Formulation of the proposed antenna

The proposed two-port radiator configuration consists of two ceramic cylindrical dielectric resonators (CDR) made up of alumina (ɛ_r = 9.8), mounted upon a FR-4 substrate (ɛ_r = 4.4). The two resonators are energized with a microstrip feed line through a rectangular slot and are offset-fed to enhance the coupling between the alumina ceramic resonator and aperture. The length of the feed line is obtained through optimization. An interdigital-shaped and semicircular arc-shaped DGS enhances the isolation between two radiators and controls the operating band. Figure 1 represents the proposed structure of a two-port DRA. Figure 2 represents the fabricated two-port MIMO radiator. The antenna dimensions have been depicted in Table 1.

Figure 1. Structure of the proposed two-port radiator: (a) 3D view, (b) Top view.

Figure 2. Fabricated antenna: (a) Top View, (b) Bottom View.

Table 1. Dimensions of proposed two-port MIMO antenna

Antenna analysis

The proposed two-port radiator has been simulated and examined using electromagnetic simulation software called HFSS. Stage-by-stage analysis of the two-port radiator is illustrated in Figs. 3–11. Initially, DRs were excited through the center-feed with the aid of a rectangular aperture, which is named Antenna-1, as displayed in Fig. 3. The frequency band was obtained 5.57–6.15 GHz having a reflection coefficient −17 dB for Port-1 at the resonant frequency of 5.84 GHz. This antenna suffered poor band coverage, poor reflection coefficient, and poor isolation. In the next step, the DRs were excited through the offset feeding technique as shown in Fig. 4, and named Antenna-2. The reflection coefficient and isolation were improved to −23.2 and −22.8 dB, respectively, covering the 5.65–6.28 GHz frequency range. The improvement in the reflection coefficient was observed due to improved impedance matching between the radiators and the feedline [Reference Kang, Li, Wang and Shi30]. The improvement in isolation was observed due to a reduction in the surface currents flowing in the adjacent radiators [Reference Chung and Kharkovsky31]. However, at this stage, the antenna also does not cover the entire upper WLAN band.

Figure 3. Antenna-1 (stage-1).

Figure 4. Antenna-2 (stage-2).

Next, a semicircular arc-shaped DGS was applied beneath the two DRs named Antenna-3 and displayed in Fig. 5(a) to achieve the desired operating band. The dimensions of the DGS were precisely estimated through a rigorous optimization process using the powerful HFSS software. This antenna improved WLAN band coverage and occupied the frequency band 5.07–6.10 GHz (desired operating band). The reflection coefficient and isolation were also enhanced to − 33 and − 31 dB, respectively, at the resonating frequency of 5.48 GHz. A parametric analysis of its different radii (A_R = 2,4,6,8 mm) was conducted to determine the effects on operating frequency and isolation. The scattering parameter (S-parameter) and surface current distribution of the ground plane (keeping Port-1 excited and Port-2 terminated) were plotted as depicted in Fig. 5(b) and Fig. 5(c). From Fig. 5(b), it can be observed that at A_R = 8 mm, the antenna achieves the desired operating band. In contrast, from Fig. 5(c), it can be analyzed that the concentration of surface currents is more toward the periphery of arc-shaped DGS (for A_R = 8 mm) located beneath DR-1, in comparison to the arc-shaped DGS beneath DR-2 leading to improved isolation. The E-field distribution of the ground plane for A_R = 8 mm is also plotted for more confirmation, as presented in Fig. 6. In this case, high electric field concentrations are observed at the periphery of the semicircular arc-shaped DGS. The concentration of fields and surface currents at the periphery of arc-shaped DGS relies on the area covered on the ground plane. The wider the area of arc-shaped DGS, the more concentration of fields and surface currents are at its periphery, which means improved isolation. A similar condition was observed in arc-shaped DGS (located on the right side) beneath DR-2 when Port-2 is excited, and Port-1 is terminated. The area covered by the semicircular arc-shaped DGS is also responsible for controlling the operating frequency span of the proclaimed antenna. The desired operating band can be achieved by varying the area of the DGS [Reference Arya, Kartikeyan and Patnaik32]. The slotted area of the DGS signifies effective inductance and is inversely proportional to effective capacitance. Enlarging the DGS area results in increased effective inductance and a lower operating frequency. Conversely, reducing the DGS area lowers effective capacitance, leading to a higher resonant frequency [Reference Khandelwal, Kanaujia and Kumar33]. In the next stage in Antenna-4, the interdigital-shaped DGS was applied between the two DRs to improve isolation, as depicted in Fig. 7(a). The operation of interdigital-shaped DGS is validated with the help of its equivalent circuit, as shown in Fig. 7(b) [Reference Balalem, Ali, Machac and Omar34]. The equivalent circuit of the proposed structure, illustrated in Fig. 7(b), is a combination of the interdigital capacitance equivalent circuit and the equivalent circuit of the DGS (represented by inductance L_p). The series circuit CL_s represents an equivalent circuit of the interdigital capacitance. A parametric analysis is conducted on various numbers (N = 5, 7, 10) of metal fingers, finger length (D_L), and spacing between fingers (D_F)by keeping the radius (A_R = 8 mm) of the semicircular arc-shaped DGS constant. It is found that for N = 5, improvements in isolation compared to Antenna-3 are not observed at resonant frequency. The Antenna-4 achieved isolation of −30.2 dB at resonant frequency. On increasing the number of metal fingers (N = 7, 10), an improvement in isolation is observed due to low surface currents amid the two radiators of the proposed antenna. Maximum isolation of −38 dB is obtained for N = 10 in the proposed antenna (Antenna-5) depicted in Fig. 8, working within the frequency spectrum of 5.07–6.08 GHz. For validation, S-parameters and surface current distribution graphs are depicted in Fig. 9(a) and (b), respectively.

