Antenna geometrical configurations

The geometrical outline and the effective design parameters for the proposed dual element MIMO antenna system is shown in Fig. 1. Where Fig. 1(a) illustrates the top view, and the bottom view is shown in Fig. 1(b). The geometry features flower shaped antenna radiators, with each element comprising five petals (minor and major radius r2 and r3) and fed by a 50 Ω transmission line. The antennas are organized in a spatial diversity configuration, where in identical elements are positioned adjacent to each other with a gap of D1 (Fig. 1(a)). The bottom side of the substrate hosts two crescent shaped defected ground structures. Subsequently, the upper edge of the ground plane is truncated as part of an enhancement strategy to improve performance. The reported MIMO antenna structure is designed over a semiflexible Rogers 5880 substrate, with dimensions measuring 32 × 20 × 0.508 mm³. The additional optimized dimensions are as follows: Ls = 32 mm, Ws = 20 mm, D1 = 6.35 mm, Wf = 2.1 mm, Lf = 11.37 mm, r1 = 3.5 mm, r2 = 2 mm, r3 = 4 mm, R1 = 5 mm, G1 = 0.57 mm, L1 = 12.36 mm, L2 = 5.29 mm. ANSYS HFSS tool is used for the design and simulation process.

Figure 1. Geometrical configurations (a) Top-view, (b) Bottom-view.

The development of the recommended MIMO antenna structure and its associated design stages are depicted in Fig. 2. The simulated S-parameters, total gain, and axial ratio (AR) are shown in Fig. 3(a–d). The first step in the design process involves conceptualizing a reference circular monopole antenna with its initial dimension of radius 6.1 mm, derived from reference [Reference Balanis32]. Subsequently, the circular radiator is modified into a semicircular structure to achieve the desired frequency response. However, for the sake of brevity, the first design step is not discussed in detail. Here the initial design stage starts with the development of a dual-element semicircular radiating patch with a complete ground plane stated as Ant_I (See Fig. 2(a)). This configuration demonstrates a nonzero resonant mode viz. TM₂₁ at 28.2 GHz, showing |S₁₁| value of approximately −6 dB. This validation is confirmed by examining the impedance plot of a single element of Ant_I (see Fig. 4(a)). Utilizing equation (1) the nonzero resonant frequency (f _r) for Ant_I is computed and found to be 27.6 GHz [Reference Modak, Lokam and Farooq33].

(1)\begin{equation}{f_r} = \frac{{{K_{nm}}{v_0}}}{{2\pi R\sqrt {{\varepsilon _r}} }}{\text{ }}\end{equation}

Figure 2. Design steps (a) Ant_I, (b) Ant_II, (c) Ant_III, (d) Ant_IV (proposed).

Figure 3. Performance evaluation (a) |S₁₁|, (b) |S₁₂|, (c) Total gain, (d) Axial ratio.

Figure 4. (a) Plot of impedance, (b) Surface current density at 27.5 GHz.

Where, “v₀” represents the velocity of light in vacuum, “R” = 6 mm refers to the radius of a semicircular patch along the horizontal direction, K _nm = 5.135 signifies the root of the derivative of the Bessel function. In order to enhance the impedance matching within the desired frequency bands of interest (25–31 GHz), Ant_I is modified by inserting five petal-shaped parasitic stubs, placed strategically overlapped to each other on both the antenna radiators, resulting in distinctive flower-shaped antenna structure. However, the ground layer remains intact. This configured antenna structure (Ant_II) improves the impedance matching. The same has been validated through the surface current distribution plot. Figure 4(b) indicates the current with higher intensity is concentrated along the upper periphery of the flower petals (marked with a circle). Conversely, minimal current density is observed at the center of the patch.

Notably, a similar current distribution pattern is maintained across other antenna element (port 2) due to their identical characteristics. From this observation it can be concluded that most of the radiations occur from the upper periphery of the flower petals, thereby establishing resonance at 27.5 GHz, with an impedance bandwidth extending from 27.3 to 27.8 GHz, which can be seen from Fig. 3(a). Although Ant_II is capable of providing a zero resonant frequency with 0.5 GHz bandwidth. However, the primary goal remains the attainment of wideband characteristics within 25–31 GHz band. To accomplish this, alterations have been made to the ground plane of Ant_III, involving the integration of a crescent-shaped slot. The crescent-shaped defected ground plane is designed by integrating circular defected ground structures (having radius R1). Later, a small circular conductor with a radius “r1” is strategically positioned over each defected ground structure, while the top layer of the antenna remains unchanged (See Fig. 2(c)).

