Four-port MIMO antenna loaded with FSS in FR2 band for wireless applications

Abstract

This work reports a four-port MIMO antenna integrated with a novel wideband frequency-selective surface (FSS). The proposed MIMO antenna is fabricated on Rogers-dielectric with permittivity 2.20 and thickness of 0.254 mm with an overall area of 30 × 36 mm². The radiating patch is achieved by merging three ring-hexagonal geometries, which are fed by an asymmetric tapered transmission line with a partial-rectangular ground printed on another surface with a pair of rectangular slots and an open-ended slot beneath the feedline. A novel de-coupling structure achieves isolation of more than 10.0 dB in MIMO configuration with a pair of radiating elements placed mirrored-adjacent sequence and the other pair placed oppositely. A novel 7 × 7 frequency-selective-surface of dimension 56 mm × 56 mm with an operating bandwidth of 10–43.30 GHz is also fabricated on the same substrate as an antenna and is placed 10.0 mm apart from the MIMO-antenna, which enhances the average peak-realized-gain by 8.0 dBi. The MIMO antenna achieves − 10.0 dB bandwidth of 3.45–7.25 GHz (Band-A) and 19.70–82.10 GHz (Band-B). The MIMO-FSS antenna achieves better diversity parameter with ECC_M−FSS$\:\le\:$ 0.02 (Band-A), 0.01 (Band-B), DG_M−FSS$\:>$ 9.998dB (Band-A), 9.996 dB (Band-B), TARC_M−FSS$\:\le\:$ − 4.0 dB (Band-A), − 6.0 dB (Band-B), CCL_M−FSS$\:\le\:$0.18 b/s/Hz (Band-A), 0.25 b/s/Hz (Band-B), MEG_M−FSS$\:\cong\:$ − 3.0 dB (Band-A and Band-B), and MEG (port_a-port_a)$\:\cong\:$0.0 dB (Band-A and Band-B). The SAR_M−FSS values at 3.50 GHz, 5.90 GHz, 24.0 GHz, 28.0 GHz, 38.0 GHz, 39.0 GHz, 41.0 GHz, 43.0 GHz, 47.0 GHz and 60.0 GHz are below threshold value of 1.60 W/Kg at 1 g of the tissue. The bending analysis at 15°, 30°, and 45° of the MIMO-FSS antenna matches the − 10.0 dB bandwidth at 0-degree bending, suggesting application in flexible electronics. The antenna also maintains stable 2D radiation patterns in principal planes at a lower frequency of 3.50 GHz & 5.90 GHz, and is acceptable in the remaining higher frequency application bands. The MIMO proposed antenna loaded with FSS also records the enhancement of peak realized gain by 5.85 dBi in Band 2.

Introduction

The advancement of technology from 1 to 6 G in the millimeter-terahertz range has witnessed the microstrip antenna revolution in the last few decades. The modern antenna demands features such as compactness, flexibility, multiple-band coverage, and SAR compatibility. Also, the super-wideband bandwidth with MIMO technology motivates the advanced design of a high-gain antenna.

The super-wideband single-port antenna^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18} terminology involves different types of radiating patches responsible for wider impedance bandwidth with modifications in the ground¹. A Shovel-shaped slotted patch with CPW-feed partial elliptical-ground, a T-shaped CPW-feed antenna with an etched semi-circular slot on the ground, offers a bandwidth of 2.90–29.20 GHz and uses a transparent Plexi-glass substrate²,³. The fractal-shaped patch known as Sierpinski in hexagonal form with rectangular CPW-ground offers a bandwidth ratio of more than 11:1 (3.40–37.40 GHz)⁴. A Mickey-shaped patch with an identical slot printed on the top surface and a half-elliptical etched ground on the opposite surface matches impedance between 1.22 and 47.50 GHz⁵ and fractal geometry⁶ inscribed within the circular patch with a chamfered edge of rectangular ground with a slot at the center produces a very wide impedance bandwidth of 2.31–105.41 GHz with Rogers5880 used as dielectric. Also, an octagonal-ring patch with offset feed and a connected closed rectangular strip with etched rectangular ground is also a candidate for super-wideband characteristics. Two angled merged elliptical patches also provide a super-wideband configuration with a higher cut-off frequency below 20.0 GHz^7,8,9. The lower cut-off frequency of 640 MHz^11,12,13 is achieved by a novel-patch (fan-shape), tapered microstrip feed, and corner-rounded ground, leading to the higher cut-off of more than 16.0 GHz. A circular-ring patch with embedded star-star fractal and half-slotted elliptical-ground¹⁴ achieves a VSWR ratio of 2:1 with a bandwidth ratio of 11.31:1. A 5G-antenna in both FR1 and FR2 bands is achieved by using a three-merged elliptical-patch with circular-slot, including modified rectangular-ground, achieving a measurable bandwidth of 1.91–43.50 GHz¹⁷.

The more insight analysis of the antenna design can also be studied by applying the theory of Characteristic-Mode-Analysis (CMA)^19,20,21,22, where Mode-11/Mode-12 corresponds to 2.45 GHz and Mode-21/Mode-22 for the resonance frequency of 5.80 GHz¹⁹. The CMA analysis is also applied to a four-port MIMO antenna with a flower-shaped patch utilizing 10 modes with mode3, mode9, and mode10, which are not involved in the contribution of bandwidth²⁰. The Eight-port MIMO antenna is subjected to five fundamental modes, with mode 1, mode 2, and mode 3 forming the most significant modes describing the operational bandwidth of 3.90–5.03 GHz²².

The single-port antenna system suffers from fading of the signals at the receiver due to the impinging of the information at various angles. This reduces the efficiency and the need to cater to the problem of fading. The multiple-port identical antenna will resolve the issue by integrating MIMO technology, which will offer spatial or polarization, or radiation diversity schemes^{23,24,25,26,27,28,29,30,31,32,33,34,35,36}. A wideband antenna with an identical patch placed orthogonally²³, achieving impedance-bandwidth of 8.31–36.14 GHz, offers isolation of more than 10.0dB, ensuring minimal interference from the neighboring elements. Also, the orthogonal sequence arrangement of the four-port tree-shaped patch is designed for 23.40–35.0 GHz millimeter waves²⁴. A unique four-port modified Chamfered square patch orthogonally placed MIMO antenna uses open complementary split-ring-resonators with defected-ground offering applications in WLAN and X-band²⁵. P-shaped patch converted to a two-element array with four-port configuration resonates at 60.0 GHz with complete-ground uses Rogers400. Dielectric material²⁷ with isolation of more than 30.0 dB. The use of a neutralization line³¹ attached between the two radiating elements acts as an isolation structure that cancels the oppositely flowing current vector and thereby reduces the interference. A 28.0 GHz MIMO-array antenna with a compact size of 28.3 mm×28.3 mm achieves isolation of more than 45.0dB at 28.0 GHz by using a defected-ground structure³³. The super-wideband MIMO antenna is also designed to achieve a bandwidth ratio of 31:1 and is useful for IoT applications³⁶.

The flexibility of the substrate in the antenna field can also be used for several wireless applications, including medical, display, and telecom communication^{37,38,39,40,41,42,43,44,45,46,47}. The flexibility of the material is the property of the material itself, and when it comes to on-body applications, they can be categorized as conductive and substrate materials. The conductive material can include pure metals, conductive polymers, conductive inks, and substrate-material including papers and textile polymers. UWB-antenna printed on an FR4 substrate with a thickness of 0.15 mm can easily be bent without compromising the operational bandwidth³⁷. Rogers-substrate with a thickness of 0.127 mm uses a meander patch fed by CPW-fed and is tested for different bending angles, which is found suitable for V2X applications³⁸. FR-4 substrate with a thickness of 0.20 mm is also suitable for flexible antenna MIMO configuration with applications for 5G sub-6.0 GHz and X-band applications³⁹. Detailed review with the use of fabric is also used as a flexible substrate, which can be used for on-body applications^{40,41,42,43,44}. Rogers3003 with a thickness of 0.25 mm is another alternative for flexible applications in millimeter-wave 28/38 GHz applications⁴⁷.

