High performance grid structured MIMO antenna with regression machine learning for high-speed sub THz and THz 6G IoT applications

Abstract

This study introduces an innovative approach that leverages machine learning techniques to optimize antenna gain for next-generation wireless communication and Internet of Things (IoT) systems operating in the Terahertz (THz) frequency spectrum. Designed on a 160 × 160 μm² polyimide substrate, the antenna is analyzed using CST-2018 simulations and RLC circuit modeling. The proposed antenna demonstrates outstanding performance by achieving high peak gains of 11.91 dB and 12.21 dB across two operational bands. Exceptional isolation values of 31.43 dB and 36.1 dB are maintained in their respective bands, along with a high radiation efficiency of 92.42% and 86.93%. The design effectively covers two wide frequency ranges: 0.081–1.36 THz (1.2 THz bandwidth) and 1.81–3.43 THz (1.6 THz bandwidth), making it highly suitable for THz communication scenarios. To enhance the validation of the model, an analogous RLC equivalent model is constructed via ADS, yielding S₁₁ that is nearly aligned with those obtained by CST-2018. Furthermore, supervised regression machine learning approaches are engaged to forecast the gain of MIMO antenna, assessing five distinct algorithms. Among these techniques, XGB Regression exhibited superior precision, attaining over 96% dependability gain in forecasting. The integration of regression models with MIMO design demonstrates potential for enhancing capacity and improving design efficiency. The suggested antenna, characterized by its compact dimensions, superior isolation, and remarkable efficiency, demonstrates significant potential for high-speed 6G applications, providing unique solutions for next-generation wireless communications.

Introduction

As global data demands surge, driven by advances in AI, immersive virtual applications, and the Internet of Things (IoT), existing GHz-based wireless communication systems are reaching their limits. The transition to the next-generation 6G network is poised to address these challenges by exploring the THz spectrum, specifically from 0.1 to 10 THz, where abundant, underutilized bandwidth holds the key to unprecedented data capacity and ultra-low latency¹. Unlike the GHz frequencies, which are increasingly saturated and unable to meet future performance demands, the THz band can provide the high-speed, high-capacity connectivity essential for emerging technologies. Researchers are now actively exploring THz communication to overcome GHz limitations, as THz waves not only enable faster data transfers but also offer shorter wavelengths, which allow for smaller, more efficient antennas and novel system architectures².

A significant focus of this research lies in integrating THz communication with Multiple Input Multiple Output (MIMO) technology. This method maximizes data throughput by using multiple antennas to send and receive concurrent signals³. This MIMO-THz combination is especially promising for 6G applications due to its ability to support robust, high-throughput links over short distances, making it highly effective for high-speed, short-range wireless communication scenarios⁴. This characteristic is particularly crucial for IoT devices deployed in dense environments, real-time analytics, and the massive interconnectivity anticipated in future smart environments⁵.

Figure 1 illustrates the diverse and evolving landscape of IoT applications that stand to benefit from the integration of THz-MIMO technologies in 6G networks⁴. The image highlights key sectors such as smart agriculture, industrial automation, rural and urban area coverage, and IoT-based smart cities, each relying on real-time data exchange, dense connectivity, and low-latency communication. Satellite communication and drone-based wireless infrastructure are also depicted as crucial components enabling widespread and flexible deployment, especially in remote and infrastructure-limited regions. These use cases align well with the performance characteristics of the proposed antenna, particularly its 0.3 THz resonance, which supports high-speed, short-range transmission with improved penetration for complex indoor or urban environments typical of IoT deployments⁶. This visual representation underscores the role of THz-MIMO in enabling seamless interaction across heterogeneous IoT ecosystems, supporting critical applications like precision agriculture, smart industry, healthcare, and urban management with robust connectivity.

Fig. 1.

Illustration of 6G-enabled IoT use cases supported by dual-band THz MIMO communication.

In high-speed short-range wireless networks, the ability to deliver ultra-fast data transmission within confined spaces—such as smart homes, industrial automation floors, or medical monitoring systems—is becoming essential. THz-MIMO architectures are uniquely suited to meet these demands due to their compact form factors and exceptional data-handling capacity⁷. IoT applications benefit uniquely from this THz-MIMO integration, as it allows devices to operate seamlessly within dense, interconnected networks while minimizing latency. Furthermore, THz-MIMO is projected to revolutionize high-speed, data-intensive sectors beyond IoT, including secure satellite communications, autonomous transportation systems, and next-generation data centers, all of which demand the kind of high-capacity, low-latency performance only achievable at THz frequencies⁸.

In the context of 6G, THz-MIMO systems thus serve as a backbone for critical applications in healthcare, defense, and smart infrastructure, where high-speed data exchange is essential for real-time monitoring, diagnostics, and decision-making. For instance, in healthcare, wearable IoT devices and remote diagnostic systems enabled by THz communication could provide instant data transfer, improving patient care in remote areas. Likewise, smart city infrastructure will rely on the seamless, ultra-fast connectivity offered by MIMO-enabled THz systems to support everything from autonomous vehicles to intelligent traffic management, creating safer, more efficient urban environments⁹. By unlocking the potential of the THz band, researchers aim to overcome GHz constraints and establish 6G networks as a foundational platform for the interconnected, data-driven world of tomorrow.