Moreover, it is widely recognized that incorporating slots over the antenna radiator or ground layer can enhance operational bandwidth. Nevertheless, this practice significantly impacts the antenna’s radiation characteristics and gain [Reference Modak, Khan and Laskar34, Reference Modak, Daasari, Shome and Khan35]. With these modifications, Ant_III provides an expanded operational bandwidth spanning from 25.3 to 30.1 GHz, with a remarkable coupling level of −30 dB. Noted, this modification results in a reduction in antenna gain to 3.5 dBi (see Fig. 3(c)). An investigation into resonance and gain is undertaken through a parametric study involving the variation of the radius “r1” (small circle). The observation from Fig. 5(a) illustrates that as the parameter “r1” increases; there is a noticeable enhancement in antenna impedance matching. This improvement continues until “r1” reaches a value of 3.5 mm, beyond which the impedance begins to degrade. Similarly, when comparing gains within the desired band, it becomes apparent that except for the case where r1 = 3.5 mm, the values of “r1” exhibit negative gains. Despite the aforementioned findings, further modifications have been implemented within the ground layer to attain circularly polarized (CP) radiation characteristics. This realization of the same has been thoroughly analyzed utilizing the CMT. It is well documented in existing literature that generating circularly polarized (CP) radiation requires the simultaneous excitation of two orthogonal characteristic modes with a 90° phase difference. This entails that the characteristic angles of these modes should ideally be characteristics angle (CA)1 = 135°, and CA2 = 225°, thereby deviating by 45° from the resonance angle of 180°. Besides, both modes should possess identical modal significance (MS) values, ensuring MS1 = MS2 [Reference Han and Dou36, Reference Sharma, Gangwar, Singh, Solanki, Rajpoot, Kanaujia, Singh and Ekuakille37]. Considering this, the ground layer of Ant_III has been modified by truncating the upper edges by a width of G1 (see Fig. 2(d)).

Figure 5. Parametric variations (a) |S₁₁|, (b) Total gain.

Now to investigate the modal behavior satisfying the CP condition, modal analysis has been sorted at a frequency of 29 GHz and is carried out utilizing the CST Microwave studio tool. The analysis of MS highlights the significance of all modes M1–M4. Specifically, M1 and M2 resonate distinctly at frequencies of 29.49 and 29.57 GHz, respectively. Conversely, M3 and M4 coincide, resonating at a common frequency of 28.65 GHz, with an associated MS value of 1 as illustrated in Fig. 6(a). At a frequency of 29.27 GHz, it has been noted that the magnitudes of modes M1–M4 coincide. This observation suggests that, at 29.27 GHz, the CA values between the modes exhibit a phase difference of 92°. This has been validated through the CA curves depicted in Fig. 6(b), where modes M1 and M3, M1 and M4, M2 and M3, and M2 and M4 exhibit a phase difference of almost 45° from the resonance angle of 180°. (CA1 and CA2 = 226°, CA3 and CA4 = 134°). The modal current distributions (J ₁ and J ₃, J ₁ and J ₄, J ₂ and J ₃, J ₂ and J ₄) corresponding to modes M1 and M3, M1 and M4, M2 and M3, and M2 and M4 are illustrated in the Fig. 7. Notably, it is evident that the current distributions in modes J ₁ and J ₃, J ₁ and J ₄, J ₂ and J ₃, and J₂ and J ₄, exhibit a high degree of orthogonality, as indicated with black arrow. However, an exception arises at mode M2, where the current flows in the opposite direction, highlighted with red color. From the 3D radiation patterns, it can be seen that only J ₁ & J ₄ radiate almost in all directions, whereas, J ₂ radiates in ±y direction having null in ±z direction, and J ₃ radiates in ±x direction (see Fig. 7(a-d)).

Figure 6. Mode analysis (a) Modal significance, (b) Characteristic angle.

Figure 7. Modal current distributions (a) J ₁ & J₃, (b) J ₁ & J ₄, (c) J ₂ & J ₃, (d) J ₂ & J ₄.

Finally, the assessment conducted using CMT confirms that by truncating the ground layer, Ant_IV demonstrates the ability to generate a significant phase difference of 92° across various modes, effectively achieving CP properties at 29.4 GHz with a 3 dB ARBW spanning from 29.1 to 29.7 GHz. Additionally, a parametric analysis is conducted to evaluate the circularly polarized radiation characteristics by varying the width “G1” of the truncated section on the ground layer. From Fig. 8, it is evident that at G1 = 0.4 mm, the antenna does not exhibit circularly polarized radiation behavior. However, at G1 = 0.8 mm, an ARBW of 0.3 GHz (29.1–29.4 GHz) is achieved. Further increasing G1 = 1 mm results in a reduction of ARBW to 0.2 GHz (29.2–29.4 GHz). This analysis reveals that as the width “G1” increases, the ARBW decreases. Therefore, the optimized dimension for G1 is determined to be 0.57 mm. Finally, the proposed antenna (Ant_IV) showcases a broad operating bandwidth extending from 25.7 to 30.6 GHz making it well-suited for body-centric applications in the healthcare domain. The simulated performances of all design iterations (from Ant_I to Ant_IV) are outlined in Table 1 for comparative analysis.