The SAR evaluation is another important parameter that suggests the application of the antenna for on-body applications^{48,49,50,51,52}. The SAR calculation of an F-shaped antenna generating a bandwidth of 24.0–51.0 GHz, which includes 28/38GHz mmWave bands with SAR for 10 g of the tissue corresponding to 0.963 W/Kg at 28.0 GHz and 0.583 W/Kg at 38.0 GHz. A fractal super-wideband antenna with a bandwidth of 1.40–20.0 GHz calculates SAR within the allowed limits for applications including GPS, PCS1900/UMTS, IMT2000, WiFi, and UWB⁴⁹. The SAR can also be reduced by embedding a dual-band electromagnetic band-gap structure with the antenna, which provides a reflection-phase shift angle in 2.40 GHz and 4.25 GHz^51,53.

Finally, several techniques are used to enhance the gain, with a frequency-selective surface being one among them^54,55,56,57. The designed FSS is the repetitive structure that is derived from the Unit-Cell, and the same Unit-Cell is verified by simulation results⁵⁴ where the reflection coefficients are near 0.0dB, indicating no power is transmitted, and the FSS acts as a band-stop filter. The 5 × 5 FSS-array is designed for WLAN applications⁵⁵, which raises the maximum level of the peak-realized-gain by 4.0 dBi. Unit-cell is designed for FSS with a frequency range of 7.00–9.00 GHz by using a circular ring with an embedded slotted rectangular structure, which enhances the peak realized gain and also improves isolation^{56,57,58,59,60}. Also, a narrowband antenna with hexagonal geometry shows the self-isolation for more than 30.0 dB, and the use of dielectric resonators in the antenna helps in achieving a high-gain of 8.24 dB^61,62. Also, a two-port MIMO antenna resonating at 28.0 GHz increases the gain to 7.20 dB where FSS is integrated. Thin substrate of thickness 0.25 mm is useful for millimeter-wave resonance frequency at 24.0, 38.0, 44.43, 49.60 & 57.0 GHz applications, and textile antenna generating low frequency resonance values of 1.80 GHz, 2.40 GHz, 3.60 GHz & 5.80 GHz are useful for wearable applications^63,64. Also, a four-port MIMO antenna utilizes RO3003 dielectric with flexible characteristics, maintains the three resonances at 24/28/38 GHz when bent at different angles^65,66.

In this work, a four-port MIMO_M−FSS antenna is proposed, which is designed on RogersRT Duroid dielectric with a height of 0.254 mm and an area of 30 mm × 35 mm, achieving Band-A bandwidth of 3.45–7.25 GHz and Band-B bandwidth of 19.70–82.10 GHz. Also, for the gain enhancement, the FSS-array technique is used, which reflects signals within the bandwidth of 10.0–43.30 GHz impinged on it at various angles. The FSS-array of size 56.0 mm × 56.0 mm fabricated on the same substrate used for the MIMO_M−FSS antenna is placed below by a distance of λ/4 mm. The MIMO_M−FSS antenna-FSS array analysis includes the following sections.

• a. (a) Section "Conceptual development of narrow-wide band antenna" discusses the development of a single-port antenna generating a narrow-wide band with validation of the result achieved by characteristics-mode-analysis and equivalent circuit model.

• b. (b) Section "MIMO antenna system" discusses the development two-port MIMO_M−FSS antenna and its related results, the FSS-array design, the Four-port MIMO_M−FSS antenna, and the MIMO-antenna integrated with the FSS-array for gain enhancement is explained.

• c. (c) Section "State-of-the-art comparison" discusses the state-of-the-art and compares it with the proposed work.

Conceptual development of narrow-wide band antenna

Single-port antenna configuration

Figure 1 illustrates the single-port antenna with multi-band and super-wideband characteristics. Figure 1a shows the 3D configuration of the antenna with the printing of a patch on the top surface of the Rogers-dielectric material and partial ground on the opposite surface. The patch, P_A, and ground GA are all printed on the dielectric material with dimensions of W_p × L_p mm². The patch, P_A, is a multiple-merged hexagonal geometry that is fed by a tapered asymmetric transmission line. The feedline is connected to a type connector for external input to excite the antenna. Figure 1b illustrates the side-view of the antenna with hp corresponding to the thickness of the substrate. Figure 1c shows the front view of the antenna with a slotted three-hexagonal geometry marked as H₁, H_2, and H₃, respectively. The outer hexagonal slotted patch is of the thickness (a₁–a₂) mm, where a₁ is the outer circum-radius and a₂ is the inner circum-radius. The second inner patch geometry marked as H₂ is a hexagonal patch with outer and inner circum-radii corresponding to b₁ and b₂. The third hexagonal ring, H₃, is also a slotted-patch with outer circum-radius of c1 and inner circum-radius of c₂. The side lengths of all three hexagonal geometries correspond to L_a, L_b, and L_c, respectively. This forms the radiating patch and is fed by a tapered feedline of widths W_a and W_b with offset distance L_a from the edge. Figure 1d corresponds to the ground printed on the opposite surface of the substrate with a dimension of W_g × Lg mm². The ground is etched by a rectangular slot of dimension g₄ × g₅ mm² and a slit of dimension g₁ × g₂ mm² placed below the tapered transmission line. Figure 1 with the geometrical structure is marked by optimal dimensions and is tabulated in Table 1.

Fig. 1

Single-port configuration (a) 3-D view (b) side-view (c) optimized dimensions in patch-view (d) optimized dimensions in ground-view.

Table 1 Optimal dimension(s).

CMA analysis

Table 2 CMA analysis of 15 modes (Mode1–Mode15).

The characteristics-mode-analysis (CMA), also known as CMA, is a computational and theoretical technique applied to design the antenna by applying the natural resonant modes to the conducting structure. The analysis is important as it gives more insight into the current distribution behavior of the structure as well as the contribution of the resonant mode in radiation. In the proposed work, which generates narrow and wideband responses, the multi-mode excitation gives information on the multiple resonant modes that are combined to form the wideband response behavior. The CMA analysis is given by calculating three important parameters, namely (a) Modal-significance (MS), (b) Characteristics-angle (CA), and (c) Eigen-values, which are plotted in Fig. 2a–c with 15 modes of excitation⁵⁹.

Fig. 2

Characteristics mode analysis (CMA) (a) modal significance (b) characteristics angle (c) eigen values.

The nth order of the Eigen-current (Jn) and the nth order eigen value (λn) are calculated as the CMA analysis is initiated by calculation of the total-surface-current.

The convergence of eigenvalue (λn) to 0 signifies the solution leading to modal significance, which is given by Eq. 1

$$\:MS\left({f}_{H}={f}_{L}\right)=\left|\frac{1}{1+j{\lambda\:}_{n}}\right|=\frac{1}{\sqrt{2}}=0.707$$

(1)

Interestingly, the modal-significance threshold values correspond to 0.707, which is half-power-beamwidth and indicates the mode value of MS$\:\ge\:$0.707 contributes to the operational-bandwidth & values of MS < 0.707 are discarded, which are termed as non-significant modes. The significance of CA contributes to understanding the behavior of the mode storing energy due to the capacitance or inductance nature of the structure and radiation due to the resonant modes. The CA is calculated by the following equation. 

$$\:{\phi\:}_{n}=180^\circ\:\: \left(1-\frac{1}{\pi\:}\:arc\:\left(tan{\lambda\:}_{n}\right) \right)$$

(2)

The phase angle condition, more than $\:\phi\:>180^\circ\:$ but $\:\phi\:<270^\circ\:,$ indicates the energy storage, which can be due to the shape of the structure. Hence, the change in shape of the radiation structure can also modify the behavior of the modes. Hence, the instantaneous change in the electric field is observed to lag in phase, and this change corresponds to the capacitive mode. However, the phase of the mode corresponds to surface current, and ranging with $\:\phi\:>90^\circ\:$ and $\:\phi\:<180^\circ\:$ also indicates the lag in phase and inherits the inductive property. However, the phase angle corresponding to $\:\phi\:>0^\circ$, $\:180^\circ\:$ indicates the perfect matching of the capacitive-inductance impedance at the most significant modes. Eigenvalues in the CMA indicate how far the particular mode in achieving resonance, which is shown in Fig. 2c. The three conditions of eigenvalue with λn = 0 correspond to the maximum resonance condition and radiation, λn < 0, the capacitive nature of the mode, which stores the electric energy & current lags voltage, and for λn > 0 also stores the magnetic energy within the structure due to the inductive nature where current leads the voltage. Hence, lag or lead by the current respective of voltage stores the energy, whereas, when both are in phase, or the angle between them is $\:0^\circ$, indicates all the energy is radiated. Also, the relation between MS and the eigenvalue is related as

$$\:MS=\frac{1}{\sqrt{1+{{\lambda\:}_{n}}^{2}}}$$

(3)