Table 1 presents a comparative analysis of multiple ongoing initiatives, delving into their conceptual foundations. It scrutinizes a range of operational parameters, including operating frequency, board dimensions, bandwidth, gain, isolation, and efficiency. Among these endeavors listed in the table, the suggested antenna stands out as the most compact, boasting the broadest bandwidth, and achieving commendable levels of isolation and gain. Referenced gains from previous works, such as 8.2 dB, 11.67 dB, 11.80 dB, 4.4 dB, 4.6 dB, 4.4 dB, 7.9, 5.17, 6.24, 11.89 and 7.5 are provided^10–19, and²⁰. In contrast, simulations in CST-2018 reveal an observed gain of 12.213dB. CST-2018 asserts a bandwidth of 1.6 THz for the proposed architecture, notably higher than the BW cited in the sources: 0.0404 THz, 0.05 THz, 0.614 THz, 0.78 THz, 1.59 THz, 0.114 THz, 0.4 THz, 0.44 THz, 0.036 THz, 0.025 THz, 0.0061 THz, and 0.723 THz. Isolation levels in the proposed layout surpass − 36.1 dB, contrasting with measured levels of −22.26 dB, ≥ 25 dB, −25 dB, −20 dB, −25 dB, −17 dB, −25 dB, −20 dB, −20 dB, −20 dB, −25 dB, −27.34 dB, and − 20 dB for the reference works^{10–19,21,22}, and²⁰. The recommended Multiple-Input Multiple-Output (MIMO) antenna exhibits outstanding performance metrics compared to alternatives, with an ECC of less than 0.0005 dB, and a DG exceeding 9.999 dB. Its radiation efficiency of 92.42% outshines values of 76.45%, 92%, 74.5%, 94%, 82%, 15%, 85.64%, 92.48%, 90%, 88.9%, and 97% cited in studies^{11,13–19,21,22}, and²⁰.

Table 1.

The performance of the MIMO antenna proposed will be compared with previous studies.

Ref	Resonance (THz)	BW (THz)	Isolation (dB)	Gain (dB)	Efficiency (%)	ECC (dB)	DG (dB)	Substrate material	Board size (µm2)	ML/ RLC
10	8.84	(8.8639- 8.8235)0.0404	−22.26	8.2	–	0.0005	9.995	RT/Duroid/6010	35 × 36	No/ No
11	0.654	(0.61–0.66) 0.05	≥ 25	11.67	76.45%	0.003	9.99	polyimide	1200 × 2200	No/ No
12	0.638	0.614	−25	11.80	–	–	–		–	No/ No
13	2.2	(1.74–2.52) 0.78	−20	4.4	92%	0.006	9.999	Polyimide	100 × 105	No/ No
14	1.89	(1.41 −3.0) 1.59	−25	4.60	74.5%	15.6 × 10–10	≈ 10	SiO2	38 × 25	No/ No
15	–	(0.093–0.207) 0.114	−17	4.4	94%	0.006	9.97	Rogers RO4835-T	2000 × 1000	No/ No
21	–	(0.35–0.75)0.4	−25	–	82%	–	–	Polyimide	600 × 300	No/ No
22	–	(0.276– 0.711) 0.44	−20	–	15%	0.01	≈ 10	polyimide	600 × 300	No/ No
16	0.445 0.540	0.021 0.036	−20	7.9	85.64	0.07	0.975	polyimide	2490 × 1600	Yes/yes
17	0.395 0.629	0.01 0.025	−20	5.17	92.48	0.0125	10	polyimide	1000 × 1200	No/ yes
18	0.128 0.178	0.004 0.0061	−25	6.24	90	0.012	9.999	polyimide	2700 × 3650	No/ no
19	4.99 8.83	5.94	−27.34	11.89	88.9	0.001	9.994	polyimide	90 × 90	Yes/ Yes
20	1.2	(0.93–1.653) 0.723	−20	7.5	97	0.01	9.99	polymide	110 × 130	Yes/ No
Proposed	0.3, 2.18	1.27, 1.62	−31.43, 36.1	11.91, 12.21	92.42, 86.93	0.0005	9.999	Polyimide	160 × 160	Yes/Yes

The integration of both RLC components and machine learning algorithms in the proposed design sets it apart from most of the works cited in the comparison. Among the studies, only a few incorporate either machine learning or RLC circuit modeling. Specifically, RLC modeling is present in^16,17, and¹⁹, while machine learning techniques are applied in^16,19, and²⁰. However, the simultaneous use of both RLC and machine learning within a single framework, as demonstrated in the proposed antenna, remains unique among these works. This combined approach not only enhances circuit-level insight but also enables performance prediction and optimization, representing a meaningful advancement in antenna design methodology. The comprehensive comparison in Table 1 highlights the novelty and significance of the proposed design in the context of current research trends.

Research gap and contribution

The rapid growth of THz technology shows great promise for future 6G wireless and Internet of Things (IoT) applications, which require very fast data transfer, high efficiency, and compact device sizes. However, many current THz MIMO antenna designs face challenges in achieving a good balance between high gain, efficiency, and small size. Most of these designs rely heavily on full-wave electromagnetic simulations, which are time-consuming and do not provide a clear theoretical understanding of the antenna’s behavior.

In addition, very few studies provide a circuit-level model, such as an RLC equivalent circuit, to explain how the antenna works. This makes it harder to optimize or modify the design. Moreover, the use of machine learning for improving antenna performance is still limited in this field, especially for predicting and optimizing key performance parameters. These gaps make it difficult to design antennas that can meet the high demands of 6G and IoT systems quickly and effectively.

This study addresses these issues and offers the following key contributions:

1. RLC Equivalent Circuit Model: A detailed RLC equivalent circuit model is proposed to explain the antenna’s operation more clearly. This model supports the full-wave simulation results and helps in understanding the antenna’s behavior from a circuit point of view.

2. Machine Learning for Fast Optimization: Machine learning methods, especially regression models, are used to predict and optimize antenna performance. This reduces the need for long simulation times and allows faster design updates.

3. High Gain, Efficiency, and Compact Size: The proposed antenna achieves high gain, high efficiency, and a compact structure, making it suitable for integration into next-generation 6G and IoT devices.

Design methodology

The transformation illustrated in Fig. 2 captures the evolution of the antenna from a compact single-element configuration to an advanced MIMO architecture. This progression is not merely a structural enhancement but a response to the ever-increasing demands for higher data throughput, enhanced signal fidelity, and broader bandwidth, particularly in the context of the upcoming 6G era²³.

Fig. 2.

Structural evolution of the antenna from a single-element to MIMO configuration.

Given the miniaturized dimensions required for THz band operation, the material selection becomes pivotal. Copper is chosen for both the radiating and ground elements due to its excellent electrical conductivity and fabrication compatibility. The entire configuration is embedded on a 10 μm-thick polyimide substrate, which offers a dielectric constant (ε_r) of 3.5 and a low loss tangent of 0.0030. This substrate provides a reliable balance of flexibility, thermal stability, and low-loss performance, key attributes for sustaining high-frequency signal integrity in 6G systems²⁴.