Figure 5. Parametric analysis for various radii (A_R) of arc-shaped DGS of Antenna-3(stage-3): (a) Structure, (b) Scattering parameters, and (c) Surface current distribution.

Figure 6. Simulated E-field distribution of ground plane at A_R = 8 mm.

Figure 7. Antenna-4 (stage-4): (a) Structure, (b) Equivalent circuit of interdigital-shaped DGS.

Figure 8. Proposed two-port antenna, Antenna-5 (stage-5.

Figure 9. Simulation analysis for various numbers (N) of metal fingers: (a) Scattering parameters, (b) Surface current distribution.

Further, by varying finger length, it is found that the resonant frequency and isolation are also altered. The shift in the resonant frequency is observed due to variation of capacitance “C”, and variation in isolation is due to increment/decrement of the path length of surface current flowing between two radiators. An increased path length provides improved isolation between two radiators. S-parameters and surface current distribution graphs are rendered in Fig. 10(a) and (b) to further validate the effect of finger length on different finger lengths. The graphs confirm that for D_L = 8 mm, the desired result (isolation of −38 dB) is obtained.

Figure 10. Simulation analysis for various finger lengths (D_L): (a) Scattering parameters, (b) Surface current distribution.

The final analysis is done on the variation of spacing between fingers (D_F). Variation in the spacing between fingers also alters the surface current path length. For D_F = 3 mm (value in proposed antenna −5), the desired isolation of −38 dB is obtained. However, there is no influence on the operating frequency of the proposed antenna by varying spacing between the fingers. For validation, the S-parameters plot and surface current distribution graphs are rendered in Fig. 11(a) and (b). Hence, from the analysis elaborated above, it is confirmed that the combination of semicircular arc-shaped DGS and interdigital-shaped DGS provides the desired operating band for the upper band of WLAN and good isolation.

Figure 11. Simulation analysis for various finger spacing (D_F): (a) Scattering parameters, (b) Surface current distribution.