Thus, the CMA analysis gives insight into the behavior of the modes that are responsible for forming the operational bandwidth and are explained in Fig. 2. Figure 2a evaluates the MS with MS$\:\ge\:$0.707 contributing to the bandwidth, where 15 modes are excited in the radiating structure. Table 2 shows the most-significant and non-significant modes’ behavior where Mode1 contributes two bandwidths corresponding to 5.49–6.90 GHz, being the first narrow-bandwidth, and 80.57–86.43 GHz being the second narrow-bandwidth. Similarly, Mode 4 and Mode 5 also contribute to three bandwidths which correspond to 7.66–11.09 GHz, 8.70–19.198 GHz, and 70.60–86.43 GHz. Similarly, Mode 9 also contributes to two bandwidths with MS$\:\ge\:$0.707, and Mode 13 is largely responsible for the wider-impedance bandwidth ranging between 21.08 GHz and 86.43 GHz. Very sharp resonances are noted at 74.22 GHz with MS = 89 and at 82.55 GHz with MS = 82.55. The remaining mode(s): Mode 2, Mode 3, Mode 6, Mode 7, Mode 8, Mode 10, Mode 11, Mode 12, and Mode 15 are non-significant modes as they do not contribute to the formation of the bandwidth due to MS < 0.707 as noted from Table 2. Figure 2b shows the graph of the CA angle concerning frequency for all 15 modes.

Table 3 CA analysis of most significant modes.

Table 3 gives more insight into the significant modes with the range of bandwidth offering capacitive or inductive nature of the structure, with resonance values also tabulated.

Figure 2c records the graph of eigenvalues concerning frequency, and it can be noted that for the most significant modes corresponding to Mode 1, Mode 4, Mode 5, Mode 9, Mode 13, and Mode 14 are closer to 0 values.

This concludes that the six significant modes help in understanding the physical radiating structure of the proposed antenna.

Evolution of the antenna (Evo. A)

The antenna shown in Fig. 1 inherits the super-wideband characteristics with additional resonating narrow bands. However, the final version of the antenna is achieved by subjecting it to four iterations, which improves the matching of impedance matching. Figure 3 illustrates the detailed iterations and also the corresponding − 10.0 dB bandwidth.

Fig. 3

Evolution of Single-port configuration (a) Evo. A₁ (b) Evo. A₂ (c) Evo. A₃ (d) Evo. A₄ (e) Evo. A₅ (f) S₁₁ (Evo. A₁ – Evo. A₅).

Figure 3a corresponds to Evo. A1, which consists of a hexagonal patch and a rectangular ground. The lower cut-off frequency is a dependent parameter on the dimension of the patch. The lower cut-off frequency is calculated by basic equations, which depend upon the height of the hexagon, side length (L_a) or radius of the hexagon (a₁), and length of the transmission line.

where a is the height of the hexagon, a₁ is the effective radius, L_m is the length of the microstrip, and lower cut-off frequency.

This antenna achieves a narrow bandwidth of 5.65–13.87 GHz with resonance centered at 11.593 GHz (S₁₁= – 34.65 dB). The second iteration, shown in Fig. 3b, corresponds to Evo. A₂ comprises a hexagonal ring and a tapered feedline, which further generates five narrow bands with bandwidths of 4.64–5.81 GHz, 14.60–16.85 GHz, 21.83–23.90 GHz, 40.76–55.87 GHz, and 75.66–80.31 GHz. The next modification is in the form of Evo. A₃, which is the addition of two hexagonal rings, H2, and H3, embedded within the hexagonal ring H1, as shown in Fig. 3c. This generates six bands with four narrow bands corresponding to bandwidths of 5.11–6.44 GHz, 8.29–10.64 GHz, 11.99–17.12 GHz, 19.13–22.94 GHz, and two wide bands offering bandwidths of 40.43–62.82 GHz, 73.29–84.43 GHz. However, to achieve a super-wideband configuration, more matching of impedance matching is required, which is achieved by iteration. A4 is shown in Fig. 3d. The tapered transmission line is offset by a distance La from the edge of the top surface. This modification of the antenna offers seven narrow bands with bandwidths in both FR1 and FR2 bands. The FR1 bandwidth includes 5.17–7.03 GHz, 9.91–10.97 GHz, 14.12–15.69 GHz and FR2 bands cover millimeter wave applications with bandwidths of 20.23–31.15 GHz, 40.95–54.54 GHz, 74.82–81.08 GHz, 89.81–99.97 GHz. However, the FR2 bands were achieved by Evo. A₄ can be further improved by subjecting the antenna to Evo. A₅ is shown in Fig. 3e. The two modifications are conducted on a rectangular ground plane, which is printed on the opposite surface of the patch. The rectangular slot of dimension g4 × g3 mm² and an open-ended rectangular slot of dimension g₁ × g₂ mm², which is placed beneath the tapered feedline, produce five bands with four narrow bands with corresponding bandwidths of 5.36–7.09 GHz, 9.85–10.86 GHz, 14.06–15.31 GHz, 19.97–30.14 GHz, and a super-wideband bandwidth of 34.64 GHz to more than 100.0 GHz. The objective of achieving a super-wideband is to include all the bands in FR2 so that a large number of applications can be embedded within a single antenna.

Parametric-study

The optimized parameters shown in Fig. 1 were achieved by subjecting the hexagonal patch with the rectangular ground to several iterations, as discussed in Fig. 3. However, this optimized dimension change will also have an impact on the operational bandwidth, and this study is known as parametric. The key parameters include a₁ (H1 radius), b₁ (H2 radius), c₁ (H3 radius), g₂ (depth of open-ended etched slot in the ground), g₃ (depth of etched slot in ground), and L_g (height of ground) when subjected to a change in physical dimension, observe the change in operational. The first parameter, a_1, which is also the radius of the hexagonal ring H1, is varied from 6.625 to 7.125 mm. The values of 6.625 mm and 6.825 mm almost overlap the first two narrow bands as observed in Fig. 4a, but the third narrow band is filtered. However, for the above-mentioned two values, the two more bands are filtered beyond 32.0 GHz, and the better-matching of impedance matching is lost. For the value of a₁ = 7.125 mm, the antenna achieves effectively four narrow bands with bandwidths of 5.25–7.10 GHz, 9.89–10.90 GHz, 14.02–15.23 GHz, and 19.83–30.13 GHz. For the same above-mentioned value. The antenna also achieves a wideband bandwidth of 34.59–86.74 GHz. The next parameter is the radius of the inner slotted hexagonal patch shown in Fig. 4b with parameter b₁. The variation of parameter b₁ is changed from 5.225 to 5.625 mm with a step size of 0.20 mm. Almost the same variation of S₁₁ for b₁ = 5.225 mm, 5.425 mm is observed in the former case of hexagonal radius a₁ = 6.625 mm, 6.875 mm. For the value of b₁ = 5.625 mm, the identical − 10.0 dB bandwidth is achieved in the case of a₁ = 7.125 mm. The variation of c₁, which is the inner-most radius of the merged ring-hexagonal geometry, is changed from 3.575 to 3.975 mm, with c₁ = 3.975 mm being the optimal dimension. The S₁₁ results for values of c₁ = 3.575 mm and 3.975 mm also overlap the S₁₁ for the initial two values of a₁ and b₁, but the matching of impedance is improved beyond 40.0 GHz as observed from Fig. 4c. The next two parameters, g₂, which is the depth of the open-ended slot in the ground placed beneath the transmission line, and g₃, which is the depth of the rectangular slot also etched in the ground, show the identical variation of S₁₁ for g₂ = 0.40 mm, 1.40 mm, and g₃ = 1.25 mm, 3.25 mm. The observations for both the parameters, g₂ and g₃, noted from Fig. 4d, e are that the value of g₂ = 0.40 mm achieves all the lower three narrow bands, but the matching of impedance deteriorates between 35.0 and 45.0 GHz. However, g₂ = 1.40 mm resolves the above problem, but the impedance match is not as good as that achieved for the optimized value of g₂ = 0.90 mm. On the other hand, the value of g₃ = 1.25 mm and 3.25 mm, the third narrow-band is filtered with antenna matching, moderate matching of impedance matching. The last optimized parameter is the height of the ground L_g, which is changed from 2.00 mm, 3.00 mm, and 4.00 mm. For L_g=2.00 mm, the antenna produces one narrow band of bandwidth 4.45–5.74 GHz with resonance centered at 5.02 GHz (S11 = − 50.78 dB), and for L_g = 3.00 mm, the bandwidth is 4.65–6.35 GHz with resonance at 5.33 GHz (S₁₁ = − 29.96 dB). For L_g = 4.00 mm, the required narrow and widebands are achieved with good matching of the impedance as shown in Fig. 4f.

