Design and characterization of a meandered V-shaped antenna using characteristics mode analysis and its MIMO configuration for future mmWave devices

This study presents a novel four-element MIMO antenna system designed for the millimeter-wave (mmWave) spectrum. Each MIMO antenna element features a meandered V-shaped radiating structure fed by a 50 𝛺 microstrip line and a partial ground plane with a square notch printed on a 0.254-mm thick RO5880 substrate. The characteristic mode analysis (CMA) of the antenna is done, which reveals that the antenna efficiently utilizes Mode 2, while Modes 1 and 4 also contribute to the resonance, resulting in a wideband response within the mmWave spectrum. A four-element pattern diversity MIMO configuration is developed to evaluate its suitability for MIMO communication, incorporating a connected ground-structure decoupling network to enhance isolation. The MIMO system achieves over 20 dB isolation between elements, with an impedance bandwidth ranging from 20.2 to 33.05 GHz and a peak gain of 6.6 dBi at 28 GHz. Fabrication and measurement validate the design, showing strong agreement with simulations. The MIMO performance metrics, including envelope correlation coefficient (ECC), diversity gain (DG), mean effective gain (MEG), total active reflection coefficient (TARC), and channel capacity loss (CCL), are within acceptable limits, suggesting that the proposed MIMO antenna system is a promising candidate for future mmWave applications.


Introduction
Fifth-generation (5G) communication represents the latest evolution in wireless technology, promising unprecedented levels of speed, reliability, and robustness with connection support for ultra-massive user devices [1].The 5G network not only enhances the consumer experience but also fuels innovation across industries, driving advancements in healthcare, manufacturing, transportation, and beyond [2,3].In addition, the 5G millimeter-wave (mmWave) spectrum represents a significant advancement in wireless communication technology, offering immense potential for high-speed data transmission and ultra-low latency.Operating at frequencies above 24 GHz, the mmWave spectrum provides a vast amount of available bandwidth, enabling data rates that far exceed those of traditional cellular networks [4].In addition, to achieve a high data rate at higher frequencies, multiple-input multipleoutput (MIMO) communication technology is utilized.For this purpose, E-mail addresses: daniyalali.sehrai@unavarra.es(D.A. Sehrai), tanweer.ali@manipal.edu(T.Ali).
there is a need to design a MIMO antenna system that can utilize spatial diversity and multiplexing techniques to enhance data throughput, reliability, and coverage [5]- [6].
The previously presented literature offers numerous works on MIMO antennas designed for mmWave spectrum [7][8][9][10][11][12][13]. In [7], the spatially separated two-element MIMO antenna with inverted arrangements was studied.The presented MIMO antenna configuration achieves an isolation of 30 and 25 dB at 27 and 38 GHz.The design presented in [8] studied the characteristics of polarization diversity of a twoelement MIMO antenna.The gain of the MIMO antenna was improved by placing an array of 7 × 7 metamaterial unit cells underneath the MIMO antenna, which also helps to achieve an isolation of 25 dB in the band of interest.In [9], an orthogonal arrangement of two-element MIMO antenna was designed.For the isolation enhancement, a slotted stub was used between the radiating elements, which accumulate the https://doi.org/surface currents, causing minimal radiation interference.Therefore, an isolation of 30 and 40 dB was achieved at 28 and 38 GHz.In [10], for isolation enhancement, a decoupling structure with slotted rings was designed between the radiators, and two orthogonal cross-shaped slots were placed in the ground plane.With this configuration, an isolation of >30 dB was maintained.In [11], the circular ring MIMO antenna performance was studied for both spatial and polarization diversity configurations.The results show no variation in bandwidth (26-35 GHz) for both diversity arrangements.It was observed that the isolation of polarization diversity in the MIMO arrangement was better than the spatial diversity configuration.In [12], multiple arcs-based radiating element was designed for mmWave MIMO applications and achieved an impedance bandwidth in the frequency range of 23.5-38 GHz.Good isolation of 23 dB was obtained with an orthogonal arrangement of radiating elements.However, the overall antenna profile is large.A tree-shaped antenna with multiple arcs was designed in [13] to get a wideband response from 23 to 40 GHz with good isolation performance, but the designed MIMO configuration was large in size.
In most of the designs presented above, MIMO antennas typically had an orthogonal structure, which restricted their scalability.On the other hand, most of the designs studied MIMO performance without a connected ground structure.However, in the proposed MIMO antenna structure, a symmetrical arrangement is utilized with a connected ground plane-based decoupling structure, which provides the flexibility to accommodate -elements based on specific system needs.The presented MIMO antenna system not only offers wide band response in the mmWave spectrum but also offers good isolation between the radiating elements with stable radiation characteristics.In addition, the characteristics of the single MIMO elements are analyzed through characteristics mode analysis (CMA) theory, and the details about them are presented in Section 2.

