Multiband THz MIMO antenna with regression machine learning techniques for isolation prediction in IoT applications | Scientific Reports

Mar 06, 2025

Scientific Reports volume 15, Article number: 7701 (2025) Cite this article

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The rapid evolution of Internet of Things (IoT) applications demands advancements in wireless communication technologies to handle increasing data rates and connectivity requirements. This article presents our novel research on utilizing machine learning techniques to enhance the efficiency of MIMO antennas for Wireless Communication and IoT applications in the Terahertz (THz) frequency band. Our research assesses antenna performance using various methodologies, including simulation and RLC equivalent circuit models. The proposed design operates at 6.51 THz, 7.48 THz, and 8.46 THz, with bandwidths of 0.7 THz, 0.69 THz, and 0.89 THz, respectively. It features a maximum gain of 13.53 dBi and compact dimensions of 160 × 75 μm2. Additionally, it demonstrates excellent isolation, exceeding −32 dB, −44 dB, and −45 dB across these bands, with over 96.5% efficiency in all operating bands. By designing a similar RLC circuit in ADS and simulating it, we validated the results obtained from CST. Both CST and ADS simulators produced comparable reflection coefficients. Furthermore, several machine learning algorithms were applied to test the design. Various metrics, including variance score, R-squared, mean squared error (MSE), mean absolute error (MAE), and root mean square error (RMSE), were used to evaluate the machine learning models. Among the five models analyzed, the Gradient Boosting Regression model exhibited the lowest error rates (4.94% MAE, 6.60% MSE, and 4.13% RMSE) and achieved the highest accuracy, exceeding 98% in predicting isolation. Considering all these factors, it is evident that this antenna is an excellent choice for the THz band in 6G wireless communication.

An antenna system that operates in the Terahertz frequency range (often 0.1 THz to 10 THz) and supports multiple-input multiple-output communication techniques is called a multiband Terahertz (THz) Multiple-Input Multiple-Output (MIMO) system. Wireless communication systems use the Multiple-Input Multiple-Output (MIMO) technology, which uses multiple antennas at the transmitter and reception ends to improve performance1. It makes use of the diversity of geography to increase network dependability and data throughput. Numerous frequency bands are intended for use by antennas. Reaching multiband operation at THz frequencies might be challenging due to the peculiarities of THz components and the recent development of THz technology in comparison to lower frequency bands. Developing antennas that can operate at THz frequencies is a significant problem because of the short wavelength and the accompanying shrinking requirements2. Long-distance communication is difficult because THz signals are highly susceptible to attenuation by the environment and absorption by different materials.3. It is difficult to develop workable THz communication systems since components like mixers, amplifiers, and modulators that function at THz frequencies are still in the early stages of research4.

THz antennas are a good fit for Internet of Things (IoT) applications that need fast data transfer since they can enable high-speed wireless connectivity5,6. Compared to other wireless communication technologies, these applications include high-definition video streaming, virtual reality (VR), augmented reality (AR), and real-time sensor data-gathering waves that show superior resilience to environmental conditions including dust, fog, and smoke7. Due to their resilience, THz antennas are ideal for Internet of Things (IoT) applications that need to operate in harsh or complicated environments, like industrial settings, outdoor monitoring systems, and emergency response scenarios8,9. THz antennas can be used for wearable health monitoring, remote patient monitoring, and imaging technology in IoT-enabled healthcare applications10,11. They provide high-definition, non-invasive imaging of biological tissues, which can help with therapy monitoring and early illness diagnosis12. Through the provision of quick wireless communication for Internet of Things (IoT) devices placed in urban environments, THz antennas can contribute to the growth of smart city infrastructure13. These gadgets can help with a number of applications, including infrastructure management, public safety, environmental monitoring, and intelligent transportation systems.

