Predictive modelling and high-performance enhancement smart thz antennas for 6 g applications using regression machine learning approaches - Scientific Reports


Predictive modelling and high-performance enhancement smart thz antennas for 6 g applications using regression machine learning approaches - Scientific Reports

This research introduces a novel design for a graphene-based multiple-input multiple-output (MIMO) antenna, specifically developed for sixth generation (6G) terahertz (THz) applications. The proposed antenna demonstrates multi-resonant behavior across three broad bandwidths: 2.479 THz (1.00-3.49 THz), 0.516 THz (3.64-4.156 THz), and 1.694 THz (4.50-6.20 THz). It achieves a peak gain of 13.41 dB, exceptional isolation of -34.2 dB, and a high efficiency of up to 90%. The design was developed using CST Studio Suite and validated through an RLC equivalent circuit model in ADS. This ensured accurate representation of its electromagnetic behavior. To improve the predictive capabilities of the antenna design process, five supervised regression-based machine learning (ML) models were employed. The models used were Extra Trees, Random Forest, Decision Tree, Ridge Regression, and Gaussian Process Regression. Among these, the Extra Trees Regression model delivered the highest prediction accuracy, achieving a mean absolute error (MAE) of 2.51%, a mean squared error (MSE) of 0.44%, and an R2 score of 98.91%. The ML models were trained using a comprehensive dataset generated from parametric variations in patch, feed, substrate, and slot geometries. The proposed antenna leverages the advanced properties of graphene to deliver outstanding performance in gain, bandwidth, efficiency, and diversity metrics. It achieves a diversity gain of 9.9993 and an envelope correlation coefficient (ECC) as low as 0.00013. The integration of machine learning and RLC modeling reduces simulation time and improves design optimization. This creates a robust framework for future 6G wireless and biomedical THz applications.

The ongoing advancement of wireless technologies has led to an increasing demand for antennas that can operate efficiently within the terahertz (THz) frequency range. The spectrum ranging from 0.1 to 10 THz is anticipated to be pivotal in facilitating sixth-generation (6G) wireless networks. The THz band offers extensive bandwidth capabilities, significantly exceeding those of 5G systems, and enables ultra-high data rates, minimal latency, and enhanced energy efficiency. The distinctive properties of THz frequencies render them appropriate for advanced applications, including real-time holographic communication, tactile internet, and massive machine-type communication (mMTC). These applications require data transmission in the terabit-per-second (Tbps) range, which is attainable via the expanded spectrum available in the THz band. Nonetheless, the practical implementation of THz systems presents numerous challenges, especially in antenna design, attributable to heightened propagation losses and susceptibility to environmental influences.

Microstrip patch antennas are renowned for their compact design, ease of fabrication, and cost efficiency. These attributes render them suitable candidates for THz communication systems. However, their performance deteriorates at elevated frequencies due to significant conductor and dielectric losses, resulting in a constrained bandwidth and diminished radiation efficiency. Slotted patch antenna designs have been introduced to enhance these performance limitations. The incorporation of slots into the patch configuration improves impedance matching and radiation properties, thereby broadening the bandwidth and enhancing overall efficiency. This alteration enables the antenna to accommodate the requirements of THz communication environments more effectively. Simultaneously, Multiple-Input Multiple-Output (MIMO) technology has become an essential element for forthcoming wireless systems. MIMO increases system capacity by enhancing spectral efficiency and spatial diversity and facilitating beamforming techniques. MIMO architectures, when combined with slotted THz patch antennas, can provide exceptionally reliable and high-speed communication, even in intricate propagation environments. The integration of MIMO with slotted patch antennas optimizes data throughput and mitigates the significant channel fading and signal degradation typically encountered at terahertz (THz) frequencies. This integrated approach offers considerable potential for developing robust and efficient communication systems that meet the stringent demands of 6G networks. Novel materials, such as graphene, are utilized to enhance the performance of MIMO-integrated THz antennas further. As wireless technology advances into the terahertz spectrum, graphene provides a revolutionary benefit in antenna design. Its exceptional electrical conductivity, mechanical flexibility, and thermal stability facilitate the creation of antennas that are both compact and low-loss while also accommodating extensive bandwidths. These attributes are ideally suited to the specifications of 6G systems, where rapid communication and device miniaturization are essential.