The evolution from a single-element to a dual-port MIMO antenna represents a strategic integration of design innovation and material engineering. This advancement not only meets the stringent performance requirements of next-generation wireless systems but also sets a strong foundation for scalable, high-efficiency THz communication technologies.

Single element antenna

To develop our single-element antenna as the initial step in its evolution, we follow a structured methodology aimed at optimizing its performance and capabilities. Figure 3(a) shows the single-element antenna. The initial phase of the design focuses on selecting suitable materials and defining accurate dimensions for optimal results. The antenna has a compact size of 75 × 77 μm², specially designed for high-frequency applications as depicted in Table 2. Copper stands as the prime radiating material chosen for its superconductivity and flexibility, which contributes to enhanced radiation and the general performance of the signal²⁵. The antenna is built on a polyimide substrate with a thickness of 10 μm, ensuring low dielectric loss and stable electromagnetic performance. A completely solid copper ground plane is placed on the opposite side to provide effective shielding and improve impedance matching.

Fig. 3.

(a) Final structure of the single-element antenna. (b) Simulated reflection coefficient (S11).

Table 2.

Key dimensions of the antenna model.

Design parameters	Symbol	Dimensions (µm)
Substrate Width	sw	77
Substrate Length	sl	75
feed Width	fw	4
feed Length	fl.	25
Slot 1 width	W1	6
Slot 2 width	W2	3.5
Slot 3 width	W3	0.75
Slot 4 width	W4	8

The patch structure consists of a periodic grid-like arrangement of interconnected rectangular sections, strategically designed to enhance both gain and bandwidth. The periodic pattern facilitates better current distribution, reducing surface wave losses and increasing radiation efficiency. Additionally, the interconnected structure enables better impedance control, minimizing reflection losses for improved signal propagation.

The antenna and the signal source are directly connected by a thin feedline that extends from the patch’s bottom center. This feedline is essential to the antenna’s design because it ensures effective energy transmission without the need for further tuning components. It contributes to the optimization of the antenna’s performance by maintaining impedance matching and resonance. The feedline is designed to maintain impedance matching, contributing to stable operation across the target frequency range.

To evaluate its performance, the antenna is simulated using CST-2018 software, where key parameters such as the reflection coefficient, gain, radiation efficiency, and bandwidth are analyzed. As shown in Fig. 3(b), the single-element antenna resonates at 1.92 THz with a very good return loss of − 38 dB and a significantly wider bandwidth of 2.85 THz, highlighting its excellent impedance matching and wideband capability. Iterative optimizations are performed to fine-tune the grid structure, ensuring superior performance in terms of both radiation characteristics and frequency response. This grid-based copper antenna, with its compact size, high conductivity, and structured design, is highly suitable for next-generation high-frequency communication systems. Employing copper for both the radiating patch and ground plane, combined with a finely tuned periodic structure, renders the design highly suitable for practical applications such as ultra-high-speed THz communication and IoT-driven wireless networks²⁶.

Design development of the single-element antenna

To optimize its suitability for 6G communication, the single-element antenna was designed using a systematic five-phase development approach. Each step introduces modifications to the structure, leading to improvements in resonance, return loss, gain, and bandwidth. Figure 4 illustrates the evolution of the antenna, while the corresponding simulation results are presented in Fig. 5, where Fig. 5a presents the S-parameter and Fig. 5b illustrates the gain. The detailed design modifications and performance comparisons for each step are discussed below.

Fig. 4.

The single antenna and the development of its design.

Fig. 5.

Analysis of (a) S-parameter, (b) Gain.

The first step begins with a basic structure consisting of a central feedline connected to a periodic grid-like patch. Two vertical stubs are placed at the far-left and far-right corners of the grid, forming a rudimentary radiating structure. However, this configuration exhibits poor performance, resonating at two distinct frequencies of 1.51 THz and 2.58 THz with return losses of − 20.37 dB and − 16.99 dB, respectively. The bandwidth is limited to 0.48 THz and 0.2 THz at the respective bands. The maximum gain is also quite low, reaching only 4.57 dB, indicating the need for significant structural refinement. To address these limitations, the second step introduces an additional periodic grid-like arrangement, positioned opposite to the original patch and connected via the two vertical stubs. This dual-sided configuration enhances current distribution and symmetry. The simulation results reveal an oscillatory response in the first frequency band with no distinct resonance. In the second band, a resonance frequency is observed at 2.5 THz, but the return loss remains poor, indicating inefficient radiation. The gain at this step is 4.2 dB, which is inadequate for THz applications. Structural modifications are introduced in the next step to address these limitations. In the third step, additional slot structures are incorporated inside the grid-like arrangement to improve impedance matching and radiation efficiency. These modifications lead to a shift in the resonance frequency to 2.9 THz, with a significant improvement in return loss. Furthermore, the gain increases to 5.85 dB, demonstrating better radiation performance. However, despite these enhancements, the bandwidth remains narrow, limiting the antenna’s applicability for THz communication. To overcome this issue, further structural adjustments are made in the fourth step. In this step, the antenna structure undergoes further refinement by introducing additional inner slot elements within the grid-like framework to enhance coupling and broaden the bandwidth. As a result, the resonance frequency shifts to 2.4 THz, and while the return loss slightly decreases compared to the previous step, the bandwidth significantly improves to 2.3 THz. Additionally, the gain increases to 7.1 dB, marking a notable improvement. However, the gain remains suboptimal for high-performance THz applications. To achieve superior performance, the antenna structure is further optimized in the final step. In the final step, further refinements are made by introducing a more complex slot pattern within the periodic grid-like structure, leading to enhanced impedance matching and radiation efficiency. This results in a well-defined resonance frequency with a very good return loss of −38 dB and a significantly wider bandwidth of 2.85 THz. The gain is also drastically increased to 9.97 dB, making the antenna highly suitable for 6G communication. This final step represents an optimized structure, ensuring superior performance across all key metrics.

The iterative design process successfully enhances the antenna’s performance by systematically improving resonance, return loss, gain, and bandwidth²⁷. The final structure achieves optimal characteristics for THz applications, demonstrating its potential for high-speed and high-frequency wireless communication in future 6G networks.