Figure 8. Parametric analysis corresponds to width G1.

Table 1. Design iterations performance comparisons

Conformability and on-body performance analysis

In wearable technology contexts, it is crucial to conduct the analysis because the configuration of the suggested antenna structure may be bent with the body’s contours when positioned on various parts of human body, such as the hand, and biceps, potentially altering its performance characteristics. This assessment entails the evaluation of performance under conditions where the antenna structure is subjected to bending along the Y-axis, with radii “Ry” as depicted in Fig. 9. Figure 10(a) illustrates the comparison of the simulated |S₁₁| values. The findings demonstrate the robustness of the suggested wearable antenna, particularly in relation to its overall impedance bandwidth across various bending radii. Nevertheless, at a bending radius Ry = 15 mm, the antenna impedance gets mismatched. This is due to the decrease in effective resonating length caused by increased bending.

Figure 9. Bending radii Ry (a) 15 mm, (b) 30 mm, (c) 45 mm, (d) 60 mm.

Figure 10. Performance evaluation (a) |S₁₁|, (b) Axial ratio.

Similarly, it has also been observed that at Ry = 30 mm the resonance is shifted toward the lower frequency. The analysis also extends the 3 dB ARBW of the proposed MIMO antenna across various bending conditions, as illustrated in Fig. 10(b). Notably, regardless of the values of Ry, the designs consistently exhibit circularly polarized radiation patterns across the operational frequency range. As the antenna is intended for on-body applications it is crucial to assess the characteristics of the antenna, including its S-parameters (|S₁₁|/|S₁₂|), and SAR, under wearable conditions. In this context, the antenna is positioned on a human body tissue model composed of three layers, including the skin (${\varepsilon _r} = 16.6,{\text{ }}\sigma = 25.8$), fat (${\varepsilon _r} = 6.09,{\text{ }}\sigma = 5.04$), and muscle (${\varepsilon _r} = 24.4,{\text{ }}\sigma = 33.6$), arranged in a cubic configuration with an overall size of 32 × 28 × 15 mm³. Noteworthy, the antenna-to-skin surface distance is maintained at 6 mm (h) which resembles the thickness of the cloth [Reference Tiwari, Kaim, Singh, Khan and Kanaujia30].

The electrical properties of different tissue layers are characterized with respect to a frequency of 28 GHz. The radiation boundaries are maintained at a significant distance ≫λ₀/2 (See Fig. 11(a)). Figure 11(b) illustrates the simulated |S₁₁|, indicating impedance mismatch occurring at 27 GHz for h = 4 and 5 mm. Simultaneously, with increasing height (h), antenna performance shows improvement. Likewise, it can also been noted that varying the height (h) does not significantly impact the performance of |S₁₂|. The assessment of SAR has been conducted, focusing on ensuring human safety. Currently, there are no established standards for accessing SAR at millimeter-wave frequency spectrums. Therefore, the validation of the proposed MIMO antenna is being conducted by adhering to existing guidelines set forth by regulatory bodies such as the Federal Communications Commission, and International Commission on Non-Ionizing Radiation Protection [Reference Shariff, Ali, Mane, Alslath, Kumar, Pathan, Kishk and Khan31]. The average specific absorption rate is witnessed to be 2.59 and 2.2 W/kg at a frequency of 28 and 30 GHz respectively, when subjected to an input power level of 100 mW through a single antenna element (see Fig. 12). To comply with the upper SAR limit, the maximum allowable power that can be delivered to the proposed antenna is 72 mW.

Figure 11. Performance comparison with respect to height (h) (a) Human body tissue model, (b) |S₁₁|, (c) |S₁₂|.

Figure 12. Specific absorption rate (a) 28 GHz, (b) 30 GHz.