Fig. 4

Parametric study (a) a₁ (b) b₁ (c) c₁ (d) g₂ (e) g₃ (f) L_g.

Time-Domain and equivalent circuit model analysis

The shape of the pulse needs to be studied for wider-bandwidth antennas when they are received due to the fact that the larger frequency needs to travel, which will suffer path losses and other degradation factors such as diffraction. The time domain analysis also adds to identifying the suffering of the signal in the form of spikes, chirps, response of the antenna for very short-time intervals of the pulse, undergoing optical phenomena such as dispersions and dispersions. The frequency domain analysis has been studied, and the performance of the proposed antenna is analyzed, such as the resonance bandwidth of the antenna, characteristics-mode-analysis. However, the vice-versa analysis, that is, the time-domain performance, is also vital, which deals with the impulse response applied to the transmitter and the reception of the pulse at the receiver. This analysis includes three main parameters: (i) Fidelity-factor, (ii) Group delay, and (iii) Impulse Response. This analysis is studied under a simulation environment with a replica of the two identical antennas placed at a far-field distance of d_f > 2 × W_SUB²/λ_o = 30 cm with a set-up shown in Fig. 5. Figure 5a represents the side_Tx-side_Rx orientation, and Fig. 5b corresponds to Face_Tx-Face_Rx, and by these two orientations, all the possible angles are included.

Fig. 5

Time domain analysis in far-field (a) SSO (b) FFO (c) Group-delay (mm-Wave range) (d) IR-response.

Hence, the threshold value of Fidelity-Factor$\:\ge\:$0.50 is required for acceptable reception of the transmitted pulse. In the proposed work and Fidelity-Factor analysis of the Tx-Rx pulse, the value corresponds to 0.89 and 0.87, respectively. Figure 5c analyzes the impulse response of the proposed antenna with a Gaussian pulse given as input. The received pulse in both orientations, side_Tx-side_Rx & face_Tx-face_Rx, is also recorded in Fig. 5c with reduced amplitude in comparison with the normalized transmitted pulse amplitude and the ringing effects. However, the amplitude of the received signal is received by using an amplifier, and the ringing effects, which are due to unwanted frequency components, are filtered, with a maximum replica of the transmitted pulse being received with low distortion.

The parameter group delay is defined as the derivative of the change in phase to the frequency with a negative sign. The transmitted signal undergoes phase-change and reduction in amplitude, which is a wave traveling phenomenon traveling at a farther distance and accounting for obstacles. Thus, the linear phase change needs to be recorded with the ideal ranging between + 0.50 and − 0.50 ns. Figure 5d records the values of group delay with phase change characteristics within the threshold limits as mentioned above.

Table 4 Components of RLC (Equivalent circuit model).

The four narrow bands and a wideband bandwidth are achieved for a single-port antenna with bandwidths of narrow-band corresponding to 5.36–7.09 GHz, 9.85–10.86 GHz, 14.06–15.31 GHz, 19.97–30.14 GHz, and a wideband bandwidth of 34.64 GHz -> 100.0 GHz. The operational − 10.0 dB bandwidth achieved by the antenna is designed in an EM-simulator. However, the operational bandwidth corresponding to − 10.0 dB can also be achieved by extracting the RLC lumped components and analyzing the conceptual Equivalent Circuit Model (ECM), and the analysis of the ECM is recorded in Fig. 6. Firstly, the resonances achieved in the operational bandwidth can be considered as the combination of parallelly connected RLC lumped components, and each parallel circuit is connected in series. Thus, the overall parallelly connected components can be simulated by the EM-Circuit simulator, ADS, and the corresponding S₁₁ is extracted. This is achieved by plotting the impedance graph shown in Fig. 6a with a shaded portion indicating the matched operational bandwidth. The values of real impedance (R) and imaginary impedance ($\:\pm\:$jX) are shown in Fig. 6a with frequencies corresponding to 6.76 GHz, 10.46 GHz, 14.56 GHz, 26.98 GHz, 41.76 GHz, 47.51 GHz, 52.31 GHz, 58.68 GHz, 67.25 GHz, 73.42 GHz, 79.18 GHz, and 84.77 GHz is the maximum resonance and best matching of impedance achieved. As discussed, each resonance frequency value corresponds to a parallelly connected RLC circuit as shown in Fig. 6c. The sweep of 1.0–100.0 GHz is applied to excite the overall ECM. Table 4 corresponds to the calculated RLC components, which are calculated from the resonance equation and the value of inductance (L) by substituting the imaginary value recorded in Table 4 for the corresponding resonance frequency, f_o. The value of each inductance calculated for the corresponding f_o is substituted in the resonance equation to obtain the Capacitance value. The value of R is noted from the impedance graph achieved directly from the EM-simulator. The corresponding twelve resonance values of frequency are marked from f₁ to f₁₂ with resistance R marked from R₁ to R₁₂, Inductance L from L₁ to L₁₂, and Capacitance C from C₁ to C₁₂ as shown in Fig. 6c. The calculated numerical values from equations corresponding to R (R₁ to R₁₂), L (L₁ to L₁₂), and C (C₁ to C₁₂) are shown in the ECM drawn in ADS, as shown in Fig. 6d, which is a screenshot of the circuit S-parameter simulator. The − 10.0 dB bandwidth achieved from the EM-simulator and extracted S-parameter from the ECM model are plotted and compared in Fig. 6b, which concludes that the ECM with lumped component values for each resonance circuit fits best in comparison to the S-parameter from the EM-simulator.

Fig. 6

Equivalent circuit model analysis (a) impedance of single-port antenna (b) S-parameter comparison (EM-Simulator and ADS) (c) conceptual model.

MIMO antenna system

The demand for high data rates and good channel capacity with improved spectral efficiencies has increased due to the increase in traffic because of a large number of wireless communication users. Section "Conceptual development of narrow-wide band antenna" focuses on a single-port antenna system with the capability of achieving both narrow and wider impedance bandwidth. The antenna S-parameter result was also verified by applying the concept of an equivalent circuit model, and due to the wider bandwidth, the study of pulse transmission with group delay was also conducted. The single-port antenna suffers from the demerits of fading, and hence, the multiple identical antenna with the same operating frequency is explored, which is termed as multi-input-multi-output, and the configuration. Thus, the MIMO system not only increases the spectral efficiency but also reduces fading.