Parametric analysis

Effect of changing top stub width (w1)

Parametric analysis is essential for optimizing antenna designs by understanding how variations in specific parameters affect performance²⁸. For the proposed antenna, the width of the top stub (w1​) was varied between 4 μm and 8 μm to evaluate its impact on bandwidth (BW), return loss, and gain. At 4 μm, the antenna operates in two distinct bands, with simulated bandwidths of 0.3 THz and 0.6 THz, but the return loss values of −25.7 dB and − 22 dB, along with gains of 2.07 dB and 6.1 dB, were inadequate for practical applications. Conversely, increasing w1​ to 8 μm resulted in moderate improvement, with a return loss of −26.3 dB, a bandwidth of 0.63 THz, and an enhanced gain of 7.76 dB. The optimal performance was achieved when w1​ was set to 6 μm, the proposed configuration. At this dimension, the antenna demonstrated remarkable improvements, achieving a return loss of −38 dB, a significantly increased bandwidth of 2.85 THz, and a high gain of 9.97 dB. These results highlight the critical impact of w1​ on the antenna’s performance, demonstrating the need for precise optimization to achieve superior operational characteristics. These results are illustrated in Fig. 6a for S11 ​ and Fig. 6b for gain.

Fig. 6.

Impact of varying top stub width on the antenna’s (a) reflection coefficient and (b) gain characteristics.

Effect on changing feed length (fl)

Parametric analysis is essential for optimizing antenna performance, and the feedline length (fl.) plays a critical role in determining impedance matching and overall efficiency²⁹. Figure 7 illustrates the effect of varying fl. on the antenna’s performance, where Fig. 7a presents the S11​ response and Fig. 7b depicts the gain. When the feedline length was set to 22 μm, the antenna exhibited an oscillatory S11​ response, preventing clear resonance identification, although the gain remained moderate at 7.97 dB. Increasing fl. to 28 μm allowed the antenna to resonate at 1.47 THz, but the return loss of −22 dB indicated poor impedance matching, and the gain further dropped to 6.2 dB. The optimal performance was observed when fl. was set to 25 μm, where the antenna resonated at 1.92 THz with a significantly improved return loss of −38 dB and a high bandwidth of 2.85 THz. Additionally, the gain increased to 9.97 dB, demonstrating superior performance. These findings highlight the crucial impact of feedline length on antenna characteristics, emphasizing the need for precise tuning to achieve optimal impedance matching, bandwidth, and gain.

Fig. 7.

Impact of varying Feed Length on the antenna’s (a) reflection coefficient and (b) gain characteristics.

Effect on changing substrate length (sl)

Parametric analysis of the substrate length (sl) is crucial in optimizing antenna performance, as it directly influences impedance matching, bandwidth, and gain³⁰. Figure 8 illustrates the impact of varying sl on the antenna’s characteristics, with Fig. 8a presenting the S11​ response and Fig. 8b depicting the gain. When sl was set to 70 μm, the antenna resonated at 0.99 THz with a return loss of −29.98 dB and a bandwidth of only 0.6 THz, which is relatively low, although a moderate gain of 8.07 dB was achieved. Increasing sl to 80 μm resulted in a high bandwidth of 2.4 THz; however, the return loss deteriorated to −26.13 dB, and the gain dropped to 6.6 dB, indicating a trade-off between bandwidth and impedance matching. The optimal performance was observed when sl was set to 75 μm, where the antenna resonated at 1.92 THz, achieving a significantly improved return loss of −38 dB and an exceptionally high bandwidth of 2.85 THz. Additionally, the gain was maximized at 9.97 dB, demonstrating a well-balanced design. These findings highlight the crucial role of substrate length in achieving optimal antenna performance, emphasizing the need for precise adjustments to enhance bandwidth, return loss, and gain.

Fig. 8.

Impact of varying Substrate Lengths on the antenna’s (a) reflection coefficient and (b) gain characteristics.

2-Port MIMO structure

Four different designs were investigated to identify the most effective configuration for the proposed MIMO antenna, as shown in Fig. 9. The patch and ground configurations remained identical to those of the single-element antenna across all designs to uphold consistent baseline behavior. In Antenna 1, the elements differ by being rotated 180 degrees from the first. This arrangement resulted in a single-band response with relatively high return loss, leading to reduced radiation efficiency. The mutual coupling was also high at −8.94 dB, demonstrating considerable interference between elements. In Antenna 2, the second element was rotated 90 degrees. This configuration enhanced the bandwidth to 1.75 THz, achieving dual resonance and favorable return loss. Although mutual coupling was reduced to −12.68 dB, indicating moderate isolation, the level of isolation was still not optimal.

Fig. 9.

Evolution of the MIMO Antenna.

Antenna 3 adopted an L-shaped structure by orienting one element vertically and the other horizontally, with the substrate cut on both sides to accommodate the shape. This configuration achieved a dual-band response at 0.99 THz and 2.07 THz. Nevertheless, the mutual coupling improved significantly to −19.68 dB for the first band and − 20.16 dB for the second band, offering better isolation than the previous setups. To further enhance performance, Antenna 4 introduced a Parasitic Decoupling Structure (PDS) between the two elements, building upon the L-shaped layout of Antenna 3. This addition was strategically designed to suppress surface currents and reduce electromagnetic interaction between ports³¹.

As a result, Antenna 4 exhibited the most optimized performance. It showed a dual-band response with a first band spanning 0.081 to 1.36 THz (bandwidth: 1.279 THz) and a second band from 1.81 to 3.43 THz (bandwidth: 1.62 THz), resonating at 0.31 THz and 2.19 THz, respectively. Moreover, it achieved an excellent mutual coupling of −36.1 dB, indicating high isolation and minimal interference. As illustrated in Fig. 10, which compares reflection coefficients and isolation for each configuration, Antenna 4 clearly outperformed the others across all key parameters—bandwidth, return loss, and isolation—and stands out as the most suitable candidate for high-performance 2-port MIMO antenna applications in the THz range.

Fig. 10.

Impact of various MIMO antenna orientations on (a) reflection and (b) transmission coefficients.