The proposed antenna exhibits multi-resonant behavior at 1.5, 3.26, 3.9, and 4.92 THz, with each mode strongly supported by a wide range of studies across adjacent terahertz frequency domains. At the lower end of the spectrum, triangular graphene antennas operating near 1.5 THz (within the 1-2 THz band) have demonstrated high-gain characteristics suitable for applications in spectroscopic analysis, Doppler radar, and biomedical imaging. This study is further complemented by MIMO antenna systems, which function effectively across 0.9-1.68 THz, confirming their compatibility with sixth-generation (6G) wireless networks that demand high capacity and low latency. Operation within the 1.41-3.0 THz range has been validated for use in explosive detection, near-field communication, and threat sensing, particularly due to the availability of wide impedance bandwidths in this band. In addition, environmental sensing in the 1.08-1.8 THz band is made possible through microfluidic-integrated antennas capable of detecting water contamination, thereby validating the viability of low-THz systems in smart monitoring applications. The 3.26 THz resonance in the proposed antenna aligns with performance peaks reported in the 2.88-4.13 THz range, where antennas have been successfully employed in biomedical sensing, IoT, multimedia transmission, imaging, and 6G communication. This resonance is also supported by a broader family of multi-resonant structures that operate at 1.39, 3.26, 4.72, 5.96, and even higher THz frequencies, emphasizing the relevance of this spectral region for high-speed, multi-channel THz communication systems. Broadband operation extending from 2.25 to 6.0 THz further substantiates the antenna's ability to support next-generation imaging, sensing, and high-throughput wireless systems. At 3.9 THz, the antenna exhibits an ultra-low return loss of approximately -46 dB, confirming its efficiency in high-integrity data transmission scenarios. The upper resonant mode at 4.92 THz is strongly corroborated by radiator-type antennas operating between 4.71 and 5.85 THz, where far-field and diversity performance have validated their suitability for wireless power transfer and energy harvesting. Twin-band performance in the 3.3-3.98 THz and 4.9-5.45 THz ranges further reinforces the proposed antenna's potential in MIMO-based biomedical THz applications. Additionally, antennas operating in the 4.55-5.85 THz band have been demonstrated to support directional, high-diversity communication within indoor wireless LAN systems. High-isolation performance has also been validated in polarization-diverse two-port antenna configurations spanning the 4.9-6.3 GHz range, confirming the applicability of this band for robust multi-user communications. Moreover, wideband terahertz antennas covering the 1.98-14.5 THz range provide further evidence of their suitability for adaptive sensing and sixth-generation wireless technologies. The 5.0 THz region is specifically supported by environmental sensing systems operating near 5.046 THz, which have demonstrated effectiveness in monitoring temperature, humidity, and pollutants. Wearable and military-grade antenna solutions designed for flexible operation in the 2.2-2.4 THz, 3.15-3.5 THz, and 4.6-4.9 THz ranges also reinforce the practicality of mid-band THz deployment in defense and field-based applications. The direct biomedical application of the 4.92 THz resonance has been validated through the successful implementation in THz imaging and diagnostic technologies. Finally, circular nano-patch antennas exhibiting resonances at 3.26, 4.69, 5.64, and 6.95 THz further validate the design's relevance to terahertz optical transmission and high-capacity 5G/6G communications, confirming the antenna's alignment with future data-intensive networking environments. Collectively, these validations affirm the efficacy and domain relevance of your antenna's resonance characteristics within the terahertz spectrum.