Experimental analysis

Fabricated prototype

This section discusses the efficacy of the suggested antenna design that has been substantiated through rigorous experimental measurements. The fabrication of the proposed antenna system is executed on a Rogers RT/duroid 5880 substrate employing a precise photolithographic etching process. Figure 13(a-b) depict the top and bottom views, respectively, of the fabricated antenna prototype. The antenna structure is excited by attaching a 2.92 mm end launch jack, screw on female socket connector 145-0711-802, up to 40 GHz (Johnson/Cinch connectivity solutions) which is linked with Anritsu MS46122B vector network analyzer for accessing S-parameters across various ports (see Fig. 13(c)). The comparison between simulated and measured |S₁₁|/ |S₂₂|, and |S₁₂| in a free-space scenario reveals a close alignment within the millimeter-wave frequency spectrum. The measured impedance bandwidth is observed to be 26–30.4 GHz (|S₁₁|), 25.6–30.5 GHz (|S₂₂|), and having a maximum isolation of −31 dB (|S₁₂|) shown in Fig. 14(a). Similarly, the practical viability of the proposed antenna’s adaptable characteristics for real-time applications is effectively demonstrated through the placement of the antenna structure on the hand and biceps (see Fig. 13(d, e)). Figure 14(b) presents a comparison of the measured behavior of S-parameters.

Figure 13. Fabricated prototypes and experimental setups.

Figure 14. Simulated and measured performances analysis (a) S-parameter in free space, (b) S-parameter in human body, (c) Total gain and axial ratio.

It is obvious that in the case of on-hand and on-biceps scenarios, the first resonance frequency is subtly shifted toward lower frequency bands. Additionally, a slight impedance mismatch is observed when compared to the simulated value at 26.8 GHz. This has been attributed to the elevated permittivity characteristic of the human body. Moreover, in both scenarios, the proposed antenna demonstrates strong matching characteristics and possesses an impressive impedance bandwidth spanning from 25.6 to 30.5 GHz (Hand) and 25.4 to 30.4 GHz (Biceps). These findings assure that relocating the antenna on the body won’t drastically affect its impedance bandwidth. The measured isolation is observed to be −27 dB at 26 GHz (Hand), and −29 dB at 26.2 GHz (Biceps). The gain and AR displayed in Fig. 14(c) exhibit a robust alignment between simulated and measured results, while the measured peak gain is determined to be 5.51 dBi, with an observed ARBW of 0.38 GHz, specifically ranging from 29.23 to 29.61 GHz. The far-field radiation characteristics (φ = 0° and φ = 90° planes) for the described antenna at two different frequencies are shown in Fig. 15. At 26.2 GHz the radiation beam is tilted to an angle $\theta $ = 300° in both planes which indicates the direction of maximum radiations. Whereas at 29.5 GHz the H-plane radiation beam is tilted at $\theta $ = 60°, and the radiation in E-plane is toward the broadside direction.

Figure 15. Radiation characteristics (far-field) (a) 26.2 GHz, (b) 29.5 GHz.

MIMO diversity parameters

This section provides a thorough analysis of the diversity parameters associated with the proposed MIMO antenna system. Beyond the traditional antenna performance metrics, assessing a MIMO antenna system requires careful consideration of supplementary performance criteria to accurately define its diversity characteristics. These include the envelope correlation coefficient (ECC) which functions as a crucial performance metric, elucidating the degree of isolation or correlation present among communication channels. In the context of uncorrelated MIMO antenna systems, it is desirable for ECC to ideally be “0.” However, practical implementations often yield ECC values frequently fall below the 0.5 threshold. Likewise, the performance analysis of a MIMO antenna system also incorporates the assessment of the diversity gain (DG) parameter. This value can be calculated utilizing the S-parameters of each antenna element, employing the universal equations (2, 3) [Reference Modak and Khan38–Reference Modak and Khan40].

(2)\begin{equation}ECC = \frac{{|S_{11}^*{S_{12}} + S_{21}^*{S_{22}}{|^2}}}{{\left( {1 - \left( {\left| {{S_{11}}{|^2} - } \right|{S_{21}}{|^2}} \right)} \right)\left( {1 - \left( {\left| {{S_{22}}{|^2} + } \right|{S_{12}}{|^2}} \right)} \right)}}\end{equation}

(3)\begin{equation}DG = 10\sqrt {1 - |ECC{|^2}} \end{equation}

The simulated and measured ECC and DG across a frequency range of 25–31 GHz is observed to be approximately <0.001 and 9.99 as illustrated in Fig. 16(a). Likewise, channel capacity loss (CCL) constitutes a crucial metric within diversity analysis. This signifies the optimal transmission of EM signals capable of achieving the highest possible data rate between the transmitter and receiver while minimizing distortion. Utilizing equations (4–6) the values of CCL can be computed.