Development and analysis of a Stepwise parasitic decoupling structure

To address the challenges of mutual coupling in MIMO systems, a systematic design strategy employing a stepwise parasitic decoupling structure was introduced and analyzed³². The progressive evolution of the antenna structure, as illustrated in Fig. 11a–d, highlights how targeted modifications can dramatically enhance isolation performance across multiple frequency bands. Figure 12 illustrates the comparative isolation performance across all design steps.

Fig. 11.

Development of a stepwise parasitic decoupling structure.

Fig. 12.

Assessing the effectiveness of different decoupling structure.

Step 1 initiated the foundational antenna design by adopting an L-shaped configuration, where one antenna element is vertically oriented and the other horizontally. The substrate is symmetrically trimmed on both sides to accommodate this structure. However, this version lacks any decoupling mechanism, resulting in relatively high mutual coupling. The isolation performance is measured at − 19.68 dB for the first band and − 20.16 dB for the second band, revealing the design’s limitations and the necessity for improvement. Step 2 introduced a solid rectangular parasitic element positioned between the two radiating structures. This straightforward decoupling structure slightly enhanced the isolation, achieving − 25.47 dB and − 23.07 dB at the first and second bands, respectively. While an improvement is noted, the results remained suboptimal, prompting further structural refinement. In Step 3, the previously solid decoupling structure was transformed into a periodic array of equally spaced hexagonal elements. This discretization aimed to suppress surface wave propagation and improve electromagnetic isolation. Although the isolation in the first band remained nearly unchanged, a noticeable enhancement was observed in the second band, where isolation improved to − 28.42 dB.

The final and most effective enhancement occurred in Step 4 (Proposed Antenna). Here, each hexagonal element from Step 3 was modified by attaching circular discs to both the top and bottom sides, forming a stylized motif resembling interconnected dumbbells or humanoid figures. This intricate geometry introduced additional current path disruptions, resulting in a substantial improvement in isolation. The antenna achieved − 31.43 dB isolation at the first band and an impressive − 36.1 dB at the second band. The isolation performance across all steps is comparatively presented in Fig. 12, which clearly illustrates the progressive enhancements achieved through each design evolution. The final structure (Step 4) outperforms all previous versions, affirming the effectiveness of the proposed parasitic decoupling strategy.

Compared to traditional decoupling techniques such as electromagnetic band gap (EBG) structures, defected ground structures (DGS), and neutralization lines, the proposed parasitic decoupling structure demonstrates several advantages. EBG and DGS often require large etched patterns in the ground plane, increasing design complexity and limiting suitability for high-frequency THz applications due to their size and substrate perturbations. Neutralization lines, although effective, generally involve precise tuning and additional transmission paths that may introduce unwanted coupling or degrade performance at higher frequencies. In contrast, the stepwise parasitic structure provides compact, symmetrical, and planar decoupling elements that do not interfere with the feed network or require complex modifications to the ground plane. The final design achieves − 31.43 dB and − 36.1 dB isolation across two operating bands—levels that are comparable to or better than those typically reported using conventional techniques—while maintaining low structural complexity and fabrication ease. These results highlight the practical benefits of the proposed approach for high-frequency, densely packed antenna systems.

Result analysis of proposed MIMO antenna

Reflection coefficient analysis

The reflection coefficient (S11​) is a critical parameter that indicates how effectively an antenna is matched to its input transmission line³³. A lower value of S11​ (more negative) reflects better impedance matching and less signal reflection, which ensures efficient power transfer from the source to the antenna³⁴. The proposed MIMO antenna exhibits dual-band functionality, covering both sub-THz and THz frequency ranges. The first band exhibits resonance at two specific frequencies: 0.31 THz and 1.07 THz, with corresponding return losses of −35.4 dB and − 30.03 dB, respectively. This band encompasses a broad frequency range from 0.081 THz to 1.36 THz, providing an impressive bandwidth of 1.279 THz, which confirms the antenna’s excellent capability to operate over a broad spectrum.

In the second frequency band, the antenna is tuned to 2.19 THz, demonstrating a notably low return loss of −55.38 dB. It effectively operates within a range of 1.81 THz to 3.43 THz. This results in an additional bandwidth of 1.62 THz, highlighting the antenna’s exceptional spectral coverage and suitability for high-data-rate THz communication. These results are visually presented in Fig. 13, showcasing the antenna’s effectiveness in handling wideband signals with minimal reflection loss.

Fig. 13.

Reflection coefficient of the proposed MIMO antenna.

Transmission coefficient (mutual coupling)

The transmission coefficient (S21​ or mutual coupling) evaluates how much power is transferred between the elements of a MIMO antenna. High isolation between antenna ports is essential to avoid interference and to ensure independent signal paths, which are crucial for the efficiency of MIMO systems³⁵. The proposed antenna demonstrates excellent isolation characteristics by achieving a minimum isolation of −31.43 dB in the first band and − 36.1 dB in the second band. These values indicate very low mutual coupling between the antenna elements, ensuring reliable diversity performance and minimal signal degradation. The transmission coefficient performance is illustrated in Fig. 14.

Fig. 14.

Transmission coefficients of the proposed MIMO antenna.

Gain and efficiency

Gain defines the antenna’s ability to direct radiated power in a specific direction, and efficiency represents how well the input power is converted into radiated power³⁶. Both parameters are fundamental in determining the performance and practicality of an antenna for real-world communication systems. The proposed MIMO antenna demonstrates high radiation characteristics across both frequency bands. In the first band, it achieves a maximum gain of 11.91 dB and an efficiency of 92.42%. In the second band, the antenna exhibits an even higher gain of 12.21 dB with a remarkable efficiency of 86.93%. These results confirm that the antenna performs with high directivity and low power loss, which is vital for long-distance and high-capacity communication links³⁷. The gain and efficiency results are jointly illustrated in Fig. 15.

Fig. 15.

Gain and Efficiency Analysis of the Proposed MIMO Antenna Configuration.

