Parametric analysis of feed

The proposed hybrid antenna resonates at four bands based on the feeding structure along with dielectric loading. The parametric analysis of the reflection coefficient curves for different feed configurations without and with DRA is shown in Fig. 2. Different resonant frequencies are emerged by changing the feed design. The first (violet color) and second (green color) reflection coefficient curves are with the full rhombic ring tapered feed and half rhombic ring tapered feed structures, respectively, without DRA. The third (blue color) and fourth (red color) reflection coefficient curves are with half rhombic ring and full rhombic ring tapered feed structures, respectively, with DRA.

Fig. 2. Reflection coefficient versus frequency.

Resonant frequencies excited for four different feed configurations without and with DRAs are shown in Table 2. The first stage shows a tapered microstrip line along with the rhombic ring. This is a feed structure, which acts as a microstrip antenna and the lower resonant frequency 3.23 GHz is excited. In the second stage, the taper microstrip line along with the lower part of the rhombic ring feed without DRA is shown. Here another resonant frequency 4.46 GHz is originated. The other two resonant frequencies 3.0 and 9.0 GHz are excited when DRA is placed above the taper feed with the half rhombic ring as shown in stage 3. Finally, the proposed hybrid MIMO DRA resonates at four frequency bands 2.5, 5.09, 6.8, and 9.0 GHz as shown in stage 4. The %bandwidth achieved at the four frequency bands are 14.6, 10.7, 4.2, and 5.3%, respectively. In stage 4, a slight shift in the first two resonant frequencies is observed. TM₁₁ and TE_01δ modes are generated at the first two resonant frequencies in stages 1 and 2, respectively. In stage 3 when DRA is loaded on the half rhombic ring structure (lower part of the rhombic ring), another HE_21δ-like mode is excited. According to reference [Reference Guha, Gajera and Kumar16], HE_21δ mode is the main source of cross-polarization. Sharma and Gangwar in [Reference Sharma and Gangwar17] mentioned that the cross-pol level is suppressed with another “U” shaped printed line in the annual ring. Here in the proposed design, cross-polarization levels are suppressed by adding the upper part of the rhombic ring, which becomes a full rhombic structure. This full rhombic ring structure along with CDRA not only suppresses the cross-polarization levels but also excites another radiating mode HE_12δ.

Table 2. Feed analysis

The resonant modes excited with the proposed design are explained as follows. The configuration of the feed structure is responsible for generating the lower resonant frequency f_{r 1} = 2.5 GHz. The surface current distribution of the feed is shown in Fig. 3. From [Reference Das, Sharma and Gangwar18], it is evident that the TM₁₁ mode is generated at 2.5 GHz due to two half variations of surface current and the resonant frequency of fundamental TM₁₁ mode for the annular ring is calculated from [Reference Das, Sharma and Gangwar19]. For the proposed tapered rhombic ring feed, the empirical formula to calculate the resonant frequency of TM₁₁ mode is given by

(1)$$f_{r, {\rm T}{\rm M}_{11}} = \displaystyle{{\,pv} \over {2\pi r_0\sqrt {\varepsilon _{rs, eff}} }}, \;$$

(2)$$p = \displaystyle{{2r_0} \over {2r_0 + T}}, \;$$

(3)$$r_0 = \displaystyle{{D_0} \over 2}, \;$$

(4)$$\varepsilon _{rs, eff} = \displaystyle{1 \over 2}( {\varepsilon_{r, sub} + 1} ) + \displaystyle{1 \over 2}( {\varepsilon_{r, sub}-1} ) \left({1 + \displaystyle{{10 \times H_S} \over T}} \right)^{{-}0.5}, \;$$

where v represents the velocity of light, r ₀is the radius of the rhombic ring, ɛ_r,sub is the permittivity of the substrate, ɛ_rs,eff is the effective permittivity of the substrate.

Fig. 3. Surface current distribution of the feed at 2.5 GHz.