Two-port MIMO system

Shannon’s capacity theorem explained the advantage of increasing the number of identical radiating elements, which increases the probability of reducing the fading of signals. Hence, the single-port antenna shown in Fig. 1 is transformed to a multi-port MIMO system where the spatial diversity is the focus. The two-port MIMO configuration is shown in Fig. 8 with analysis including the S-parameter result plot and the interaction of the surface-current-density (SCD) distribution with the neighboring antenna. Figure 7a shows the 3D model of the MIMO antenna with a pair of radiating patch antennae marked as A₁ and A₂, which are placed adjacent and mirrored. The new dimension of the two-port antenna corresponds to W_TP × L_p = 30 × 18 mm², with both the antenna excited by Feed1 and Feed2 SMK connectors as shown in Fig. 7a. Also, the edge-to-edge distance of E_d = 0.75 mm is maintained between the adjacent mirrored radiating patches, ensuring low mutual coupling between them. Figure 7b represents the mirrored-adjacently placed MIMO antenna A₁ and A₂ with a distance of D₁ = 15.0 mm between both centers. Also, the spacing between the transmission line corresponds to D₂ = 8.00 mm. Figure 7c gives the detailing of the common ground which serves both for the A₁ and A₂ radiating patches. The overall dimension of the ground corresponds to W_g1×L_g = 30.0 × 4.0 mm². The inter-spacing between the open-ended etched slot corresponds to D₄ = 8.40 mm, and the distance between the two rectangular etched slots corresponds to D₃ = 25.50 mm. The two-port MIMO configuration produces S₁₁/S₂₂ reflection coefficients and S₁₂/S₂₁ transmission coefficients as plotted in Fig. 7d. The S₁₁/S₂₂ − 10.0dB bandwidth includes five narrow bands with bandwidths of 2.91–7.07 GHz, 10.0–10.84 GHz, 14.12–15.53 GHz, 19.75–21.26 GHz, 22.50–31.39 GHz, and a wideband matched impedance bandwidth of 33.87 GHz to more than 100.0 GHz. The antenna, however, offers poor isolation of more than 5.0 dB in the first narrow band but gradually increases and is more than 10.0dB in the remaining four narrow bands. The MIMO antenna isolation becomes better for a wider impedance bandwidth of 33.87 GHz to more than 100.0 GHz with isolation of more than 15.0 dB. Also, the signals with resonance or selected frequency are given as input to the MIMO antenna, and the interaction between the neighboring radiating elements will occur; hence, high isolation is needed, which is achieved in the proposed two-port MIMO antenna by achieving spatial diversity. Figure 7e–j shows the simulation of surface-current-density (SCD) distributed over the surface and ground with a scale ranging between 0.0 and 100.0 A/m. Figure 7e corresponds to the SCD contour plot at 6.30 GHz with antenna port A₁ being excited and antenna port A₂ being matched with a termination impedance of 50Ω. The observation is that the maximum SCD is accumulated within the transmission line and the outer hexagonal ring, H1. However, the mutual coupling is very low between Antenna A₁ and Antenna A₂ as both antennae are placed in a mirrored-adjacent sequence. This indicates that the signal fed to antenna A1 at 6.30 GHz is independent of antenna A₂. Similar behavior or SCD distribution is observed at FR2 frequency bands of 24.0 GHz, 28.0 GHz, 38.0 GHz, 43.0 GHz, and 60.0 GHz, respectively, observed from Fig. 7f–j. This analysis confirms that the two-port MIMO system can be further extended to a four-port MIMO system by using a suitable decoupling element placed between the independent grounds.

Fig. 7

2-Port MIMO (a) 3-D View (b) Patch details (c) Common-ground details (d) S-parameter results; SFD at (e) 6.30 GHz (f) 24.0 GHz (g) 28.0 GHz (h) 38.0 GHz (i) 43.0 GHz (j) 60.0 GHz.

Fig. 8

Single cell and array-FSS (a) 3-D view of single cell FSS (b) optimal dimensions of single cell FSS (c) simulation model of single cell FSS (d) FSS-Array (proposed) (e) Top-view of fabricated FSS printed on top-surface (f) S-parameter of proposed FSS (g) Parametric study of Single Cell FSS.

Frequency-selective-surface

The frequency-selective surface is defined as the reflective surface printed over the thin substrate with three major objectives: reflecting, transmitting, or absorbing the electromagnetic signal impinged on it. The FSS used in the proposed work is placed beneath the antenna, which reflects the energy in a forward direction, increasing the peak-realized gain at the selected frequency. The FSS has been termed a spatial filter due to the reason that FSS blocks or allows (passes) EM waves with resonance frequencies in free space. Figure 9 gives insight into designing the FSS for the proposed four-port MIMO antenna, which can reflect the desired resonance frequency when placed underneath the antenna. Figure 8a shows the modeled single-unit FSS-Cell which utilizes Rogers-dielectric of thinness 0.254 mm. The FSS unit cell shown in Fig. 8a consists of a thin metallic patch of copper metal with a thickness of 0.035 mm, printed on the top surface. The FSS structure is of the size Ux × Uy = 8.0 mm× 8 .0 mm. The outer patch is the rectangular ring of thickness 0.50 mm with square(s) of dimension U₁ × U₂ = 7.50 mm × 7.50 mm and U₃ × U₄ = 6.50 mm × 6.50 mm as shown in Fig. 8b. Moreover, square patches of dimension U₇ × U₈ = 1.0 mm × 1.0 mm are placed along the sides of the outer square ring, and all are interconnected by a horizontal-vertical strip of thickness 0.50 mm. The inter-spacing between the square patches is 1.25 mm, and between the horizontal/vertical strips is 1.75 mm, as shown in Fig. 8b. Lastly, a circular patch of Radius, R2 = 1.25 mm, is placed at the center of the metallic structure. This forms the FSS patch, which generates a wide range of bandwidth. The simulation model of the single-unit FSS-cell is shown in Fig. 8c, which is placed within the 3D rectangular cuboid. The two opposite faces are assigned with boundary condition Et = 0, and the other pair is assigned with boundary condition Ht = 0. The two faces of the cuboid are assigned as Port1 and Port2, as shown in Fig. 8c.

Fig. 9

Four-port MIMO configuration (a) 3D view (b) MIMO patch details (c) Common-ground details (d) S-parameter (e) Fabricated photograph (3D view) (f) Front-ground view; 2D radiation in E- & H-plane at (g) 3.50 GHz (h) 5.90 GHz (i) 28.0 GHz (j) 60.0 GHz.

Figure 8d, e represent the simulation model of the FSS-array and the fabricated prototype to be integrated with the proposed four-port MIMO antenna. The simulated S-parameter results are recorded in Fig. 8f with the FSS unit cell successfully achieving an operational reflective bandwidth of 10.0–43.30 GHz. Hence, the proposed FSS is integrated with the proposed four-port MIMO antenna for gain enhancement in the FR2-millimeter wave. The S₁₁/S₂₂ grazes the 0.0 dB observed in Fig. 8f, indicating all the signals that are impinged on FSS from Port1 are reflected. The S₁₂/S₂₁, which are the transmission coefficients, suggest very little power is transmitted from Port1 to Port2 via FSS. This indicates that the proposed FSS acts as a band-stop filter for a bandwidth of 10.0–43.30 GHz. Figure 8g shows the parametric study in terms of the overall size of the proposed FSS. When the size is scaled by a factor of 1.50 with a new dimension corresponding to U_x(1.50) × U_y(1.50) = 12.0 mm × 12.0 mm, the printed patch is also scaled up in dimension by a scaling factor of 1.50 and observes the operating bandwidth shifting to 9.23–31.08 GHz. For the scaling factor of 0.50, the new dimension of FSS is U x _(0.50) × U_y(0.50) = 4.0 mm × 4.0 mm, and the operating bandwidth moves away from the proposed operating bandwidth on the higher frequency side. For the unscaled structure FSS, U_x = × U_y = 8.0 mm × 8.0 mm, the operational bandwidth of 10.0–43.30 GHz is well suited for FR2 band applications. As the application of FSS defines, the repetitive structure of the unit FSS cell, an array of 7 × 7 FSS, is achieved by using the repetitive unit FSS cell shown in Fig. 8a. The 3D model of array-FSS is the dimension of U_xx×U_yy = 56.0 mm × 56.0 mm. The distance between the two adjacent cells is 0.50 mm, and from the edge is 0.25 mm. Figure 8e shows the prototype of the fabricated FSS-7 × 7 array with a 3D-view and the top-view printed on Rogers substrate, which can be integrated with an MIMO antenna and acts as a reflector to achieve high gain in FR2 millimeter bands.