The graphical representation in Fig. 12 illustrates the reflection coefficient ($\left| {{S_{11}}} \right|$), isolation ($\left| {{S_{12}}} \right|$) for Port-1 of all antennas (Antenna-1 to Antenna-5) and their impedances. The simulated S-parameters and impedance of the designed radiator have been presented in Fig. 13(a) and Fig. 13(b) respectively. The reflection coefficients of Port-1 and Port-2 are determined to be −37.1 and − 34.1 dB, covering the frequency band of 5.07–6.08 and 5.06–6.07 GHz, respectively. The impedance of the antenna was found to be close to 50 Ω. The E-field distribution of Port-1 and Port-2 of the proposed two-port radiator at resonant frequencies 5.46 and 5.43 GHz is demonstrated in Fig. 14(a) and (b) in XY- and YZ- plane, respectively. It can be observed that HE_11δ mode is excited for Port-1 and Port-2 in the proposed two-port radiator. The resonance frequency of the CDR antenna for HE_11δ mode is computed using the equations (1–3 [Reference Mongia and Bhartia35, Reference Petosa36].

(1)\begin{equation}{f_r} = \frac{{6.321v}}{{2\pi X\sqrt {{\varepsilon _{r,eff}} + 2} }}\left[ {0.27 + 0.36\left( {\frac{X}{{2{H_E}}}} \right) + 0.02{{\left( {\frac{X}{{2{H_E}}}} \right)}^2}} \right]\end{equation}

Figure 12. Simulation analysis of Antenna-1 to Antenna-5: (a) Reflection coefficient, (b) Isolation, and (c) Impedance.

Figure 13. Simulated antenna parameters of the proposed two-port radiator (Antenna-5): (a) Scattering parameter and (b) Impedance.

Figure 14. E-field distribution of proposed two-port radiator (a) Port-1at 5.46 GHz and (b) Port-2 at 5.43 GHz.

In the case of the CDR antenna, the speed of light is depicted by $v,$ the effective relative permittivity is represented by${\text{ }}{\varepsilon _{r,{\text{ }}eff}}$, the radius is demonstrated by “X”, (X = D/2), and the equivalent height ${H_E}$ of the proposed two-port radiator is assessed as per Ref. [Reference Mongia and Bhartia35]:

(2)\begin{equation}\varepsilon_{r,{\text{ }}eff{\text{ }}} = \frac{{{H_E}}}{{\frac{{{H_{DRA}}}}{{{\varepsilon _{alumina}}}} + \frac{{{H_{sub}}}}{{{\varepsilon _{sub}}}}}}\end{equation}

and

(3)\begin{equation}{H_{E = }}{H_{DRA}} + {\text{ }}{H_{sub}}\end{equation}

The computed resonant frequency (theoretical) is determined to be 5.8 GHz while the simulated is observed to be 5.84 GHz (Antenna-1). The computed and simulated frequencies of resonance are observed to be in close contiguity.

Equivalent circuit of proposed antenna

The equivalent circuit model with calculated RLC parameters (Table 2) is depicted in Fig. 15 to validate the scattering parameter response of the proclaimed two-port antenna. The rectangular aperture and arc-shaped DGS beneath the DR consist of an RLC circuit. The rectangular aperture interfaces with a microstrip transmission line and CDR through an impedance transformer. The coupling between arc-shaped DGS and DR is done via an LC circuit.

Figure 15. Equivalent circuit model of two-port radiator.