A comparison of several antenna designs is shown in Table 1, with a focus on operational metrics including isolation, gain, efficiency, diversity gain, resonance frequency, bandwidth, and ECC as well as philosophical underpinnings. The suggested antenna sticks out from the others because of its cutting-edge features and excellent performance metrics. Bandwidth values show considerable variation, with measurements including 0.05 THz, 0.78 THz, 0.6 THz, 0.4 THz, 1.28 THz, 0.04 THz, 0.44 THz, and 1 THz for the reference works14,15,16,17,19,20,21 and22 and 0.03 THz, 0.04 THz, 0.06 THz for reference work18. However, the suggested design produces much wider bandwidths of 0.68 THz, 0.88 THz, and 0.7 THz, demonstrating its ability to cover a broad range of frequencies. Isolation levels in the proposed layout surpass −36 dB, −44 dB, and −46 dB, contrasting with measured levels of  ≥ 25 dB,  > −20 dB,  > −25 dB,  > −25 dB,  > −15 dB,  > −20 dB,  > −22.26 dB,  > −20 dB,  > −20 dB and  > −20 dB in the cited sources14,15,16,17,18,19,20,21,22 and23. This high level of isolation indicates how well the suggested antenna can eliminate interference. The gain values reported in the references are 11.67 dBi, 4 dBi, 15 dBi, 5.49 dBi, 5 dBi, 8.2 dBi, 8.2 dBi, 3.9 dBi and 8.28 dBi14,15,16,17,18,19,20,21, and23. However, the proposed architecture produces significantly larger gains (13.53 dB). The proposed design also achieves an efficiency of 99.9%, outperforming values of 76.45%, 92%, 85.24%, 60%, 79.16%, and 98% cited in studies14,15,17,18,21, and22. The proposed antenna demonstrates exceptional ECC and diversity gain metrics, with an ECC of 0.00006 and a diversity gain (DG) of 9.9997 dB. Comparatively, other designs exhibit ECC values of 0.003, 0.006, 0.01, 0.015, 0.2, 0.0015, 0.0005, 0.01, and 0.004859 in the literature14,15,16,17,18,19,20,21 and22, and diversity gains of 9.99 dB in the literature14,15,17, and22 and 9.79 dB, 9.995 dB and 10 dB in the literature18,20 and21. The remarkably low ECC and high diversity gain of the proposed design indicate its superior performance. Notably, the proposed design incorporates both machine learning techniques and RLC components, which sets it apart from the referenced designs. While none of the referenced designs incorporated ML and RLC components. This innovative approach underscores the advancements in antenna technology presented by the proposed design. Overall, the comprehensive evaluation presented in Table 1 highlights the significant advancements and superior performance metrics of the proposed antenna design compared to other initiatives, showcasing its potential to lead the field of antenna technology.

Embarking on a journey to redefine antenna technology for the forthcoming 6G era, our design trajectory unfolds through a deliberate evolution, transitioning from a rudimentary single-element antenna to an intricate Multiple-Input Multiple-Output (MIMO) configuration. Figure 1 deconstructs the internal components of the antenna and its evolution. Figure 2 shows the reflection coefficient and gain and efficiency curves, respectively, for single-element, and MIMO. This shift is driven by our need for increased efficiency, performance, and flexibility in wireless networks in order to meet the increasing demands of higher data rates, lower latency, and more network capacity in the context of the 6G paradigm24. This progress is supported by the deliberate selection of materials for our antenna components. We use graphene as the patch material because of its exceptional mechanical resistance, conductivity, and flexibility. Copper is used as a grounding element to balance out graphene’s electromagnetic properties and provide the best possible signal grounding and radiation efficiency. Furthermore, we choose polyamide as the substrate material because of its favorable dielectric characteristics. With a low-loss tangent of 0.003 and a dielectric constant of 3.5, it promotes optimal signal propagation while reducing attenuation and energy loss. Through the seamless integration of these materials, our antenna design embodies a holistic approach to achieving superior wireless communication systems tailored to the exigencies of future 6G applications.

Steps of the antenna design process. (a) Single element; (b) MIMO Antenna.

Analysis of (a) Reflection Coefficient, (b) Gain, and (c) Efficiency Across Each Design Step of the Antenna.

Our antenna design journey unfolds with meticulous attention to detail, beginning with the creation of a single-element antenna. Figure 3 shows the proposed single-element antenna. This initial phase is marked by careful consideration of material selection, where graphene emerges as the preferred choice for the patch element. Positioned atop the substrate, graphene offers exceptional conductivity and mechanical robustness, setting the stage for optimal antenna performance. On the other hand, copper is chosen to serve as the grounding element and is positioned deliberately on the opposite side of the substrate. Precise dimensions are essential to achieve optimal signal transmission and attenuation reduction, with a thickness of 2 µm for the patch and ground elements and 11 µm for the substrate. Here’s the equation for how the size of the patch is calculated25.

Top and bottom view of the single-element antenna.

In the given context, the symbols used represent the following quantities: λ represents the wavelength, c represents the speed of light, ’f ’denotes frequency, \({\upvarepsilon }_{\text{r}}\) denotes a dielectric constant, the Effective Dielectric Constant is represented by \({\upvarepsilon }_{\text{eff}}\)

Several changes are made to the patch element to improve antenna performance even more. These consist of two insets on either side of the feedline, two 45-degree slots at the upper corners, and an I-shaped slot added in the middle. On top of the first slot, a V-shaped slot is also thoughtfully included. These carefully considered design changes are intended to enhance a number of antenna properties, including as radiation pattern, bandwidth, and impedance matching. To maximize antenna performance, comprehensive parametric analysis and refinement are carried out once design alterations are implemented. The finished size of the antenna is 75 by 75 µm, which will allow it to work with future 6G applications. The antenna is then simulated with CST software, allowing for a comprehensive assessment of its performance attributes. Through simulation, one can learn more about how the antenna behaves at different frequencies and operating situations, which is useful in validating the antenna’s appropriateness for practical uses.