Diversity performance analysis

The envelope correlation coefficient (ECC)

The Envelope Correlation Coefficient (ECC) is used to evaluate the level of correlation between the radiation patterns of different antenna elements in a MIMO system. A low ECC value ensures better spatial diversity and less interference between channels. Ideally, ECC should be less than 0.5 for acceptable diversity performance, with values closer to zero indicating excellent isolation and decorrelation. ECC is calculated by the formula³⁸:

1

The proposed design exhibits a remarkably low ECC of 0.00015, which confirms the antenna’s capability to provide independent radiation characteristics for each port and outstanding MIMO performance. The ECC values are presented in Fig. 16.

Fig. 16.

Envelop Correlation Coefficient (ECC) of the proposed MIMO antenna.

Diversity gain (DG)

Diversity Gain (DG) quantifies the improvement in signal reception due to the diversity techniques applied in a MIMO antenna system. It helps counter the effects of multipath fading by leveraging multiple, independently faded signal paths. The DG value theoretically reaches a maximum of 10 dB in an ideal scenario³⁹. DG can be calculated by the equation⁴⁰:

2

The proposed design highlights the excellent DG of 9.99925, which is nearly perfect, indicating superior multipath mitigation and highly reliable performance in diverse propagation environments. This confirms the antenna’s capability to maintain robust connectivity even under challenging channel conditions. The DG performance is shown in Fig. 17.

Fig. 17.

The DG offered by the proposed antenna.

Radiation pattern

A 2D radiation pattern is a two-dimensional graphic representation of an antenna or other electromagnetic radiation source⁴¹. Light, microwaves, and radio waves are examples of this radiation. Figure 18 displays the two-dimensional patterns for the magnetic field (H field) and electric field (E field). The E-field’s main lobe magnitude is 12.1 dBV/m at an angle of φ = 0 degrees, and the 3 dB angular beam width is 29.4° at an angle of φ = 90 degrees. Even though the electric field pattern (E Field) is recorded at 2.19 THz and the major lobe’s magnitude reaches 20.5 dBV/m at 90 degrees, these two findings seem to be at odds. The principal lobe in the H field has an angular beam width of 16.6° at φ = 90 degrees and a magnitude of −48.7 dBA/m at φ = 0 degrees. The H Field’s main lobe magnitude is −42.4 dBA/m at a 90-degree theta angle.

Fig. 18.

Visualization of the simulated radiation behavior of the recommended MIMO Antenna.

RLC equivalent circuit

To advance antenna technology, an in-depth analysis of its electromagnetic behavior was carried out using an RLC (resistance–inductance–capacitance) circuit model. This approach aimed to clarify the intricate interactions within the antenna’s electrical structure and provide an accurate representation of its performance. The R-L-C traits were meticulously derived from antenna simulations using advanced simulation software such as CST-2018 Studio, ensuring precision in circuit modeling. Additionally, through circuit modeling in Agilent ADS, the analysis was further refined to investigate the antenna’s behavior thoroughly.

We dismantled the antenna structure into its fundamental electrical elements and developed a comprehensive circuit model to precisely represent its behavior. In this model, the slots of the antenna structure are effectively captured. Each capital ‘I’-shaped patch is modeled using two parallel circuits: one comprising an inductor 1​ and a capacitor 1 in parallel, and the other consisting of a parallel combination of 2 and 2. These two parallel networks are connected in series with capacitors 4 ​ and 5. Additionally, each small ‘i’-shaped patch is represented by a parallel circuit formed by inductor 3​ and capacitor 3, and there is a capacitance formed between each capital I-shaped path and small i-shaped patch.

The circuit model accurately represented the electrical behavior of the feedline—an essential part of the antenna system—by incorporating fundamental parameters such as resistance (Rx), capacitance (C), and inductance (L). These components were crucial in defining the antenna’s impedance and transmission characteristics. Through the precise integration of these discrete elements, a detailed model was developed that closely emulated the performance of the single-element antenna. To account for mutual coupling in a MIMO configuration, the model was extended by incorporating a series combination of L1–2 and C1–2, which effectively represented the mutual impedance between antenna elements. The complete equivalent circuit of the MIMO antenna, illustrated in Fig. 19, demonstrates how this approach enhances performance analysis by accurately representing the interactions among the various antenna elements. The accuracy of the RLC model was verified through simulation in Agilent ADS. To ensure the model’s precision, a comparative analysis was conducted between the results obtained from ADS and those from CST-2018 Studio, with particular emphasis on the S11 parameter. Figure 20 presents this comparison, offering a detailed evaluation of the RLC model’s fidelity in replicating the antenna’s electromagnetic behavior. The complete list of RLC component values used in the model is provided in Table 3.

Fig. 19.

Final equivalent circuit for the proposed MIMO Antenna.

Fig. 20.

Reflection coefficient Analysis: CST and Equivalent Circuits in ADS.

Table 3.

Lumped element values (R, L, and C) for the equivalent circuit model of the designed THz MIMO antenna.

Parameter	Value	Parameter	Value	Parameter	Value	Parameter	Value
L1-2	1.2 pH	L6	0.126 pH	C3	0.0243 pF	C10	1.7 pF
L1	2.25 pH	L7	1.358 pH	C4	33.19 pF	C11	2.5 pF
L2	0.0238 pH	L8	11.36 pH	C5	0.058 pF	C12	5.68 pF
L3	5.36 pH	C1-2	22.325pF	C6	0.968 pF	C13/14	7.35 pF
L4	1.89 pH	C1	2.365 pF	C7/C8	0.1 pF	C15/16	8.76 pF
L5	0.21 pH	C2	5.684 pF	C9	7.2 pF	R1	50.25 Ω

Antenna optimization through machine learning techniques

Commercial electromagnetic modeling tools such as CST, HFSS, FEKO, and IE3D require significant time to design antennas and face optimization challenges⁴². Designing and fabricating a miniature antenna that can generate a signal consistently is a very challenging and time-consuming process when it comes to such sophisticated structures, with hundreds of slots on both the ground plane and the upper surface of the patch. Traditional design methods are not non-linear, so they tend to be a little less efficient as they require more time and effort. To overcome these limitations, machine learning (ML) regression models have been utilized to predict antenna characteristics and speed up designs^43,44. ML leverages data from experiments or simulations to help explore design spaces much faster. This enables the reliable prediction of antenna size and performance metrics, which speeds the design process and thus accelerates project delivery. Machine Learning regression models are becoming more relied upon by researchers to predict antenna properties and optimize designs accordingly, combating these challenges. Data collected either by experiments or simulations allows for the accelerated exploration of design spaces through machine learning (ML). This allows for the prediction of antenna size and performance parameters with an unusual degree of accuracy, which considerably condenses the time it takes to perform the work⁴⁵.