Design of meandered V-shaped antenna
Fig. 1 illustrates the design of the meandered V-shaped antenna proposed in this study along with the parameters, while Table 1 provides complete information about the design dimensions.The antenna is designed on a 0.254-mm-thick RO5880 substrate with a relative permittivity (  ) of 2.2.The physical dimensions of the antenna are 12 × 14 mm 2 , while the electrical dimensions are 0.1305 0 × 0.1119 0 , where  0 represents free-space wavelength @28 GHz.The resonant length of the antenna is obtained through a meandered V-shaped radiator, while the wideband characteristics are achieved with the introduction of a small square notch at the partial ground plane.This notch serves as a key component in enhancing the antenna's bandwidth, enabling robust performance across a broad frequency range.
A step-by-step design procedure for the meandered V-shape radiator is shown in Fig. 2. In the initial stage (see Fig. 2a), the foundational  design comprised of two strips arranged in a V-shaped manner is designed, which is fed by a 50 Ω microstrip feed line.In the subsequent stage, shown in Fig. 2(b), vertical strips were added to the first stage design, forming a V-shaped radiator.Finally, in the proposed stage (see Fig. 2c), the existing strips were mirrored to create a meandered V-shaped antenna.
To understand the operational principle of the design, CMA is applied to the structure, whose physical characteristics are difficult to model with conventional mathematical methods.Also, for a wideband structure, CMA provides information on the multiple resonant modes that can be combined to achieve the wideband response.CMA analysis starts by calculating the total surface current on the antenna structure, which is the vector summation of the th-order eigen current (  ) and eigenvalue (  ) [14].The solutions to these   and   are obtained by solving the generalized eigenvalue equation on a loss-free conducting material as [15]: In Eq. ( 1),   represents the complex coefficient.The other parameters derived from the solution of the eigenvalue are the modal significance (MS) and characteristic angle (CA).The MS determines the significance of the mode when its solution to the eigenvalue converges to zero.It can be derived as: CA relates the phase lag between the electric field and surface current to the structure capacitance, inductance, or resonant mode.The phase between > 180 • to < 270 • indicates that the incident electric field accumulated in the structure may be due to the structure's shape or material property.This also leads to a potential difference in the structure.Therefore, when an electric field changes instantaneously, a lag is observed in the surface current.The mode that experiences this effect is termed the capacitive mode.On the other hand, CA from > 90 • to < 180 • indicates that the phase lag of surface current to that of an incident electric field is due to the structure's or material's inductive property [16].For CA of 180 • , the antenna structure has the natural resonant mode, which radiates the complete energy without storing it in the near-field region.
For CMA, an antenna must have a conducting structure to feed the signal and a reference plane or structure as ground, and it can be applied to the structure as a whole.The electric field incident on both surfaces generates the corresponding surface currents that result in generating various modes.Depending on the structure at various frequencies, these surface currents may have certain phase differences.Thus, these modes can be purely resistive, inductive, or capacitive.For the proposed design, the characteristics are studied using the CST Microwave Studio by applying an integral equation solver to the analysis setup.The CMA theory is applied with five modes, considering loss-free substrate to the first antenna development stage, as shown in Fig. 2(a).
The MS results in Fig. 3(a) indicate that Modes 1 to 3 are significant from 24 to 31.5 GHz, with a value close to unity.Mode 5 has a very narrow bandwidth with a resonance of 17.37 GHz.The significance of this mode is undesirable, as it is outside of the interested band.The observation from the CA indicates that Mode 1 is naturally resonant from 22.5-33 GHz.Modes 2 and 3 have phase lead and lag by 10 • relative to Mode 1 before and after 30.09 and 25.43 GHz, respectively, and the phase changes linearly, as shown in Fig. 3(b).The other two modes are non-resonant, as Mode 4 has the capacitive effect and Mode 5 has the inductive effect.These two modes have a 30 • phase difference relative to resonant Mode 1 (see Fig. 3b).The variation in the phase difference affects the resonant Mode 1/ 1 , resulting in an impedance mismatch.
The surface current distribution in the ground plane and radiator at 28 GHz is shown in Fig. 4 with black and red arrows, respectively.In  1 ,   the current is out-of-phase at the edges of the ground plane, and there is a minor current in the radiator. 2 and  3 have a similar current pattern that is along the -direction in the ground plane and the -direction in the radiator.However,  4 and  5 have opposite current directions due to capacitive and inductive modes.
In stage 2, as shown in Fig. 2 Modes 3 and 4 have almost 0 • phase differences till 25.5 GHz and converge at 31 GHz (see Fig. 5b).The structural modification reversed the surface current flow compared to stage 1.  1 has an out-of-phase current in the ground plane (see Fig. 6). 2 and  3 have in-phase currents in the ground and radiator, as shown in Fig. 6.They have -polarization with opposite directions in the radiator.
In the proposed design (see Fig. 2c), the increase in the stub length altered the significance of the modes.Mode 2 is now significant with its natural resonance from 21.5 to 29 GHz.On the other side, the significance of Mode 1 is shifted higher to 28 GHz.Modes 3 and 5 are significant from 29 GHz to beyond 35 GHz.However, Mode 4 is significant with a bandwidth of 23-27 GHz, as depicted in Fig. 7(a).The CA in Fig. 7(b) indicates that  2 has a negligible phase difference between the surface current and an incident electric field from 23 to 29 GHz, which makes it the dominant resonant mode.In the case of  1 , the structure exhibits a capacitive effect until 28 GHz and later an inductive effect.However, the phase difference is minimal to < 15 • .A similar response can be observed in  4 , as shown in Fig. 7(b). 3 and  5 store the electric field from 15 to 28 GHz, leading to a large phase delay in the surface current.This phase delay reduces to close to zero from 30 to 35 GHz (see Fig. 7b).Therefore, the modes contributing to the desired bandwidth with minimum phase delay are  1 ,  2 , and  4 from 21.5 to 28 GHz and  3 and  5 from 28 to 35 GHz.
To evaluate the radiation mechanism of structure through CMA, the understanding of modal significance and characteristic angle, shown in Fig. 7, is very crucial.As explained before,  1 ,  2 , and  4 are significant in different frequency bands from 22 to 30 GHz, and  3 and  5 are significant from 28 to 34 GHz; therefore, the total far-field pattern is the summation of  1 ,  2 , and  4 and the summation of  3 and  5 .Note that, in the proposed case, between the patch and ground, there is a dielectric, due to which the analysis for that particular portion is omitted, and the radiation patterns are estimated only with respect to the patch and ground plane.As a result, nulls along the ± -axis occurred.
The surface current and its respective radiation patterns for  1 ,  2 , and  4 at 22.5, 26, and 28 GHz are presented in Fig. 8.The surface current of  1 has a similar current distribution with the in-phase current in the ground and radiator, as shown in Fig. 8(a).The slight change in the surface current is due to the small phase difference at varied frequencies, as shown in Fig. 7(b).The in-phase current has resulted in bidirectional radiation along the -axis.The gain linearly increases at  1 from 6.34 to 8.5 dBi as the frequency increases. 2 has out-ofphase surface current in the ground and radiator, leading to horizontal polarization (along the -axis), resulting in the dual-beam pattern along the ± -axis and nulls at ±180 • in the azimuthal plane (Fig. 8b).The gain at  2 is ranging from 4 to 4.51 dBi over 22.5-28 GHz. 4 has a uniform in-phase current on the antenna structure over the desired band, resulting in a dual-beam pattern in the ± -axis with nulls at ±45 • H. Elmannai et al.  in the azimuth plane, as depicted in Fig. 8(c).The in-phase current in  3 at 28 and 30 GHz results in vertical polarization, leading to radiation in the ±-axis with nulls at ±45 • in the azimuth plane, as shown in Fig. 8(d).Similar current distribution and radiation pattern (except at 30 GHz) are seen for  5 with out-of-phase current.Therefore, the vector sum of  1 ,  2 , and  4 with in-phase and out-of-phase current results in wide bandwidth from 21.5 to 28 GHz, and the vector sum of  3 and  5 contributes to bandwidth from 28 to 35 GHz.

