1, DG ̴ 10 dB, MEG ratio ≤ 3 dB, TARC < -5 dB, and CCL ≤ 0.5 b/s/Hz for the whole frequency range. The maximum realized gain is 5 dBi at a frequency of 17.2 GHz. Antenna efficiency is more than 95% for the entire bandwidth. The self-isolating configuration provides minimum isolation between antenna elements which is further improved using a stub in the ground plane. The proposed arrangement finds prospective application in various UWB/SWB systems.

Footnotes

Authors’ note

Ramswaroop Tiger is currently affiliated with Prasar Bharati, Doordarshan Kendra, Raipur, Chhattisgarh, India.

ORCID iDs

Shilpa Kharche

Biswajeet Mukherjee

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Sharawi

. Printed MIMO Antenna Engineering. Norwood, MA: Artech House, 2014.

Jensen

Wallace

. A review of antennas and propagation for MIMO wireless communications. IEEE Trans Antennas Propag 2004; 52: 2810–2824.

Waldschmidt

Kuhnert

Schulteis

, et al. Analysis of compact arrays for MIMO based on complete RF system model. 2003 IEEE Top Conf Wirel Commun Technol 2003; 53: 286–287.

Federal Communications Commission revision of Part 15 of the commission’s rules regarding ultrawideband transmission systems (2002) FCC, Washington, DC, First Report and Order FCC, 02. V48.

Liu

Cheung

Yuk

. Compact MIMO antenna for portable devices in UWB applications. IEEE Trans Antennas Propag 2013; 61: 4257–4264.

See

Abd-alhameed

Abidin

, et al. Wideband printed MIMO / diversity monopole antenna for WiFi / WiMAX applications. IEEE Trans Antennas Propag 2012; 60: 2028–2035.

Garg

Jain

. Isolation improvement of MIMO antenna using a novel flower shaped metamaterial absorber at 5.5 GHz WiMAX band. IEEE Trans Circuits Syst II Express Briefs 2020; 67: 675–679.

Ikram

Sharawi

Shamim

, et al. A multiband dual-standard MIMO antenna system based on monopoles (4G) and connected slots (5G) for future smart phones. Microw Opt Technol Lett 2018; 60: 1468–1476.

Lin

Sung

Chen

, et al. Isolation improvement in UWB MIMO antenna system using carbon black film. IEEE Antennas Wirel Propag Lett 2017; 16: 222–225.

10.

Moradi Kordalivand

Rahman

Khalily

. Common elements wideband MIMO antenna system for WiFi/LTE access-point applications. IEEE Antennas Wirel Propag Lett 2014; 13: 1601–1604.

11.

Kaboutari

Hosseini

. A compact 4-element printed planar MIMO antenna system with isolation enhancement for ISM band operation. AEU - Int J Electron Commun 2021; 134: 153687.

12.

Sharawi

Khan

Numan

, et al. A CSRR loaded MIMO antenna system for ISM band operation. IEEE Trans Antennas Propag 2013; 61: 4265–4274.

13.

Kayabasi

Toktas

Yigit

, et al. Triangular quad-port multi-polarized UWB MIMO antenna with enhanced isolation using neutralization ring. AEU - Int J Electron Commun 2018; 85: 47–53.

14.

Pannu

Sharma

. Miniaturize four-port UWB-MIMO antenna with tri-notched band characteristics. Microw Opt Technol Lett 2021; 63: 1489–1498.

15.

Singh

Tripathi

Mohan

. Closely-coupled MIMO antenna with high wideband isolation using decoupling circuit. AEU - Int J Electron Commun 2021; 138: 153833.

16.

Abbas

Hussain

Sufian

, et al. Highly selective multiple-notched UWB-MIMO antenna with low correlation using an innovative parasitic decoupling structure. Eng Sci Technol an Int J 2023; 43: 101440.

17.

Kim-Thi

Hung Tran

Tu Le

. Circularly polarized MIMO antenna utilizing parasitic elements for simultaneous improvements in isolation, bandwidth and gain. AEU - Int J Electron Commun 2021; 135: 153727.

18.

Modak

Khan

. A slotted UWB-MIMO antenna with quadruple band-notch characteristics using mushroom EBG structure. AEU - Int J Electron Commun 2021; 134: 153673.

19.

Zhao

Zhang

, et al. A compact four-port MIMO antenna for UWB applications. Sensors 2022; 22: 5788.

20.

Ray

. Design Aspects of Printed Monopole Antennas for Ultra-Wide Band Applications 2008;2008. https://doi.org/10.1155/2008/713858 .

21.

Sharawi

. Printed multi-band MIMO antenna systems and their performance metrics [wireless corner]. IEEE Antennas Propag Mag 2013; 55: 218–232.

22.

Sharawi

Hassan

Khan

. Correlation coefficient calculations for MIMO antenna systems: a comparative study. Int J Microw Wirel Technol 2017; 9: 1991–2004.

23.

Tian

Lau

Ying

. Multiplexing efficiency of MIMO antennas. IEEE Antennas Wirel Propag Lett 2011; 10: 183–186.

24.

Taga

. Analysis for mean effective gain of mobile antennas in land mobile radio environments. IEEE Trans Veh Technol 1990; 39: 117–131.

25.

Karaboikis

Papamichael

Tsachtsiris

, et al. Integrating compact printed antennas onto small diversity/MIMO terminals. IEEE Trans Antennas Propag 2008; 56: 2067–2078.

26.

Chae

Park

. Analysis of mutual coupling, correlations, and TARC in WiBro MIMO array antenna. IEEE Antennas Wirel Propag Lett 2007; 6: 122–125.

27.

See

Abd-Alhameed

Abidin

, et al. Wideband printed MIMO/diversity monopole antenna for WiFi/WiMAX applications. IEEE Trans Antennas Propag 2012; 60: 2028–2035.