Four-port MIMO antenna

Section "Two-port MIMO system" discussed a two-port MIMO antenna, and the relevance of increasing the number of identical-radiating elements was also explained with the help of Shannon’s capacity theorem. More radiating elements placed in the desired orientation achieved spatial diversity as achieved in a two-port antenna with an adjacent-mirrored sequence. The advantage of the two-port MIMO is that the fading of the signals is reduced to a large extent, and this motivates an increase in the number of radiating elements from two to four, which is significantly discussed in Section "Four-port MIMO antenna". Figure 9 illustrates the four-port MIMO configuration, which offers more resistance to fading of the receiving signals, thereby increasing the efficiency as well as achieving higher data rate transmission. The 3D version of the proposed four-port MIMO antenna is shown in Fig. 9a with four radiating elements marked as A₁, A₂, A₃, and A₄, respectively. The radiating patches A₁ and A₂ are mirrored-adjacently placed with common-ground G₁ shared by both the patch. The antennae A₃ and A₄ are also the replica arrangement of the pair of antennas A₁ and A_2, but are orthogonal to each pair of radiating elements. The antenna pair, A₃ and A₄, also shares the common ground marked as G₂. Both grounds are interconnected by a decoupling structure (DCS). All four antennae, A₁, A₂, A₃, and A₄, are connected to the SMK connector for input-signal excitation of 1.0–90.0 GHz. Figure 9b shows the top view of the MIMO antenna with the overall dimension of the antenna corresponding to W_P × L_P1=30 mm × 36 mm. The center-to-center spacing between the adjacent-radiating elements is D₁ = 15.0 mm, while the spacing between A₁-A₄ or A₂–A₃ is G = 8.50 mm. Figure 9c shows the ground configuration of the proposed four-port MIMO antenna. As mentioned, the radiating-patch A₁-A₂ shares the common-ground G₁ of dimension W_g1 × L_g= 30 mm × 4  mm, and radiating-patch A₃–A₄ shares the common-ground G₂ of the same dimension as G₁. The distance between the G₁ and G₂ is L_D = 28 mm with a novel de-coupling structure placed between the edge-center of both the grounds. The decoupling structure also serves as the common ground of the overall MIMO antenna, which is continuous and resolves the issue of a disconnected ground. However, in the real-time system MIMO applications, when integrated with the transmitter-receiver module, the common ground will serve as the reference voltage level to 0 V. The decoupling structure also includes a pair of rectangular strips of dimension L_a×W_c=10 mm × 1.0 mm. Both strips are connected to stubs of length L_B = 8 mm and width 3 mm. The stub is also embedded with two rectangular strips of dimension L_X × W_A=0.5 mm × 4 mm as shown in Fig. 9c. The S-parameter graph is also represented in Fig. 9d with S₁₁= − 10.0 dB bandwidth of 2.90–7.29 GHz (Band-A) and 20.25–88.02 GHz (Band-B). The isolation between ports marked as S₁₂, S₁₃, and S₁₄ is also plotted in Fig. 9d, with adjacent port isolation of more than 5.0dB in Band-A and more than 15.0 dB in Band-B. The isolation of S₁₃ and S₁₄ is more than 10.0 dB in Band-A and greater than 25.0 dB in Band-B as observed in Fig. 9d. Figure 9e, f show the photograph of the fabricated prototype of a four-port MIMO antenna. The fabricated antenna is integrated with an FSS array to increase the gain in the millimeter-wave FR2 bands.

Figure 9g, h show the plot of the 2D-radiation pattern in the E and H planes at 3.50 GHz and 5.90 GHz. At these two values of frequency, the antenna exhibits dipole and omnidirectional simulated-measured radiation patterns with acceptable cross-polarization. However, at frequency values of 24.0 GHz and 28.0 GHz, as shown in Fig. 9i, j, the 2D radiation pattern does deteriorate from the pattern of the dipole antenna, which is due to the following reasons.

• d. (a) Surface current and propagation of higher-order modes.

• e. (b) Material losses and dispersion of the signal, which is largely related to conducting copper losses at higher frequencies.

• f. (c) Radiation anomalies of planar antenna inheriting edge effects.

• g. (d) Fabrication tolerances include a very minor error in the deviation of size.

The FSS, which is designed and proposed in Fig. 8, achieves the objective of gain enhancement of the proposed four-port MIMO antenna shown in Fig. 9. The MIMO antenna, when integrated with the FSS array, increases the gain within the bandwidth occupied by the FSS. This is due to the reason that the FSS acts as a reflector or band-stop filter when placed near the MIMO antenna. Figure 10 shows the integration of FSS with a Four-port MIMO antenna and the corresponding simulated-measured S-parameters results. Figure 10a shows the simulated model screenshot where the FSS is placed beneath the four-port MIMO antenna with a distance of d₁ = 3.50 mm. The distance corresponds to the lower cut-off frequency at 43.0 GHz, with the value of λ being in the range of $\:\frac{\lambda\:}{2}\le\:{d}_{1}\le\:\frac{\lambda\:}{4}$. The optimal distance is achieved by parametric variation of d₁, and at d₁ = 3.50 mm, the optimal result in the form of enhanced peak-realized gain at specified frequency values is achieved. Figure 10b shows the photograph of the MIMO antenna integrated with an FSS array, which is separated by foam. The 3D view of the proposed integrated MIMO-FSS is fabricated by using a photo-lithographic method, which achieves more precision in dimension and more accuracy in measured results. Figure 10c, d show the plot of simulated and measured reflection coefficients for all four ports corresponding to S₁₁, S₂₂, S₃₃, and S₄₄. The − 10.0 dB simulated bandwidth corresponds to 2.72–7.25 GHz in Band-A and 20.35–84.06 GHz in Band-B. It can be observed that the bandwidth generated by all the individual radiating elements overlaps with each other due to the perfectly symmetrical geometry achieved in the simulation environment under ideal conditions, with perfect matching of all the ports to 50Ω. The measured S₁₁, S₂₂, S₃₃, and S₄₄ graphs are plotted in Fig. 10d with an overlapping bandwidth of 3.45–7.25 GHz in Band-A. However, the bandwidth achieved in Band-B by all four radiating elements corresponds to 19.70–82.10 GHz. As per the observations, the deviation in overlapping is observed between 53.0 GHz and 80.0 GHz, but within a −10.0 dB impedance bandwidth. Figure 10e, f record the transmission coefficients S₁₂, S₁₃, and S₁₄ for both bands, Band-A and Band-B, in Simulation-Measured results. Figure 10e corresponds to simulated transmission coefficients with Band-A recording a minimum isolation of more than 5.0 dB, while Band-B offers a minimum isolation of more than 15.0 dB. The measured transmission coefficients or isolation correspond to more than 10.0 dB in Band-A and 18.0 dB in Band-B. The isolation achieved between all four inter-spaced radiating elements is sufficient to achieve better spatial diversity. The advantage of the decoupling structure was to provide common-ground connectivity between isolated ground G₁ and G₂. However, the decoupling structure also plays an important role in canceling the current vector flowing in the opposite direction, which is shown in Fig. 10g, j and is the surface-current-density distribution graph at frequency values of 3.50 GHz, 5.90 GHz, 24.0 GHz, and 28.0 GHz. The antenna A₁ is excited in all four cases, while antennae A₂, A_3, and A₄ are terminated by a matched impedance of 50Ω. At a lower frequency of 3.50 GHz SCD simulation, the isolation is better between antenna A₁ and A_2, but the signal radiated by Antenna A₁ induces minor SCD flow in antenna A₄. However, this is a very low coupling for which the isolation corresponds to more than 5.0 dB (S₁₄). For the remaining frequency values of 5.90 GHz, 24.0 GHz, and 28.0 GHz, the impact of excitation of antenna A₁ is also much less, resulting in higher values of isolation.

Fig. 10

Four-port MIMO antenna integrated with FSS (a) 3D view (b) Top-view and MIMO antenna loaded with FSS connected to VNA (c, d) Simulated-Measured reflection-coefficients (e, f) Simulated-Measured transmission-coefficients; SCD at (g) 3.50 GHz (h) 5.90 GHz (i) 24.0 GHz (j) 28.0 GHz.

The MIMO_M−FSS antenna, which includes four radiating elements A₁, A₂, A_3, and A_4, radiates the electromagnetic signals independently. However, their orientation ensures not only the inter-spaced isolation but also maintains the desired operational bandwidth. Hence, the correlation between the radiation patterns generated by individual antennae is measured by the Envelope-Correlation-Coefficient (ECC_M−FSS).

$$\:{\gamma\:}_{c\left(MIMO\right)}=\frac{\underset{0}{\overset{2\pi\:}{\int\:}}\underset{0}{\overset{\pi\:}{\int\:}}\left(({XPRE}_{\theta\:.m}\left(\theta\:,\phi\:\right)\:{E}_{\theta\:,s}^{*}\:\left(\theta\:,\phi\:\right){P}_{\theta\:}\left(\theta\:,\phi\:\right)+\:{E}_{\phi\:.m}\left(\theta\:,\phi\:\right)\:{E}_{\phi\:,s}^{*}\:\left(\theta\:,\phi\:\right){P}_{\phi\:}\left(\theta\:,\phi\:\right)\right)sin\theta\:\:d\theta\:\:d\phi\:\:}{\sqrt{{\gamma\:}_{m}^{2}}\sqrt{{\gamma\:}_{s}^{2}}\:}$$

(4)