Table 2. Calculated values of equivalent circuit elements

Experimental results

The circuit model for interdigital DGS utilized for isolation enhancement is depicted by inductors “Lp” and “Ls” and capacitor “C”. The S-parameters extracted from the equivalent circuit have been compared with S parameters obtained through HFSS, and the parameters obtained from the measurement are rendered in the “Experimental results” section. The extracted S-parameters from the equivalent circuit of the antenna are compared with the simulated S-parameters (using HFSS) and experimentally observed S-parameters whose plots are depicted in Fig. 16(a–c). Scattering parameter measurement is performed using Keysight N9917A Fieldfox Vector Network Analyzer (VNA), presented in Fig. 17. Table 3 demonstrates the distinction between the simulated, circuit model, and measured input parameters. Figure 16(a) and (b) and Table 3 reveal that the simulated fractional bandwidth for Port-1 is 18.11% and for Port-2 is 18.14%. The circuit model indicates a bandwidth of 18.16% for Port-1 and 18.52% for Port-2, while the measured bandwidths are 25.40% and 25.87% for Port-1 and Port-2, respectively. The isolation (mutual coupling) obtained through simulation, circuit modelling, and measurement, as rendered in Fig. 16(c), are observed to be −38, −39.27, and −35.5 dB, respectively. The simulated S-parameters and S-parameters extracted from the equivalent circuit mentioned in Fig. 15 are found close to each other with slight variation, possibly due to distinct mathematical techniques utilized by HFSS and circuit modeling software [Reference Khaleel, Hamad, Parchin and Saleh37]. The distinctness in experimental S-parameters is also noticed, which may be due to the adhesive used to mount DRA on the substrate and other fabrication discrepancies. By applying an adhesive material, a thin dielectric layer is introduced between the substrate and the CDR. This arrangement results in a reduction of the effective permittivity within the proposed structure. Consequently, the quality factor decreases while the bandwidth experiences an improvement, as evidenced by the measured results [Reference Aras, Rahim, Asrokin and Abdul Aziz38]. Figure 18(a) and (b) depicts the comparison amidst the simulated and experimentally observed far-field radiation patterns regarding the E-plane and H-plane for Port-1 and Port-2, respectively.

Figure 16. Comparison between simulated (using HFSS), circuit model, and experimental S-parameters of the proposed two-port radiator: (a) S_11, (b) S₂₂, and (c) S_12.

Figure 17. Experimental setup for measurement of S-parameters of the proposed two-port radiator: (a) Reflection coefficient (S₁₁) and (b) Isolation. The radiation efficiency of the proposed two-port radiator (Antenna-5) exceeded 93% for both Port-1 and Port-2, respectively. The gain and radiation pattern measurements were conducted in an automatic anechoic chamber, as illustrated in Figure 20.

Figure 18. Comparison between simulated and measured radiation pattern: (a) Port-1 at 5.58 GHz and (b) Port-2 at 5.6 GHz.

Table 3. Comparative analysis between simulated (using HFSS), circuit model, and measured input parameters

It is noticeable that in the broadside direction, i.e. (θ = 0, ϕ = 0), the antenna shows maximum radiation, and the cross-polarization is found below co-polarization for both the ports below −25 dB, which is required for any low loss MIMO radiator. Close consistency was noticed amidst the simulated and measured radiation patterns for both ports. In Fig. 19, the comparison between the simulated and measured gain plots for Port-1 is depicted, and they were found to be close to each other. The measured gain for Port-1 at resonant frequency was found to be 5.5 dB. The comparison between simulated and measured gain for Port-2 has not been incorporated due to its identical nature to that of Port-1.

Figure 19. Comparison between simulated and measured Gain.

The block diagram to measure the far-field gain and radiation patterns is illustrated in Fig. 20(a). The gain measurement of the proposed antenna utilizes the gain-comparison method, requiring a reference antenna with a known gain and a horn antenna whose gain is not known. These measurements are managed by software on a PC, with the computer transmitting synchronization pulses via Ethernet to the VNA at the start of each procedure. The antennas must be coaxially aligned. The positioner aligns the antennas by adjusting the antenna under test’s (AUT’s) height, azimuth, and elevation for maximum received power, computed using the Friis transmission equation [Reference Balanis39]. For far-field radiation pattern measurement, the horn antenna and AUT are placed in the chamber for line-of-sight communication, with absorbers mitigating reflected EM radiation. The AUT rotates through azimuth, elevation, and polarization axes using a position controller.The horn antenna is energized by a VNA, causing it to radiate, while the AUT receives these signals in S₂₁ mode, interfaced with the VNA which extracts the results and feeds them to PC software to plot the far-field patterns. Measurement precision is affected by system interconnections and RF cable movement, while accuracy depends on motor movements, probe influence, and RF connectors. All measuring instruments are calibrated before antenna measurement to minimize errors. Figure 20(b) shows the physical arrangement within an automatic anechoic chamber for experimental assessment of radiation patterns and gain.

Figure 20. Far-field measurement setup (for radiation pattern and gain): (a) Block diagram (b) Anechoic chamber.