The electric field distributions of other resonating modes are shown in Figs 4(a)–4(c). Due to dielectric loading of the tapered feed, another three resonant frequencies are originated. At 5.09 GHz, feed acts like a vertically placed magnetic dipole [Reference Mongia and Bhartia20] and TE_01δ mode is generated. The mathematical formula to calculate TE_01δ mode in DRA [Reference Gupta, Sharma, Das and Gangwar21] is given by

(5)$$f_{r, {\rm T}{\rm E}_{01\delta }, } = \displaystyle{{2.327v} \over {2\pi d\sqrt {\varepsilon _{dr, eff} + \!1} }}\left\{{1 \!+\!\, 0.2123\left({\displaystyle{d \over {H_{eff}}}} \right)\!-\!0.00898{\left({\displaystyle{d \over {H_{eff}}}} \right)}^2} \right\}, \;$$

where,

(6)$$\varepsilon _{dr, eff} = \displaystyle{{H_{eff}} \over {\displaystyle{H \over {\varepsilon _{r, {\rm DRA}}}} + \displaystyle{{H_S} \over {\varepsilon _{r, sub}}}}}, \;$$

(7)$$H_{eff} = H + H_S, \;$$

where d = D/2 represents the radius of CDRA. H _eff and ɛ_dr,effare the effective height and effective permittivity of the proposed radiator.

Fig. 4. Electric field distribution in CDRA: top view at 5.09, 6.8, and 9.0 GHz, respectively.

HE_21δ-like and HE_12δ modes are generated at 6.8 and 9.0 GHz, respectively. At these two frequencies, feed behaves like a magnetic quadrupole and electric dipole, respectively, oriented along the transverse direction. There is no comprehensive formula to calculate the resonant frequency of HE_21δ-like and HE_12δ available in the literature. But in [Reference Kajfez, Glisson and James22], it is given that the ratio of the resonant frequency of HE_12δ to HE_11δ is 1.14. The empirical relation to calculate HE_11δ mode in CDRA is given by

(8)$$f_{r, {\rm H}{\rm E}_{11\delta }} = \displaystyle{{6.321v} \over {2\pi d\sqrt {\varepsilon _{dr, eff} \!+\! 2} }}\left\{{0.27 \,\!+\!\, 0.36\left({\displaystyle{d \over {2H_{eff}}}} \right) + 0.02{\left({\displaystyle{d \over {2H_{eff}}}} \right)}^2} \right\}.$$

Parametric analysis of DGS

DGS is one of the simplest and efficient techniques to improve the isolation in MIMO systems. DGS is a defect intentionally placed on the ground plane. It acts as a band pass filter. It alters the direction of the surface currents on the ground plane. Due to DGS, the currents flowing from antenna 1 to antenna 2 decreases, thus enhancing the isolation. The shape and size of the DGS slot control both the fundamental resonant frequency and higher order resonances.

The optimization of DGS is shown in Fig. 5. With a view to reduce the mutual coupling, the initial step in the design process is reducing the length of the ground plane, shown in Fig. 5(a). The partial ground plane reduces the back-lobe radiation by suppressing the surface wave, enhances bandwidth, and provides good impedance matching. After optimizing the partial ground plane, a rectangular-shaped slot with dimensions W_SL = 4 mm and L_SL = 11.2 mm are etched at the center of the partial ground plane, shown in Fig. 5(b) as DGS1. Altering the position of DGS1 from the center creates an impedance mismatch. So, for proper impedance matching, the slot has to be placed at the center of the partial ground. The isolation achieved with the center slot is 21.49 dB. For further enhancement of isolation, dual L-shaped slots with dimensions W_SSL = 3 mm, L_SSL = 13.2 mm, W_S = 1 mm, and L_S = 6 mm are cut from the ground plane on either side of the center slot. The two L-shaped slots are placed in the partial ground, facing and opposing each other, respectively, as DGS2 and DGS3, illustrated in Figs 5(c) and 5(d). After consenting with the dimensions of the feed structure and DGS, a parametric analysis is performed to optimize the dimensions of DGS to get better isolation.

Fig. 5. Optimization of defected ground structure: (a) partial ground plane without DGS, (b) DGS1, (c) DGS2, (d) DGS3.