Recent studies have extensively documented the progress in THz communication and MIMO antenna technologies, highlighting their critical role in advancing 6G technology. The proposed antenna design is evaluated against various referenced designs, underscoring its superior performance in terms of bandwidth, gain, isolation, efficiency, and diversity metrics. The design in operates at dual resonances of 0.445 THz and 0.540 THz with Limited bandwidths of 0.021 THz and 0.036 THz, respectively. Despite achieving moderate gain (7.9 dB) and efficiency (85.64%), it suffers from low isolation (-20 dB) and high ECC (0.07), which indicates poor mutual decoupling and limits its MIMO performance. Its relatively large footprint (12.39 λ₀ × 7.96 λ₀) µm also constrains integration into compact systems. The antenna inresonates at 7.5 THz and offers a wide bandwidth of 5.9 THz, making it suitable for broadband communication. However, its moderate gain (8.3 dB) and weak isolation (-16 dB) reduce its reliability for high-speed data transmission. Additionally, the lack of efficiency data and absence of ML or RLC integration limit its adaptability in advanced systems. Referencepresents a design resonating at 2.2 THz with a 0.78 THz bandwidth and high efficiency (92%). Nonetheless, the gain is low (4.4 dB), and isolation remains weak (-20 dB), while ECC (0.006) suggests only modest decoupling. Though the board is compact (0.498 λ₀ × 0.52 λ₀) µm, the absence of ML optimization and diversity gain data restricts its viability in high-performance environments. In, the antenna resonates at 0.395 THz and 0.629 THz with very narrow bandwidths of 0.01 THz and 0.025 THz. While efficiency is excellent (92.48%) and isolation is satisfactory (-20 dB), low gain (5.17 dB), limited bandwidth, and relatively large board dimensions (4.98 λ₀ × 5.97 λ₀) µm diminish its competitiveness for compact and high-throughput THz systems. The design in resonates at 0.128 THz and 0.178 THz with extremely narrow bandwidths (0.004 THz and 0.0061 THz). Although it shows excellent isolation (-25 dB), high efficiency (90%), and superior diversity performance (DG: 9.999 dB), the low bandwidth and absence of ML or RLC integration make it inadequate for real-world broadband THz applications. In, the antenna operates at 0.472 THz with a 0.435 THz bandwidth. Despite its strong diversity gain (DG: 9.99 dB) and adequate isolation (-20 dB), it underperforms in gain (3.9 dB) and suffers from a high ECC (0.458), indicating substantial inter-element coupling. Its board size (2.99 λ₀ × 1.49 λ₀) µm further limits suitability for miniaturized applications. Reference functions at 0.654 THz with a narrow bandwidth (0.04 THz) but delivers high gain (11.3 dB), strong isolation (≥25 dB), and excellent diversity characteristics (ECC: 0.003, DG: 9.99 dB). However, its low efficiency (76.45%) and large physical size (5.97 λ₀ × 10.95 λ₀) µm severely impair its integration into compact systems and raise power consumption concerns. The design in resonates at 0.514 THz with a bandwidth of 0.4 THz and achieves favorable isolation (-25 dB), efficiency (85.24%), and diversity gain (DG: 9.99 dB). Still, its moderate gain (5.49 dB), coupling (ECC: 0.015), and board dimensions (2.99 λ₀ × 1.49 λ₀) µm restrict its effectiveness in space-constrained and high-performance MIMO systems.

The proposed antenna represents a notable enhancement, functioning at multiple resonances of 1.492 THz, 3.26 THz, 3.923 THz, and 4.924 THz, encompassing a broad frequency range of 1-3.49 THz, 3.64-4.156 THz, and 4.50-6.20 THz, respectively. The design attains an extraordinarily broad bandwidth of 2.479 THz, 0.5156 THz, and 1.694 THz, surpassing current studies in bandwidth coverage. A gain of 13.41 dB and an efficiency of 90% signify a design that is both highly efficient and powerful. The proposed design guarantees robust isolation of -34.2 dB, markedly diminishing interference. The ECC value of 0.00013 and DG of 9.9993 dB affirm exceptional MIMO performance. The proposed antenna distinguishes itself from previous designs by incorporating machine learning techniques and RLC components, thereby providing adaptability and enhanced performance. The diminutive board dimensions of (0.498 λ₀ × 1.742 λ₀) µm further augment its integration potential. The proposed design offers an optimized solution for next-generation THz communication systems due to its superior bandwidth, high gain, strong isolation, and innovative application of ML and RLC components. Overall, the results presented in Table 1 demonstrate that the proposed antenna achieves superior performance across key indicators, which positions it as a frontrunner in the continuous development of antenna technology.