Diversity parameters of MIMO antenna

ECC, DG, MEG, TARC, and CCL are the metrics to determine the diversity performance of the proposed two-port radiator [Reference Sharawi3]. The level of field correlation among the various antenna elements in the MIMO radiator is determined by the ECC performance parameter, which is a crucial diversity performance parameter. It illustrates how the radiation patterns of the individual radiator elements would affect each other when all the ports are operated concurrently. ECC can be estimated using scattering parameters and far-field patterns. The MIMO antenna having higher radiation efficiency (∼90%) is estimated using scattering parameters, and those having lower radiation efficiency are calculated using the far-field method. Equations (4) and (5) present an estimation of ECC for a dual port MIMO radiator using scattering parameters and the far-field method [Reference Blanch, Romeu and Corbella40]. The proposed two-port radiator attains high radiation efficiency (>93%) within the band of interest, so equation (4) can be utilized to calculate ECC for the proposed two-port radiator. ECC should be less than 0.5 in any MIMO radiator.

(4)\begin{equation}ECC = |{{{\varrho }}_{12}}{|^2}{\left| {\frac{{\left| {{{\text{S}}_{12}}{{*}}{{\text{S}}_{12}} + {{\text{S}}_{21}}{{*}}{{\text{S}}_{22}}} \right|}}{{|(1 - {{\left| {{{\text{S}}_{11}}} \right|}^2} - {{\left| {{{\text{S}}_{21}}} \right|}^2})\left( {1 - {{\left| {{{\text{S}}_{22}}} \right|}^2} - {{\left| {{{\text{S}}_{12}}} \right|}^2}} \right){|^{1/2}}}}} \right|^2}\end{equation}

(5)\begin{equation}EC{C_F} = {\text{ }}\frac{{{{\left| {{\iint}_{4\pi }\left[ {{A_i}\left( {\theta ,\varphi } \right)\!*{A_j}\left( {\theta ,\varphi } \right)d\omega } \right]} \right|}^2}}}{{{{\iint}_{4\pi }}{{\left| {{A_i}\left( {\theta ,\varphi } \right)} \right|}^2} {\iint}_{4\pi }{ \left| {{A_j}\left( {\theta ,\varphi } \right)} \right|}^{2}d\omega }}\end{equation}

Figure 21 represents the comparative analysis of the simulated and experimentally observed ECC for the proposed two-port radiator. The simulated and experimentally observed ECC are found within optimal limits. DG, a crucial parameter, refers to the enhancement in signal-to-noise ratio observed in multiple antenna systems when compared to single antenna systems. For the MIMO antenna design, a high DG value is imperative, nearly 10 dB in the operational bandwidth, to ensure good reliability and performance [Reference Sharawi3]. Equation (6) is adapted to estimate the DG of the proposed two-port radiator [Reference Sharawi3].

(6)\begin{equation}{\text{DG}} = 10\sqrt {1 - {\text{EC}}{{\text{C}}^2}} \end{equation}

Figure 21. Comparison between simulated and measured ECC.

A comparison between the simulated and measured DG is depicted in Fig. 22, and it can be seen that the simulated and measured DGs are similar to each other within the band of operation. MEG serves as another significant diversity parameter.

Figure 22. Comparison between simulated and measured DG.

It is a metric utilized to compare the power captured by a diversity radiator in a fading environment with the power received by an isotropic radiator. Suppose the statistical environment is homogeneous with equal vertical and horizontal polarization power densities. MEG corresponds to half of the radiation efficiencies [Reference Nasir, Jamaluddin, Khalily, Kamarudin, Ullah and Selvaraju23]. For the ith port MIMO antenna, MEG is estimated using equation (7) as reported in Ref. [Reference Nasir, Jamaluddin, Khalily, Kamarudin, Ullah and Selvaraju23].