A rigorous parametric analysis is performed to optimize the dimensions of the ground plane, DGS slot positions and dimensions. As seen in Fig. 6, change in the length of the ground plane shifts the resonant frequencies and affects the reflection coefficient as well. Change in the width of L-slot W_s in DGS not only shifts the resonant frequency but also lowers the isolation level. The parametric analysis graph of the transmission coefficient is shown in Fig. 7. It illustrates the improvement in the isolation levels without DGS and with DGS1, DGS2, and DGS3 at the four resonant frequencies. Isolation improvement in the four frequency bands without and with DGS is shown in Table 3.

Fig. 6. Parametric analysis of partial ground.

Fig. 7. Transmission coefficient of MIMO antenna.

Table 3. Isolation analysis due to DGS

The surface current distribution at 2.5 GHz with DGS is shown in Fig. 8. It is observed that on both sides of the center slot and L-shaped slots in the ground plane, surface currents flow in opposite directions along the length of the slot and get cancelled at the edges. Due to this, the currents flowing in the ground plane take a longer path to travel from antenna 1 to antenna 2, thus enhancing the isolation.

Fig. 8. Surface current distribution at 2.5 GHz.

The prototype of the fabricated antenna is shown in Fig. 9.

Fig. 9. Fabricated proposed antenna structure: (a) top view, (b) bottom view, (c) feed design.

The simulated and measured scattering parameters of the proposed MIMO DRA are shown in Fig. 10. In the measured results, the resonant frequencies are slightly shifted due to the fabrication tolerances at the feed point.

Fig. 10. Scattering parameters: (a) reflection coefficient, (b) transmission coefficient.

The comparison of the proposed MIMO antenna with other multi-band antennas in terms of isolation is detailed in Table 4.

Table 4. Comparison of the proposed MIMO work with other multi-band MIMO systems

The simulated and measured Co-Pol and X-Pol radiation patterns of E-plane and H-plane of the proposed hybrid MIMO antenna are shown in Fig. 11. The cross-pol level is below 20 dB compared to the Co-Pol at all the four resonant frequencies.

Fig. 11. E-plane and H-plane Co-Pol and X-Pol radiation patterns at (a) 2.5 GHz, (b) 5.09 GHz, (c) 6.8 GHz, and (d) 9.0 GHz.

The gain of the proposed MIMO antenna is shown in Fig. 12. At the four resonant frequencies, the respective gain values are shown in Table 5.

Fig. 12. Gain versus frequency plot.

Table 5. Gain versus frequency

The diversity performances of the MIMO system are evolved from envelope correlation coefficient (ECC) and diversity gain (DG) [Reference Mohammad Saadh, Ashwath, Ramaswamy, Ali and Anguera28].

ECC is a parameter used to find how much the adjacent signals are correlated to each other. In terms of S-parameters, ECC (ρ _e) is given in equation 9. The practical value of ECC should be <0.5 for a good radiator. For the proposed antenna, simulated and measured ECC is <0.05, shown in Fig. 13. The measured values of ECC are calculated by substituting the S-parameters in equation 9.

(9)$$\;\;\;\;\rho _e = \displaystyle{{S_{11}S_{12}^\ast{ + } S_{21}S_{22}^\ast } \over {( {1-{\vert {S_{11}} \vert }^2-{\vert {S_{21}} \vert }^2} ) ( {1-{\vert {S_{22}} \vert }^2-{\vert {S_{12}} \vert }^2} ) }}, \;$$

where S ₁₁ is the reflection coefficient and S ₁₂ is the isolation.

Fig. 13. Envelope correlation coefficient (ECC).

DG is another diversity parameter that shows us an increase in the signal-to-noise ratio of a MIMO system. In terms of ECC, DG is given by the formula

(10)$${\rm DG} = 10\sqrt {1-{\vert \rho \vert }^2} .$$

For a MIMO system, a DG of 10 is acceptable. The simulated and measured DG performance curve is shown in Fig. 14.

Fig. 14. Diversity gain.