The rapid advancement of terahertz (THz) technology has created significant opportunities for both 6G wireless connectivity and advanced biomedical diagnostics. Nonetheless, current THz MIMO antenna designs encounter ongoing difficulties in concurrently attaining high gain, efficiency, and compactness -- essential criteria for incorporation into next-generation communication systems and biomedical instruments. Contemporary methodologies predominantly rely on numerical simulations, often lacking a circuit-level analytical framework that could enhance theoretical understanding and provide greater design versatility. The design process is frequently impeded by protracted full-wave simulations and the limited use of machine learning techniques, which constrain optimization capabilities and predictive performance modelling.

This study's principal contributions in addressing these difficulties are summarized as follows:

The fundamental structure of graphene exhibits a captivating hexagonal arrangement of carbon atoms, creating a one-atom-thick honeycomb pattern. This exceptional material is part of the carbon allotrope family, which encompasses graphite, carbon nanotubes, and fullerenes, but is distinguished by its remarkable electrical properties. The sp-hybridised carbon bonds in this atomic monolayer result in remarkable electron mobility, making graphene the premier electrical conductor for advanced applications. The intrinsic properties of graphene are especially advantageous in antenna design, as its conductivity can be accurately regulated by modifying essential parameters, usually utilizing a chemical potential (μc) of 0.5 eV and a relaxation time (τ) of 1 ps for a 0.01 μm-thick layer in simulation settings. This precise tunability enables the development of high-performance antennas that operate within the 0.1-10 THz spectrum, presenting exceptional prospects for miniaturized, reconfigurable wireless devices that maintain excellent radiation properties while advancing the limits of traditional antenna technology.

Addressing spectral efficiency, data throughput, and adaptive functionality in the terahertz (THz) spectrum is crucial for 6G communications, necessitating a shift from single-element antennas to advanced multiple-input multiple-output (MIMO) architectures, as shown in Fig. 1. This transition necessitates structural innovations and the use of advanced materials. This study introduces a THz MIMO antenna system utilizing graphene as its foundation. Through the optimization of surface plasmon confinement and impedance matching, the system leverages graphene's plasmonic characteristics, exceptional electron mobility (>200,000 cm/V·s), bias-tunable conductivity, and additional benefits. This design, constructed on a 6.6 polyimide substrate (dielectric constant: 3.5, loss tangent: 0.0027), ensures minimal dielectric loss, thermal stability, and mechanical durability. Incorporated heat dissipation channels mitigate thermal degradation, facilitating reliable performance at elevated frequencies. Enhancing spatial diversity and channel capacity is accomplished by strategically placing engineered decoupling structures to increase isolation while maintaining compactness, thereby mitigating the mutual coupling characteristic of MIMO configurations. The synergistic integration of graphene and polyimide enables high radiation efficiency and gain throughout the THz spectrum, facilitates reconfigurable operation, and allows for miniaturization and reduced ohmic loss. This study establishes the foundation for next-generation THz MIMO systems by optimizing materials, plasmonic, and decoupling techniques to fulfil the performance and scalability demands of 6G networks.

Our single-element antenna's evolution starts with a thorough design approach aimed at maximizing performance by means of meticulous material selection and dimensional accuracy. This first phase uses known electromagnetic principles to compute the microstrip patch parameters, forming the basis of our antenna system. The design process uses these basic equations to identify the best antenna size.

The design of a single-element microstrip patch antenna begins with calculating its critical dimensions using a systematic approach. First, the operating wavelength (λ) is determined using Eq. 1, where c is the speed of light and f is the lowest resonant frequency. Next, the width (W) of the patch is calculated using Eq. 3, ensuring optimal radiation efficiency. The effective dielectric constant (ε_eff), which accounts for fringing fields, is derived from Eq. 2, where ε_r is the substrate's relative permittivity and h is its thickness. The patch length (L) is then computed using Eq. 4, where ΔL represents the length extension due to fringing effects, given by Eq. 5. These equations ensure precise tuning of the antenna's dimensions, enabling efficient performance at the target frequency while accounting for substrate properties and electromagnetic edge effects. The final design is further refined through simulation and experimental validation to achieve optimal impedance matching and radiation characteristics.