(7)\begin{equation}{\text{ME}}{{\text{G}}_{\text{i}}} = 0.5\left[ {1 - \mathop \sum \limits_{{\text{j}} = 1}^{\text{N}} |{{\text{S}}_{{\text{ij}}}}{|^2}{\text{ }}} \right]\end{equation}

MEG-1 and MEG-2 are the mean effective gain of the two-port MIMO antenna. The ratio of MEG-1 to MEG-2 (MEG-1/MEG2) for a decent MIMO antenna system with the same power level should be ≤3 dB. For better performance, the difference should be between 0 and −3 dB [Reference Sharawi3, Reference Nasir, Jamaluddin, Khalily, Kamarudin, Ullah and Selvaraju23]. A comparison between simulated and measured MEG is reported in Fig. 23. It is observed that the measured MEG is close to the simulated MEG within the band of operation. Another important diversity parameter is the CCL. CCL is of significant importance as a diversity performance metric, signifying the maximum achievable message transmission rate for delivering a signal repeatedly through a communications system. The following formula (equation 8) can be used to compute it [Reference Chae, Oh and Park41]:

(8)\begin{equation}\begin{aligned} {\text{CCL}} & = - {\text{lo}}{{\text{g}}_{2{\text{ }}}}{\text{det}}\left( {\begin{array}{*{20}{c}} {{{{\beta }}_{11}}}& {{{\beta }}_{12}} \\ {{{{\beta }}_{21}}}& {{{\beta }}_{22}} \end{array}} \right) \\ {{{\beta }}_{11}} &= (1 - \left( {{{\left| {{{\text{S}}_{11{\text{ }}}}} \right|}^2} + {{\left| {{{\text{S}}_{12}}} \right|}^2}} \right) \\ {{{\beta }}_{22}} &= (1 - \left( {{{\left| {{{\text{S}}_{22{\text{ }}}}} \right|}^2} + {{\left| {{{\text{S}}_{21}}} \right|}^2}} \right) \\ {{{\beta }}_{{\text{ }}21}}& = - \left( {{{\text{S}}{{*}}}_{22}^{}{{\text{S}}_{21}} + {{\text{S}}{{*}}}_{12}^{}{{\text{S}}_{21}}} \right) \end{aligned}\end{equation}

Figure 23. Comparison between simulated and measured MEG.

The highest permissible limit for CCL is 0.4 bits/s/Hz for any MIMO antenna structure. A comparison between simulated and experimentally observed CCL curves has been presented in Fig. 24. It is found that both simulated and measured values of CCL are within optimal limits. However, some variations exist among simulated and experimentally observed values because of fabrication and measurement tolerances, as discussed in the “Experimental results” section. Another crucial MIMO performance metric for accurately describing the MIMO radiator is TARC. TARC is a technique for a two-port radiator that compresses all the data from the S-parameters into a single curve. The two-port MIMO antenna system’s resonant frequency and impedance bandwidth are thus calculated using a single TARC curve. TARC can be calculated using equation (9) for a dual port MIMO radiator [Reference Sharawi3, Reference Chae, Oh and Park41].

(9)\begin{equation}TARC (\Gamma_{a}^{t}) = \sqrt{\frac{\left(\left({\left|S_{11}+S_{12 e^{\,j\theta}}\right|}^{2}\right) + \left({\left|S_{21}+S_{22 e^{\,j\theta}}\right|}^{2}\right)\right)}{2}}\end{equation}

Figure 24. Comparison between simulated and measured CCL.

where S₁₂ is the isolation amidst the two ports, S₁₁ and S₂₂ are the reflection coefficients of Port-1 and Port-2 of the antenna framework, and θ is the phase angle of the input feed.

Figure 25(a) and Fig. 25(b) illustrate the TARC curves for the proposed two-port radiator setup. Figure 25(a) shows the simulated TARC, while Fig. 25(b) presents the measured TARC plot. A variation in the simulated and measured TARC plots is observed. This may be due to the fabrication tolerances of the proposed prototype two-port radiator. The phase angle of the input feed varies between 0° and 180° with an interval of 30° to determine the resonating behavior of the proposed radiator. It can be observed in Fig. 25 that, regardless of the phase angle of the input feed, the effective impedance and resonant peak bandwidth remain constant. A comparative analysis between the proposed work and existing MIMO antennas available in literature in terms of isolation technique, isolation, operating band, ECC, DG, and fabrication complexity has been reported in Table 4.

Figure 25. Comparison between simulated and measured TARC: (a) Simulated (b) Measured.

Table 4. Comparative analysis between proposed work and existing work available in the literature