Proposed MIMO antenna configuration
The proposed meandered V-shaped antenna, shown in Fig. 1, is then transformed into a four-element MIMO antenna system, as shown in Fig. 9.In MIMO configuration, two elements are positioned horizontally adjacent to each other with a 10-mm gap.Additionally, two vertically mirrored elements are spaced apart by 8 mm.To improve isolation between the radiating elements, all four antennas shared a common ground plane connected via a circular stub acting as a decoupling structure.This MIMO configuration helps to achieve pattern diversity in the band of interest.
Fig. 10(a) shows simulated reflection coefficient response of MIMO antenna system exhibiting bandwidth of 13.4 GHz from 19.6 to 33 GHz.The simulated efficiency and gain of the MIMO antenna are shown in Fig. 10(b).The efficiency is plotted for Ant 1 and Ant 2, while the gain is plotted for a single MIMO element.The radiation efficiency ranges from 94.5% to 97%, while the total efficiency varies in the range of 80%-90%.Moreover, the gain of the antenna increases as the frequency increases, as shown in Fig. 10(b).A slight degradation in the gain value is noted at 30 GHz, which could arise due to slight impedance mismatching (see Fig. 10a).
The isolation performance without and with the decoupling structure is shown in Fig. 11.The isolation among side-by-side elements, such as Ant 1 and Ant 2, without the isolating structure, is observed to be ≥15 dB, while for other antennas, with reference to Ant 1,    the isolation is >20 dB, as shown in Fig. 11(a).With decoupling structure, an improvement in the isolation is observed for adjacent antenna elements, which is noted to be ≥27.5 dB, while for the other elements, with reference to Ant 1, a slight improvement is observed in the isolation, as shown in Fig. 11(b).