Graphene serves as the material for both the patch and ground elements, each possessing a consistent thickness of 3 micrometers. The antenna dimensions are 100 × 100 μm, featuring a patch of 75 × 88 μm with slots. The configuration comprises a central small horizontal elliptical slot, two vertically aligned elliptical slots flanking the central area, and three star-shaped slots positioned in the upper section. Two insets border the feedline, and the ground features a triangular slot (resembling a pyramid-shaped window) at the base, partitioned into three smaller apertures by two slender vertical rectangular bars positioned one unit apart, with the remainder of the ground remaining intact. The design modifications aim to enhance gain, bandwidth, and reflection coefficient. The antenna is modelled in CST Studio Suite to evaluate performance metrics, including return loss, radiation pattern, and gain, offering insights into its behavior across different operating conditions. Figure 2 illustrates the comprehensive geometry, encompassing all features. Table 1 provides a comprehensive breakdown of various dimensions in micrometers, along with their respective acronyms.

The evolution of the single-element antenna design unfolds through four distinct stages, as shown in Fig. 3, each marked by iterative refinements aimed at optimizing performance. In Stage 1, the design begins with a simple rectangular patch element, incorporating two insets on either side of the feedline to enhance performance. However, simulation results fail to align with the intended specifications, showing no discernible resonant frequency, as depicted in Fig. 4(b). To address these shortcomings, Stage 2 introduces a more refined structure featuring a central small horizontal elliptical slot flanked by two vertically aligned elliptical slots. This modification is intended to improve the antenna's characteristics. While simulations reveal some enhancements compared to the initial design, the results still fall short of the desired performance. This result confirms the presence of resonant frequencies, but the return loss remains inadequate. Additionally, as shown in Fig. 4(b), the efficiency reaches a maximum of 72%, indicating progress but leaving room for further optimization. In Stage 3, the ground plane is modified to include a triangular slot at the base, resembling a pyramid-shaped window. This slot is further divided into three smaller apertures by two slender vertical rectangular bars. These modifications yield significant improvements, leading to an enhanced efficiency of 81%, as shown in Fig. 4(c), and a maximum gain of 8.5 dB, as illustrated in Fig. 4(a); however, they fail to improve the resonant frequency. However, while efficiency improves, the gain remains largely consistent with the previous stage. For the final stage, Stage 4, from another stage, yields five resonant frequencies at 1.5 THz, 2.5 THz, 3.3 THz, 4 THz, and 4.9 THz, along with a substantial bandwidth and an efficiency of 84%. Moreover, the gain reaches an impressive 8.93 dB, marking a significant improvement. Through this systematic and iterative process of refinement, the single-element antenna evolves from a basic structure into a highly optimized design that meets the required specifications. Each stage builds upon the insights gained from the previous iteration, demonstrating the effectiveness of progressive design enhancements in achieving the final, optimized outcome.

This work investigates the impact of substrate material choice on the performance of a graphene-based antenna, where graphene serves as both the radiating patch and the ground plane. The interaction between the substrate and antenna characteristics is analyzed by evaluating two distinct substrate materials: silicon and polyimide. The performance metrics, including gain and reflection coefficient, are depicted in Fig. 5(a) and b for each material. In contrast, silicon accommodates multiple resonances but is constrained by narrow bandwidth, moderate return loss, and inferior gain from the proposed material. Conversely, polyimide offers outstanding performance, featuring a broad bandwidth (1 to 1.9) THz and (2 to 4.23) THz, significant return loss, and five distinct resonant frequencies. Furthermore, it attains a maximum gain of 8.93 dB within the operational bandwidth, exceeding that of silicon. The results indicate that substrate selection is crucial for enhancing the performance of graphene antennas. Polyimide demonstrates superior efficacy among the evaluated materials, providing optimal enhancements in bandwidth, gain, and impedance matching without notable disadvantages, thereby establishing it as the preferred substrate for high-efficiency THz antennas.