The ECC_M−FSS calculation helps in quantifying the degree of correlation between the signal received by each of the radiating elements by the receiver. The more similar the radiation patterns, the better the diversity and the higher the data throughput. The value of ECC_M−FSS lies between 0 and 1, with 0 indicating the exact replication of radiation patterns by each of the radiating elements, while 1 indicates the highly deteriorated radiation patterns due to maximum interference between them. The values of ECC_M−FSS for the operational bandwidth must be ideally less than 0.50, which are calculated by Eq. 4, and are used for the 3D radiation method. The above-said equations use S-parameter values to calculate ECC_M−FSS with simulated and measured values in Band-A corresponding to less than 0.18 and 0.22, as noted in Fig. 11a, b. The Band-B values of simulated-measured ECC_M−FSS correspond to 0.108 and 0.12. The values of ECC_M−FSS achieved in Band-A and Band-B are below 0.50, which is the desired threshold value for practical applications.

$$\:{DG}_{\text{M}-\text{F}\text{S}\text{S}}=10\sqrt{1-{\left|{\rho\:}_{e}\right|}^{2}}$$

(5)

Fig. 11

Diversity-parameters (a, b) Simulated-Measured ECC_M−FSS (3D Radiation method) (c, d) Simulated-Measured DG_M−FSS (3D Radiation method) (e–f) Simulated-Measured TARC_M−FSS (g, h) Simulated-Measured CCL_M−FSS (i, j) Simulated-Measured MEG_12(M−FSS) (k, l) Simulated-Measured MEG_13(M−FSS) (m, n) Simulated-Measured MEG_14(M−FSS).

The Diversity-Gain (DG_M−FSS) measures the signal reliability of the MIMO-radiating elements. Figure 11c, d record the values of DG_M−FSS in Band-A and Band-B, which are calculated by Eq. (5). The DG_M−FSS also signifies the mitigation of fading effects, thereby evaluating the merit of improvement in signal quality or error-reduction rate. The values of DG_M−FSS ideally must be more than 9.95 dB. Figure 11c, d record the simulated-measured values of DG_M−FSS in Band-A and Band-B. In both the bands (Band-A and Band-B), the values are greater than 9.95 dB, and in Band-B values of DG_M−FSS graze the 10.0 dB, achieving maximum diversity. However, in the simulated results of DG_M−FSS in Band-A, the values are above 9.86 dB.

$$\:{\varGamma\:}_{a}^{t}=\frac{\sqrt{{\left|{S}_{11}+{S}_{12}{e}^{j\theta\:}\right|}^{2}+{\left|{S}_{21}+{S}_{22}{e}^{j\theta\:}\right|}^{2}}}{\sqrt{2}}$$

(6)

The Total-Active-Reflection-Coefficient (TARC_M−FSS) indicates the overall return loss of the entire four-port MIMO antenna. TARC_M−FSS also measures how much power is reflected when all the MIMO antennas are excited. The individual S-parameters (S₁₁, S₂₂, S₃₃, S₄₄) correspond to the performance of individual ports, but the MIMO system calculates the reflection coefficient cumulatively for all the ports. The TARC_M−FSS is calculated from Eq. (6), and the TARC_M−FSS for the proposed MIMO-FSS antenna is plotted in Fig. 11e, f. The simulated values are more than 3.20dB in Band-A and more than 6.0dB in Band-B. The measured values record more than 4.0dB and 6.0dB in Band-A and Band-B, respectively.

$$\:{\rho\:}_{mm}=1-{\sum\:}_{n=1}^{4}{\left|{S}_{mn}\right|}^{2}$$

(7)

$$\:{\rho\:}_{ms}=-\left({S}_{mm}^{*}{S}_{ms}+{S}_{sm}^{*}{S}_{ms}\right)$$

(8)

Channel-Capacity-Loss quantifies the amount of reflection in the data-rate transmission, which is due to the non-idealities in the MIMO antenna system. The CCL_M−FSS depends on the perfect achievement of spatial diversity with higher isolation. Equations (7, 8) and the corresponding simulated-measured values of CCL are plotted in Fig. 11g, h. The simulated and measured CCL_M−FSS are less than 0.40 b/s/Hz in Band-A and Band-B. The simulated CCL_M−FSS in Band-A and Band-B are less than 0.50 b/s/Hz and 0.30 b/S/Hz, respectively. Also, the measured CCL_M−FSS corresponds to less than 0.18 b/s/Hz and 0.25 b/s/Hz in Band-A and Band-B, as noted in Fig. 12.

$$\:{MEG}_{ms}=0.5\left[1-\sum\:_{s=1}^{K}{\left|{S}_{ms}\right|}^{2}\right]$$

(9)

$$\:{MEG}_{m}=0.5\times\:(1-{\left|{S}_{mm}\right|}^{2}-{\left|{S}_{ms}\right|}^{2})$$

(10)

$$\:{MEG}_{s}=0.5\times\:(1-{\left|{S}_{ss}\right|}^{2}-{\left|{S}_{sm}\right|}^{2})$$

(11)

The ratio calculates the MEG_60.0 GHz, which is given by

$$\:\frac{{MEG}_{m}}{{MEG}_{s}}=\frac{0.5\times\:(1-{\left|{S}_{ms}\right|}^{2}-{\left|{S}_{ms}\right|}^{2})}{0.5\times\:(1-{\left|{S}_{ss}\right|}^{2}-{\left|{S}_{sm}\right|}^{2})}$$

(12)

Mean-Effective-Gain (MEG_M−FSS) can be explained as the power produced by the diversity four-port MIMO_M−FSS antenna compared to that of the power accepted by the antenna, which can produce an omnidirectional pattern. It is also defined as the average power received by any of the radiating elements. The S-parameter method of calculation ECC is achieved by Eq. (4), with MEG_M−FSS obtained by each port corresponding to −3.0dB, and the ratio of MEG between two ports is nearly 0.0 dB. Figure 11i–n shows the plot of simulated and measured MEG_M−FSS. Figure 11i, k, m show the MEG plot between port₁–port₂, port₁-port_3, and port₁-port₄ with values of MEG_M−FSS for individual ports corresponding to −3.0 dB and the ratio 0.0 dB. However, the deviation of MEG_M−FSS for individual ports and ratios is observed in Fig. 11j, l, n, which is due to the conductor losses at higher frequencies.

Fig. 12

SAR_M−FSS analysis of Four-port MIMO_M−FSS antenna integrated with FSS (a) 3D Simulation model (b) distance between the antenna-FSS and phantom-model; SAR analysis at (c) 3.50 GHz (d) 5.90 GHz (e) 24.0 GHz (f) 28.0 GHz (g) 38.0 GHz (h) 39.0 GHz (i) 41.0 GHz (j) 43.0 GHz (k) 47.0 GHz (l) 60.0 GHz (m) S-parameter graph.

The specific absorption rate (SAR_{− FSS}) is defined as the power absorbed by the body tissue per kg, with tissue containing three layers of skin, fat, and muscle. The SAR calculation becomes important when the proposed MIMO antenna with FSS is used for on-body applications. Devices like laptops, tablets, mobile phones, etc. can be easily embedded with the proposed MIMO-FSS antenna, and hence, the direct interaction of electromagnetic signals with the human body will occur. Figure 12a, b show the environment model of the proposed MIMO-FSS placed near the human-head-phantom, and on excitation of the antenna by an input EM-wave, the depth of penetration is studied by calculating the SAR_M−FSS, which is frequency dependent. The human-head-phantom model can be considered as the formation of tissue with three layers of skin, fat, and muscle. Hence, the electromagnetic properties of all three layers, including permittivity, conductivity, and loss tangent with mass density, need to be known, which are tabulated in Table 5. The SAR values are calculated by Eq. (13) with the applied electric field⁶⁷.

$$\:{SAR}_{\text{M}-\text{F}\text{S}\text{S}}=\frac{\sigma\:{\left|E\right|}^{2}}{\rho\:}$$

(13)

σ-conductivity of body tissue (S/m). E-applied electric field (V/m).

The ρ-mass density of the body tissue (kg/m³).