Fabrication and measurements
A prototype of the MIMO antenna is developed (see Fig. 12) for the verification of the simulated data presented above.The S-parameters are measured using a vector network analyzer (VNA) that can operate up to 40 GHz.A commercially available SMA connector that operates in the mmWave frequencies is used for testing purposes.It is noted that Ant 1 operates well from 20 to 33 GHz, while Ant 2 resonates in the frequency range of 19-32 GHz.On the other hand, Ant 3 works from 20 to 32 GHz, as shown in Fig. 13(a).The measured bandwidth of Ant 4 is narrower (see Fig. 13a) compared to the simulated data, ranging from 22 to 32 GHz.The slight disturbance in resonance behavior in the measured results is likely due to setup inaccuracies.The measured isolation (see Fig. 13b) between the adjacent antenna elements is noted to be >27.5 dB, while for the other elements, with reference to Ant 1, the isolation is >20 dB, as shown in Fig. 13(b).Furthermore, the measured isolation performance is well matched with the simulated response (see Fig. 11b).
The far-field patterns at 28 GHz for E-and H-planes are measured using the standard procedure, as shown in Fig. 14.Due to the symmetry of the proposed structure, only adjacent MIMO elements are considered, and the results are shown in Fig. 15.A typical bi-directional (monopole-like) radiation pattern is observed for both radiators in the E-plane (see Figs. 15a and 15c), while an omnidirectional radiation pattern with some distortions is observed for the H-plane, as shown in Figs.15(b) and 15(d).It is also observed that system offers pattern diversity characteristics in the E-plane.Furthermore, the  cross-polarization (X-pol) component of the patterns is noted to less than −10 dB.