In the parametric analysis of our antenna, we investigate the effect of varying substrate thickness (st) while maintaining all other design parameters constant. This analysis aims to assess its influence on key performance metrics, including return loss, bandwidth, and gain. When the substrate thickness is increased to 9 μm, a notable reduction in return loss and bandwidth is observed, as depicted in Fig. 6(b). Additionally, this adjustment results in a decrease in gain, as shown in Fig. 6(a). Such a reduction in return loss and bandwidth is undesirable for THz applications, making this thickness value unsuitable despite its bandwidth enhancement. Furthermore, the gain performance does not meet the desired criteria. Conversely, when the substrate thickness is decreased to 3 μm, the reflection coefficient worsens, although the gain remains comparable to that observed at the increased thickness. However, in both cases of thickness variation, the return loss remains unsatisfactory, further emphasizing the antenna's sensitivity to variations in substrate thickness. This analysis underscores the critical role of substrate thickness in determining the antenna's resonant frequency, return loss, bandwidth, and gain. Among the tested values, the proposed substrate thickness of 6.6μm demonstrates the most optimal performance, making it the preferred choice for achieving the desired antenna characteristics.

Patch thickness is a crucial determinant that affects antenna performance, especially in terahertz (THz) applications -- departing from the prescribed patch thickness results in significant alterations to antenna performance. For example, augmenting the patch thickness beyond the optimal design specification leads to the appearance of two separate resonant frequencies at 3.8 THz and 5.4 THz, as depicted in Fig. 7(b). This configuration provides a broad bandwidth but exhibits inadequate gain and return loss performance. The gain curve is notably inferior to the proposed curve, as illustrated in Fig. 7(a). Although the bandwidth is satisfactory, the diminished return loss hurts the antenna's overall efficiency. In contrast, decreasing the patch thickness from the suggested value results in a singular resonance at 6.3 THz and an enhanced return loss of -33 dB. This configuration demonstrates the lowest gain curve of all tested setups, rendering it unsuitable for practical THz applications. These findings indicate that modifying the patch thickness -- whether by increasing or decreasing it beyond the prescribed value adversely affects critical performance metrics. The suggested patch thickness attains an ideal equilibrium, offering the most favorable compromise among return loss, bandwidth, and gain. Consequently, the accurate optimization and regulation of patch thickness are crucial in designing effective THz antennas.

The width of the feed Line has a substantial impact on critical antenna performance parameters, including the reflection coefficient, gain, efficiency, and operational bandwidth. An optimally designed microstrip feed Line guarantees effective energy transfer, thus improving overall antenna performance. With a feed Line width of 10 µm, the antenna demonstrates two separate resonant frequencies at 2.4 THz and 3.37 THz, corresponding to return losses of -36 dB and -23 dB, respectively. This configuration exhibits an extensive operational bandwidth of approximately 2.25 THz, spanning from 1.95 THz to 4.2 THz, as shown in Fig. 8(b). Nonetheless, the maximum gain under this condition is constrained to 6.5 dB, which is inadequate for THz applications. Augmenting the feed Line width to 30 µm leads to a decline in the reflection coefficient, whereas the gain remains relatively constant in comparison to the 10 µm scenario. Conversely, when the suggested feed Line width of 50 µm is utilized, the antenna attains five resonant frequencies with enhanced return loss and bandwidth. The maximum gain reaches 8.93 dB (within the bandwidth), the highest of all evaluated configurations, as illustrated in Fig. 8(a), making it the most efficient design. These findings underscore the critical importance of feed line width in enhancing antenna performance. The proposed configuration achieves an exceptional reflection coefficient, enhanced gain, and broad bandwidth, demonstrating its effectiveness for THz applications. This underscores the importance of meticulous feed line engineering to achieve an optimal balance among gain, bandwidth, and efficiency in high-performance THz antenna designs.