The two lower frequency values of 3.50 GHz and 5.90 GHz, which are out of the band of FSS, offer SAR_M−FSS values of 0.603 W/kg and 0.992 W/kg. However, frequency values of 24.0 GHz, 28.0 GHz, 38.0 GHz, 39.0 GHz, and 41.0 GHz lie within the operating bandwidth of the FSS-array and significantly reduce SAR with values corresponding to 0.0742 W/kg, 0.246 W/kg, 0.196 W/kg, 0.165 W/kg, and 0.278 W/kg. The higher values of frequency corresponding to 43.0 GHz, 47.0 GHz, and 60.0 GHz are also out of the band of FSS and offer SAR values of 0.395 W/kg, 0.427 W/kg, and 1.14 W/kg. The application of the FSS-array in the proposed work, which acts as a band stop filter for the partial millimeter-Wave FR2 band, not only enhances the peak-realized gain bit but also reduces the SAR_M−FSS values. However, the calculated values⁶⁷ conclude that the maximum SAR_M−FSS value is less than 1.14 W/kg with a minimal value of 0.0742 W/kg at 24.0 GHz, which is in the operating band of FSS. This analysis concludes that the proposed MIMO_M−FSS antenna with integrated FSS is suitable for on-body application in sub-6.0 GHz 5G, WLAN, V2X, and FR2 millimeter-wave bands.

The higher data-rate transmission has emerged as one of the needs for modern wireless communication. Also, wearable antennae have found a significant place in modern communication, which demands the flexible nature of the antenna. The flexible antenna finds numerous applications not only in the medical monitoring of vital body parameters but also in the entertainment industry and military applications. The proximity of the human body can be explained as antenna backward radiation absorbed by the human body tissue. Hence, the controlled SAR within the value of 1.60 W/kg for 1 g of tissue is essential. However, the proposed work reports a compact antenna designed on a Rogers thin substrate of thickness 0.254 mm, which can be easily bent at different angles without breaking. Hence, the proposed MIMO antenna is well-suited for a wide range of wearable applications in the current scenario and future wireless applications with low SAR values. The proposed work also includes the integration of FSS with the MIMO antenna and is tested for SAR at different frequency values. Also, the FSS uses Rogers 0.254 mm substrate, which can also be bent at different angles. Figure 13 shows the bending analysis of the MIMO-FSS integrated antenna with different angles ranging from 0 degrees to 45 degrees. Figure 13a–d show the bending of the MIMO-FSS antenna at 0 degrees (no bending), 15-degree bending, 30-degree bending, and 45-degree bending with corresponding − 10.0d B bandwidth of 2.85–6.85 GHz (Band-A) and 20.0–70.0 GHz shown in Fig. 13e. The S-parameter results conclude that at different bending angles, the − 10.0 dB bandwidth is not deviated, and all the applications mentioned earlier are suitable for applications in the field of flexible electronics. Figure 13f compares 2D radiation patterns in the E-H plane at 15°, 30° and 45° which are plotted at 3.50 GHz. The comparison shows little deviation of the 2D radiation patterns in both planes and suggests the proposed work can be easily integrated with the conformal devices.

Fig. 13

Bending analysis (a) 0 degree bending (no bending) (b) 15 degree bending (c) 30 degree bending (d) 45 degree bending (e) S-parameter graph (f) 2D radiation patterns at bending angles of 15, 30 & 45 degree bending.

The MIMO_M−FSS antenna integrated with FSS needs to be tested in the far-field region with the test antenna placed as a receiver and the horn antenna acting as a transmitter. The proposed MIMO-FSS antenna is placed within the anechoic chamber as shown in Fig. 14a, b shows the plot of peak-realized-gain with and without integration of FSS. The MIMO antenna without FSS offers a peak-realized gain of 1–2 dBi in Band-A and an average peak-realized gain of 5.0 dBi in Band-B. On the other hand, the measured peak-realized-gain corresponds to 2.61 dBi at 3.50 GHz, 2.46 dBi at 5.90 GHz, 3.88 dBi at 24.0 GHz, 3.98 dBi at 28.0 GHz, 4.02 dBi at 38.0 GHz, 4.12 dBi at 39.0 GHz, 4.22 dBi at 41.0 GHz, 4.32 dBi at 43.0 GHz, 4.37 dBi at 47.0 GHz and 4.45 dBi at 60.0 GHz in the absence of FSS. Figure 14b also includes the simulated-measured peak-realized-gain of the MIMO antenna integrated with FSS. The simulated average peak-realized-gain rises to 11.58dBi while the measured average peak-realized-gain records a value of 10.0 dBi in Band-B. The measured peak-realized-gain is enhanced in Band-B by 5.85 dBi, which is due to the integration of FSS with MIMO antenna. Figure 14b, including the radiation efficiency in Band A, at frequencies 3.50 GHz & 5.90 GHz, records the values of 82.89% & 83.94%. On the other hand, in Band B, the radiation efficiency corresponds to 88.66% at 24.0 GHz, 89.27% at 28.0 GHz, 90.71% at 38.0 GHz, 90.85% at 39.0 GHz, 91.42% at 41.0 GHz, 91.93% at 43.0 GHz, 90.98% at 47.0 GHz, and 84.61% at 60.0 GHz. Figure 14c, d show the plot of 3D radiation patterns at 24.0 GHz, 28.0 GHz with gain corresponding to 10.3 dBi, 10.0 dBi, respectively. The 3D radiation patterns indicate that the back lobes of the patterns are reflected from the FSS surface, which functions as a band-stop filter between 10.0 GHz and 43.3 GHz. Also, 2D-measured radiation patterns are plotted in Fig. 14e, f at 24.0 GHz & 28.0 GHz, which show that the patterns are highly directional.

Fig. 14

Far-field analysis of MIMO-FSS antenna (a) Photograph of MIMO-FSS placed within the anechoic chamber (b) peak-realized-gain (PRG) comparison without & with FSS and radiation efficiency; 3D radiation at (c) 24.0 GHz (d) 28.0 GHz; Simulated and measured 2D radiation patterns at (e) 24.0 GHz (f) 28.0 GHz.

State-of-the-art comparison

Table 5 Comparison of the proposed work.

The proposed MIMO antenna integrated with a novel FSS-array is compared with the previously published work, as shown in Table 5. The antenna is compared with size, isolation achieved, technique, FSS integration, maximum peak-realized-gain achieved, CMA analysis, SAR, and bending analysis. The minimal area occupied by the MIMO antenna is 18.0 mm × 8.50 mm⁴⁷, but no gain enhancement technique is used. It is also observed that in any of the previously published works, at least one of the analyses is missing for concrete validation. Also, the antenna with a two-port configuration utilizes a frequency-selective surface with a maximum peak-realized gain of 15.0 dBi and occupies an area of 25 mm × 30 mm. However, the number of ports is limited to two, and hence the proposed MIMO-FSS antenna includes the key analysis of SAR, banding, and CMA with a maximum peak-realized-gain of 14.89 dBi with extremely controllable SAR value and a minor deviation in the bending of S₁₁ results of the proposed work. These added features of the proposed MIMO-FSS antenna make it suitable for a wide range of applications in Band-A and Band-B.

Conclusions and future scope

The experimental analysis of a four-port MIMO antenna was designed, fabricated, and tested for SAR as well as for conformal operation. The Rogers substrate was the common dielectric used in MIMO (1296 mm²) and FSS-array (3136 mm²) design. The proposed MIMO includes dual bands (3.45–7.25 GHz, 12.70–82.10 GHz) with integrated FSS operating between 10.0 and 43.30 GHz. The peak-gain is enhanced by 8.0 dBi where FSS is placed beneath MIMO-antenna reflecting EM-signals which are incident from different angles. Measured diversity metrics remain within acceptable limits: ECC ≤ 0.50, DG > 9.95 dB, TARC ≤ 0 dB, CCL ≤ 0.40 b/s/Hz, MEG ≈ − 3 dB, and MEG balance ≈ 0 dB across both bands. SARM-FSS values at 3.50, 5.90, 24.0, 28.0, 38.0, 39.0, 41.0, 43.0, 47.0, and 60.0 GHz comply with the SAR limit of 1.60 W/kg (1 g tissue). The design achieves peak-realized gains of 2.89–3.36 dBi in Band-A and 10.0–10.3 dBi in Band-B, with consistent radiation patterns. Conformal testing at 15°, 30°, and 45° shows that FR2 performance remains within the − 10 dB bandwidth.

The FSS geometry can be further optimized by using fractal, meta-surface-inspired, or also using periodic layouts. The reconfigurable FSS can also be used, where PIN diodes, MEMS switches are a few options. The stretchable substrates can also be used for flexible applications, such as polyimide, PDMS.