MIMO performance parameters
Studying MIMO parameters is essential for evaluating MIMO antenna performance because they provide a comprehensive understanding of how the system will function in practical scenarios.Various MIMO performance parameters such as envelope correlation coefficients (ECC), diversity gain (DG), mean effective gain (MEG), total active reflection coefficient (TARC), and channel capacity loss (CCL) are calculated [19,20].ECC is a key metric parameter, as it quantifies the correlation between two elements.The ECC value below 0.5 indicates good MIMO performance.When the ECC exceeds 0.5, the performance deteriorates as the correlation gets high between elements and propagation paths.It can be determined using either S-parameters or far-field patterns.In this study, the ECC is calculated using the latter method, as outlined in Eq. ( 4).
where  1 (, ) and  2 (, ) are the far-field radiation patterns of the two antennas. is the elevation and  is the azimuth angle.The three-dimensional (3D) radiation patterns are measured for each MIMO antenna at some fixed frequency points.Further, providing these values in Eq. ( 4) and solving the equation results in measured ECC.The comparison between simulated and measured ECC is shown in Fig. 16.ECC values of 0.0055 and 0.002 were obtained for the lower and upper cut-off bands, respectively, as shown in Fig. 16.
The DG plots for the MIMO antenna are presented in Fig. 17 The results presented in Fig. 17(b) demonstrate that all possible combinations achieve a gain exceeding 9.99 dB over the operational band.The MEG is calculated using Eq. ( 6).For optimal performance, a 3 dB limit is desired.The calculated MEG difference between any radiating elements is less than 0.5 dB, as shown in Fig. 17(b).Similarly, CCL (see Fig. 17b) is found to be less than 0.4 bps/Hz satisfying acceptable limits.Furthermore, in MIMO antenna systems, TARC measures the efficiency of signal transmission and reception, with lower values indicating minimal reflection losses.For the proposed MIMO antenna, the TARC is found to be less than 10 dB across the band of interest, as shown in Fig. 17 Table 2 presents a comparison between the proposed MIMO antenna system and previously published literature.The comparison covers aspects such as physical and electrical size, bandwidth, isolation between MIMO elements, peak gain of a single radiating element, ECC, and ground plane configuration.The proposed MIMO antenna system stands out with its well-established design, good isolation, reduced size, and connected ground plane configuration.Based on the results achieved, the proposed MIMO antenna system is a promising candidate for future mmWave devices.

Conclusions
This article presents the design of a four-element meandered Vshaped MIMO antenna with a wideband response ranging from 20 to 32 GHz.Using CMA theory, the behavior and mode excitations of the proposed antenna structure are analyzed, and it is identified that Mode 2 is the efficient and dominant mode, while Modes 1 and 4 have some contribution in achieving the wideband response.The surface current distribution and radiation pattern behavior are thoroughly examined through CMA.In MIMO antenna configuration, for isolation enhancement between radiating elements, a novel decoupling structure in the ground plane is introduced, and an isolation of >20 dB is observed.Furthermore, the MIMO antenna maintains stable radiation characteristics across the entire bandwidth, with a maximum gain of
(b), the resonances of modes have been affected as the radiator length has increased.Mode 2 is significant from 21 to 30.5 GHz, Mode 2 is from 25.5 to 30 GHz, and Mode 3 is from 27.2 to 35 GHz, as shown in Fig. 5(a).The significance of Mode 4 is beyond the desired bandwidth, and the same as with Mode 5. Modes 1 and 2 have a constant phase difference of 20 • till 24 GHz, which decreases further and converges at 27 GHz, as shown in Fig. 5(b).

Fig. 8 .
Fig. 8. Surface currents and radiation properties of the proposed design shown in Figs. 1 and 2(c) using CMA.

Fig. 11 .
Fig. 11.Simulated isolation performance of the proposed MIMO antenna system (a) without and (b) with decoupling structure.

Fig. 14 .
Fig. 14.Measurement setup for the characterization of far-field radiation properties.
(a).It can be calculated using the below-mentioned equation.

Fig. 15 .
Fig. 15.Simulated and measured far-field radiation characteristics of adjacent radiators of the proposed MIMO antenna system.

Table 1
Design parameters and dimensions of the proposed mmWave antenna (in millimeter).

Table 2
Comparison among proposed MIMO antenna with state-of-the art literature.