Preparing data sets and selection of algorithm

Machine learning predictions of antenna optimization require a robust dataset of input/output pairs⁴⁶. Known inputs are the antenna dimensions, qualities of materials, and slot configurations, while outputs include performance measurements such as gain, bandwidth, return loss, or radiation efficiency. ML models trained on this dataset can learn complex relationships between design variables and performance metrics, facilitating precise predictions⁴⁷. In this work, the antenna was designed using CST-2018 Studio, a widely used electromagnetic simulation software. After running multiple optimizations with input variables such as d, dlw, dor, sl, st, sw, and t, which are described in Section III, the corresponding outputs recorded various performance indicators, and a complete dataset was created. 1. In this dataset, ML models are trained, and predictions are matched against CST-2018 for the electromagnetic behavior’s anticipated efficiency of the suggested MIMO antenna, which is based on five different regression machine learning algorithms applied to 99 data samples obtained from CST MWS simulations. 80 per cent of the data is used for training, while 20 per cent is reserved for evaluation. The machine learning algorithm processes the training dataset meticulously after generating the features and labels. Once the model is trained and validated, it can utilize various input parameters, including bandwidth, to make accurate predictions for multiple outputs. The development process of the machine learning model is illustrated in Fig. 21.

Fig. 21.

Schematic illustrating the necessary steps for creating machine learning algorithms.

Regression machine learning model analysis

Regression machine learning models play a crucial role in advancing THz antenna design by enabling precise predictions of key performance metrics such as gain, return loss, bandwidth, efficiency, and resonant frequency, based on various design parameters, including geometrical dimensions, substrate material characteristics, operating frequency, and fabrication tolerances. These models aid researchers in understanding the complex and often non-linear relationships between input parameters and antenna performance, thus streamlining the design process. Common techniques like linear regression, polynomial regression, and support vector regression (SVR) are employed for simpler correlations, while more intricate interactions are addressed using advanced models such as random forests, gradient boosting, and neural networks. To ensure robust model performance, practices such as cross-validation and hyperparameter optimization are implemented, along with evaluation metrics like Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and R² score to quantify prediction accuracy.

Decision tree regression

Decision Tree Regression is a non-parametric supervised learning technique used to model the relationship between a target variable and one or more explanatory factors by dividing the data into subsets based on feature values⁴⁸. This process results in a tree-like structure where each internal node represents a decision criterion based on a specific feature, each branch denotes the outcome of that criterion, and each leaf node indicates a predicted value for the target variable⁴⁹.

XGB regression

XGBoost, or Extreme Gradient Boosting, is a powerful machine-learning technique recognized for its effectiveness in solving regression problems⁵⁰. It enhances the traditional gradient boosting framework by integrating advanced regularization methods, enabling parallel processing, and employing tree pruning. These features work together to improve both prediction accuracy and computational efficiency⁵¹.

Extra trees regression

Extra Trees Regression, short for Extremely Randomized Trees, is an ensemble learning technique that builds multiple decision trees using random selections of data and features⁵². Unlike traditional decision trees, Extra Trees adopt a higher level of randomization by randomly choosing split points and attributes. This approach can lead to improved generalization and reduced overfitting⁵³.

Gaussian process regression (GPR)

Gaussian Process Regression (GPR) is a powerful, non-parametric method for modelling complex, non-linear relationships in data. It offers predictions along with uncertainty estimates, making it especially useful in fields such as robotics, geostatistics, and machine learning⁵⁴.

Poisson regression

Poisson Regression is a statistical method used to model count data and contingency tables. It assumes that the response variable follows a Poisson distribution, where the mean is equal to the variance. This assumption implies that the data exhibit equidispersion, meaning the variability is proportional to the mean⁵⁵.

Performance evaluation criteria for regression models

Performance measurement metrics are applied to evaluate the efficiency and accuracy of machine learning models. The evaluation of regression models is typically carried out using statistical metrics that measure predictive accuracy and goodness-of-fit. Key metrics include Mean Absolute Error (MAE), which assesses the average magnitude of errors; Mean Squared Error (MSE) and Root Mean Squared Error (RMSE), both of which impose greater penalties on larger errors to highlight significant deviations; R-squared (R²), which indicates the proportion of variance in the target variable explained by the model; and the Explained Variance Score, which evaluates how well the model’s predictions align with observed data. Together, these metrics provide comprehensive insights into model accuracy, reliability, and predictive effectiveness, facilitating model optimization and selection.

The Mean Absolute Error (MAE) is a regression statistic that measures the average magnitude of the absolute differences between predicted values () and actual values () in a dataset⁵⁶. This metric provides a straightforward assessment of model prediction accuracy, expressed in the same units as the target variable⁵⁷. Here is the given expression:

3

where, n = number of errors = error absolute.

Mean Squared Error (MSE) is a fundamental metric used in regression analysis and statistical modeling that quantifies the average squared deviation between actual and predicted values. This metric serves as an indicator of the quality of an estimator or predictor, with a lower MSE signifying a better fit to the data⁵⁸.

4

Regression analysis and machine learning often utilize Root Mean Squared Error (RMSE) as a metric to assess the accuracy of a model’s predictions. This measure calculates the square root of the mean of the squared differences between the observed and predicted values, providing insight into the average magnitude of the residuals⁵⁹.

5

Regression analysis and machine learning often utilize Root Mean Squared Error (RMSE) as a metric to assess the accuracy of a model’s predictions. This measure calculates the square root of the mean of the squared differences between the observed and predicted values, providing insight into the average magnitude of the residuals⁶⁰.

6

Regression analysis utilizes the Explained Variance Score as a metric to assess the accuracy with which a model predicts the variability of the target variable. This score indicates the extent to which the model’s predictions can explain the observed variation in the data. A lower explained variance score suggests that the model’s predictions account for little of the variability in the target variable, whereas a higher score signifies that the model effectively captures the variability⁶¹.