The development of graphene-based microstrip MIMO patch antennas is detailed in this section. These antennas are constructed by extending the single-element design into a 2-port MIMO configuration. This design capitalizes on the advantages of spatial diversity, which results in enhanced communication security, increased channel capacity, effective utilization of multipath environments, and optimized signal reception and interference suppression. To achieve an optimal MIMO antenna design, careful attention was given to the alignment of antenna elements, incorporating a double decoupling structure composed of graphene material with a height of 8 μm to significantly enhance isolation performance. Figure 9 depicts three distinct configurations utilized in the antenna design. Every configuration employs the identical patch and ground structure as the single-element antenna to guarantee performance consistency. Uniform edge-to-edge spacing of 150 μm is upheld across all configurations to guarantee accurate alignment and optimal separation between elements. In the initial configuration (a) (Ant 1), illustrated in Fig. 9(a), the two elements are arranged adjacently with a 0-degree orientation. The second configuration (b) (Ant 2), illustrated in Fig. 9(b), positions the elements in a 180-degree orientation, with the second element inverted in relation to the first. In the third configuration (c) (Ant 3), depicted in Fig. 9(c), the elements are oriented at 90 degrees and arranged adjacently with a perpendicular alignment. The performance of the three types of MIMO configuration antennas is evaluated in terms of resonant frequencies, return losses, impedance bandwidths, and isolation. Antenna 1 exhibits four resonances at 1.47 THz, 2.47 THz, 4.05 THz, and 5.00 THz, with corresponding return losses of -32 dB, -26 dB, -30 dB, and -36 dB, respectively, and achieves a 1.9 THz bandwidth within the 2.4-4.3 THz range where S₁₁ remains below -10 dB. Antenna 2 operates at five resonances -- 2.57 THz (-28 dB), 3.29 THz (-27 dB), 3.90 THz (-37 dB), 5.00 THz (-37.7 dB), and 5.90 THz (-34.5 dB) -- and maintains a similar 1.9 THz bandwidth from 2.3 to 4.2 THz under the -10 dB threshold. In contrast, Antenna 3 delivers enhanced performance with six well-defined resonances at 1.49 THz (-56.20 dB), 2.50 THz (-24 dB), 3.26 THz (-32.09 dB), 3.92 THz (-31.02 dB), 4.92 THz (-46.05 dB), and 5.78 THz (-24 dB). It supports three distinct wideband regions where S₁₁ stays below -10 dB: 1.00-3.49 THz (2.49 THz), 3.69-4.16 THz (0.47 THz), and 4.50-6.20 THz (1.70 THz). The performance analysis, informed by the reflection coefficient Fig. 10(a), indicates that Antenna 3 demonstrates the most advantageous characteristics. Furthermore, the mutual coupling results depicted in Fig. 10(b) demonstrate that Antenna 3 attains the lowest mutual coupling of -34.2 dB throughout the entire frequency band, surpassing Antenna 1 (-25.88 dB) and Antenna 2 (-16.27 dB). These results identify Antenna 3 as the most efficient configuration, providing enhanced isolation and reflection capabilities. The comparative analysis offers essential insights into the impact of element orientation on MIMO performance, directing the choice of Antenna 3 as the most suitable design for the intended application.

The MIMO antenna design and evaluation process is a cyclical workflow that commences with the specification of system requirements, including frequency range, gain, and application-specific criteria. An individual-element antenna is initially designed and simulated in CST Microwave Studio, with critical parameters such as S11 (return loss), gain, and efficiency assessed. Should performance be inadequate, parametric sweeps and material optimizations will be performed until an optimized single-element design is achieved. The design is subsequently expanded to a two-port MIMO configuration, wherein essential parameters such as S21 (mutual coupling), ECC (Envelope Correlation Coefficient), DG (Diversity Gain), and radiation patterns are examined. Should the results be unsatisfactory, additional decoupling methods (such as defected ground structures and parasitic elements) or substrate enhancements (including low-loss materials and EBG structures) will be implemented. Upon validation of MIMO performance, a corresponding RLC circuit model is constructed in ADS for system-level integration. The flowchart presented in Fig. 11 illustrates the step-by-step progression of the design process, beginning with the initial single-element configuration, progressing through the development of the MIMO antenna system, and culminating in the implementation of the equivalent RLC circuit model. The design approach is finalized, having successfully validated across both electromagnetic and circuit simulation environments, marking the completion of the overall antenna development framework.

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