(4)\begin{equation}{C_{Loss}} = - Lo{g_2}\left( {\left| {{\Psi ^R}} \right|} \right)\end{equation}

(5)\begin{equation}{\Psi ^R} = \left[ {\begin{array}{*{20}{c}} {{a_{11}}}&{{a_{12}}} \\ {{a_{21}}}&{{a_{22}}} \end{array}} \right]\end{equation}

(6)\begin{equation}{a_{ij}} = -\! \left[ {S_{11}^*{S_{12}} + S_{21}^*{S_{12}}} \right]\end{equation}

Figure 16. Diversity parameters (a) ECC and DG, (b) CCL, (c) TARC, (d) MEG.

The measured value from Fig. 16(b) is determined to be less than 0.4 bits/s/Hz, thereby falling within an acceptable range. The total active reflection coefficient (TARC) is also a crucial parameter in MIMO antenna system. This refers to the fluctuation in the reflection coefficient caused by alterations in the phase angle of the signal introduced into the port. Mathematically it can be expressed using equation (7) [Reference Eslami, Nourinia, Ghobadi and Shokri41].

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

(8)\begin{equation}MEG1 = 0.5\!\left[ {1 - \left| {{S_{11}}{|^2} - } \right|{S_{12}}{|^2}} \right]\end{equation}

(9)\begin{equation}MEG2 = 0.5\!\left[ {1 - \left| {{S_{12}}{|^2} - } \right|{S_{22}}{|^2}} \right]\end{equation}

(10)\begin{equation}MEG = MEG1/MEG2\end{equation}

Figure 16(c) shows the computed TARC value for the designed antenna. The input signal phase is systematically adjusted in increments of 45°, spanning from 0° to 180°. In all phase angles the TARC value is observed to be consistently remains below −10 dB across the entire operating frequency range. Similarly, mean effective gain (MEG) is a crucial metric in diversity analysis, measuring the ratio of the average power received by the antenna under test to that of a reference antenna in the same environment. Equations (8–10) represents the general equation to calculate the MEG [Reference Roy, Biswas, Ghosh, Chakraborty and Sarkhel19]. Figure 16(d) presents the MEG for port 1 (MEG1) and port 2 (MEG2), along with their difference (MEG1/MEG2). It is clear that the MEG ratio remains below −3 dB. A comparative analysis is carried out between the proposed antenna and findings from existing literature, as summarized in Table 2. It is observed that the designed MIMO antenna system presented in references [Reference Pandey, Biswas and Chakraborty15–Reference Jayant, Srivastava and Kumar17, Reference Roy, Biswas, Ghosh, Chakraborty and Sarkhel19, Reference Illahi, Iqbal, Ramey and Sulaiman22–Reference Dwivedi, Narayanaswamy, Penmatsa, Singh, Sharma and Singh26, Reference Tiwari, Kaim, Singh, Khan and Kanaujia30, Reference Shariff, Ali, Mane, Alslath, Kumar, Pathan, Kishk and Khan31] exhibits a large circuital area, although, the operating bandwidth in references [Reference Xu and Zhang23, Reference Kumar, Nandan, Srivastava, Kumar, Singh, Marcy, Mostafa and Kanaujia24, Reference Tiwari, Kaim, Singh, Khan and Kanaujia30] is quite good compared to the proposed MIMO antenna design. Subsequently the antenna gain in references [Reference Jayant, Srivastava and Kumar17, Reference Kumar, Nandan, Srivastava, Kumar, Singh, Marcy, Mostafa and Kanaujia24, Reference Kumar, Pattanayak, Verma, Sabat and Prasad28, Reference Iqbal, Basir, Smida, Mallot, Elfergani, Rodriguez and kim29, Reference Shariff, Ali, Mane, Alslath, Kumar, Pathan, Kishk and Khan31] is high. It is further observed that the presented antenna in references [Reference Peng and Du18, Reference Alaal, Elsayed, Farahat, Hussein and Deeb27, Reference Iqbal, Basir, Smida, Mallot, Elfergani, Rodriguez and kim29] features compact dimensions but fails to achieve optimal performance in terms of operating bandwidth, gain, isolation, and CP characteristics. Beside the analysis of performance behavior using the CMT is missing. In contrast, the proposed work introduces a novel circularly polarized dual-port MIMO antenna, which has been designed, fabricated, and thoroughly investigated using the theory of characteristic modes. The proposed antenna structure demonstrates acceptable performance characteristics, making it suitable for body-worn applications in the millimeter-wave frequency bands.

Table 2. Comparative performance analysis of the proposed MIMO antenna with the existing literature

BW: bandwidth, CP: circular polarization, NA: not available.