7

Result analysis M/L

Table 4 provides a comprehensive evaluation of various regression algorithms employed for predicting antenna gain, utilizing key performance metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Square Error (RMSE), R² (Coefficient of Determination), and Explained Variance Score (EVS). Among the evaluated models, the Extreme Gradient Boosting (XGB) Regressor stands out, achieving the highest accuracy with an R² of 96.23% and an EVS of 97.89%, while maintaining low error rates (MAE: 0.90%, MSE: 0.95%, RMSE: 2.07%). This indicates a remarkable balance between predictive precision and generalization capability. Figure 22 illustrates the comparative accuracy of each algorithm using a bar chart, where the XGB Regressor clearly dominates in both R² and EVS metrics. This visual affirmation highlights its superior ability to model complex nonlinear relationships in the gain prediction task. Figure 23 complements this analysis by depicting the error-based comparison across different models. Notably, the XGB Regressor exhibits the lowest RMSE (2.07%). The XGB Regressor’s optimal blend of accuracy and minimal prediction error justifies its selection as the optimal model.

Table 4.

The gain prediction performance.

Algorithm	MAE	MSE	RMSE	R 2	EVS
Decision tree	4.29%	2.08%	7.32%	80.65%	82.14%
XGB Regressor	0.90%	0.95%	2.07%	96.23%	97.89%
Extra Tree Regression	2.28%	2.18%	3.12%	84.39%	86.12%
Gaussian Process Regression	4.06%	2.93%	5.04%	83.47%	85.23%
Poisson Regression	3.09%	2.00%	6.16%	90.29%	91.85%

Fig. 22.

Performance comparative bar chart (accuracy).

Fig. 23.

Bar chart for performance comparison (error).

Table 5 showcases a detailed point-by-point comparison between the simulated gain values and the predicted values generated by the XGB Regressor for twenty distinct test samples. The predicted outcomes exhibit an exceptionally close alignment with the simulated values, reflecting minimal deviation and near-zero residual error across the entire test set. This further reinforces the model’s robustness and high fidelity in approximating actual antenna behavior. Figure 24 presents a visual comparison of simulated and predicted gain values, effectively capturing the trend consistency between both datasets. The plotted results demonstrate how accurately the XGB Regressor tracks the gain variation across a range of 10.779 dB to 12.5313 dB, showcasing its strong capability in capturing intricate patterns and subtle fluctuations in the data. This excellent agreement between predicted and actual values substantiates the XGB Regressor as the most promising and reliable model for gain prediction in antenna design applications, making it a powerful tool for anticipating performance improvements with high confidence.

Table 5.

Simulated and predicted gain comparison using gradient boost regression.

No	Simulated gain	Predicted gain	No	Simulated gain	Predicted gain
1	11.4427	11.13101	11	11.4664	11.51797
2	11.6969	11.6674	12	11.5649	11.55462
3	11.724	11.47568	13	11.4338	11.47562
4	11.8589	11.78017	14	11.4185	11.38666
5	11.5808	11.47608	15	11.5119	11.5074
6	11.5276	11.49824	16	10.779	10.89766
7	11.2112	11.37577	17	11.1001	11.27269
8	12.5313	12.51612	18	12.4704	12.35794
9	11.5221	11.475	19	11.4611	11.44397
10	11.4152	11.47568	20	11.4961	11.47485

Fig. 24.

Comparison of Simulated and Predicted Gain.

Fabrication challenges and environmental effects at THz frequencies

While the proposed THz MIMO antenna shows promising simulated performance, practical implementation at terahertz frequencies presents several challenges. Fabrication tolerances at THz scales are extremely tight, where even micron-level deviations can significantly affect resonance frequency and impedance matching. Surface roughness, alignment accuracy, and layer thickness variations can introduce losses and shift performance metrics such as return loss and bandwidth. Additionally, material inconsistencies, especially in high-frequency dielectric substrates, may impact efficiency and radiation characteristics. Environmental factors, such as humidity and temperature, may also contribute to performance variation. Therefore, future work will focus on precision fabrication methods and tolerance-aware design adjustments to ensure robust real-world performance, particularly in complex indoor environments typical of 6G applications.

Conclusion

This research demonstrates the successful integration of machine learning techniques into the design and optimization of a high-performance THz antenna for wireless communication and IoT applications. The proposed compact antenna, developed on a polyimide substrate with dimensions of just 160 × 160 μm², achieves exceptional performance metrics—high peak gains of 11.91 dB and 12.21 dB, superior isolation levels exceeding 31.43 dB and 36.1 dB, and a notable efficiency of 92.42%. Covering two ultra-wide frequency bands (0.081–1.36 THz and 1.81–3.43 THz), the antenna proves highly suitable for short-range, high-speed data transmission in emerging THz applications. The inclusion of machine learning not only enhances antenna performance but also significantly accelerates the design process, offering a scalable approach for future development of intelligent, compact, and efficient antennas in next-generation wireless systems. The antenna’s settings were meticulously fine-tuned utilizing a cutting-edge machine learning approach, resulting in impressive predictive metrics with error levels of 0.95 for MSE, 2.07 for RMSE, and 0.90 for MAE. This antenna has undergone rigorous validation through CST-2018 simulations and RLC circuit modeling in ADS. It is designed to support steady, high-speed data transmission even in challenging 6G communication environments, showcasing its exceptional resilience and efficiency. Plans are in place for the antenna to be manufactured in the future, allowing empirical data to confirm the simulation results, a crucial step before actual deployment. By incorporating metamaterials, further enhancements in bandwidth, gain, and efficiency could be realized, unlocking new opportunities for advanced THz applications.

Author contributions

Conception, design, data collection, analysis, simulation K.H.N.,, N.S, and writing the original manuscript were carried out by N.J.S.S & J.H.N., and M.N.; Supervision J.J.T and M.A.H; All authors performed the analysis and interpretation of the data as well as reviewed the writing and presentation of the whole manuscript.

Funding

This research work was funded by Umm Al-Qura University, Saudi Arabia under grant number: 25UQU4300346GSSR11.

Data availability

The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.