The process of improving the single-element antenna involves a rigorous series of iterative design modifications with the goal of realizing its maximum potential for peak performance. The single-element antenna’s evolutionary path is seen in Fig. 4, which starts with its original design and progresses through several optimization stages. Every stage of the design process is illustrated, demonstrating how the antenna changes to satisfy the required requirements.

Evolutionary Progression of the Single Element Antenna Design.

Figure 5 presents the results corresponding to each phase in the development process mentioned in Fig. 4 where Fig. 5a illustrates the gain, and Fig. 5b displays the reflection coefficient Initially, the antenna design consists of carefully placed insets on either side of the feedline, together with a 45-degree rotating slot on top of each inset. With a bandwidth of 0.3 THz, this first design produces a single resonance frequency that operates at 8.35 THz. It also has a noteworthy maximum gain of 10.2 dBi. Building on these foundations, the second stage involves adding more design components and more improvements to the antenna. Among these is the addition of an I-shaped slot in the patch’s center, which is offset by a V-shaped slot that has been rotated 90 degrees at the patch’s peak. A dual resonance frequency response with frequencies centered at 6.2 THz and 7.2 THz and bandwidths of 0.32 THz and 0.295 THz, respectively, is the result of this iterative improvement. Over the corresponding frequency bands, the associated gains significantly improve to 7.9 dBi and 9.65 dBi, respectively.

Performance Metrics of Single Element Antenna Evolution: (a) Gain; (b) S11.

Even with these improvements, there’s still room for improvement, which means that the third stage of evolution will see further modifications. Two L-shaped slots are added to this design, and they are placed in the upper corners of the patch. With this tactical improvement, the resonance frequency profile becomes more varied and appears at three different frequencies: 6.48 THz, 7.47 THz, and 8.5 THz. Each frequency band is defined by a higher gain profile and a larger bandwidth. Maximum gains of 7.8, 10.2, and 12.3 dBi are attained across the appropriate frequency bands, indicating the highest level of intended antenna performance. The single-element antenna evolves throughout a rigorous sequence of design iterations, ultimately achieving the desired performance metrics through iterative improvements and smart design tweaks.

We thoroughly investigate how a number of significant parameters impact the antenna’s performance using parametric analysis, offering valuable insights into their individual functions and relationships within the design framework. By closely evaluating and varying these factors, we get significant insights into how properties such as substrate thickness, patch length, and slot width affect resonance frequency, bandwidth, return loss, and gain. By varying some of these characteristics while keeping others constant, we are able to gain a comprehensive understanding of their impact on the properties of the antenna. This enables us to choose optimization strategies and design decisions with knowledge.

We conducted a comprehensive parametric analysis in which we altered slot 1 width (s1w) while keeping the other parameters constant in order to examine the impact of this parameter on antenna performance. Our primary goal was to determine the relationship between slot dimensions and significant antenna characteristics, including as gain, bandwidth, return loss, and resonance frequencies. Figure 6a illustrates the gain and Fig. 6b the reflection coefficient for different values of slot 1 width (s1w). Resonance frequencies were shifted to 6.1 THz and 8.76 THz with increased bandwidths of 0.27 THz and 0.3 THz when the slot width was increased. But this also resulted in insufficient gains and return losses of 7.71 dBi and 9.64 dB, respectively, pointing to a decline in antenna efficiency. Conversely, reducing the slot width maintained the resonance frequencies at 6.1 THz and 8.67 THz but narrowed the bandwidths to 0.2 THz and 0.18 THz. While return loss improved slightly in the first band, it was still suboptimal in the second. The gains exhibited a different trend, increasing to 7.5i dB and 10.4 dBi. This analysis highlights the critical influence of slot 1 width on antenna performance, demonstrating how adjustments affect bandwidth, return loss, and gain. These findings underscore the importance of precise parameter optimization in antenna design, as changes in one element can significantly impact overall performance.

Impact of s1w variation on antenna performance (a) Gain; (b) Reflection Coefficient.

To thoroughly explore the impact of patch length (pl) on antenna performance, we embarked on a comprehensive parametric study, systematically varying this parameter while keeping all others constant. Figure 7a presents the gain, and Fig. 7b shows the reflection coefficient for different values of patch length (pl). Increasing the patch length from the proposed value resulted in the emergence of two resonance frequencies at 7.59 THz and 8.49 THz. While the bandwidth expanded to 0.29 THz and 0.36 THz for the respective bands, the corresponding return losses of 16.81 dB and 24.25 dB fell short of our desired thresholds. Additionally, the measured gains at these frequencies were recorded at 7.25 dBi and 8.64 dBi, respectively, indicating a compromise in antenna efficiency. On the other hand, an altered result was obtained by shortening the patch length. With a reduced patch length, there was just one resonance frequency observed, at 7.6 THz with a bandwidth of 0.37 THz. The gain of 7.64 dBi and the return loss of 21.67 dB, however, did not meet our targeted performance targets at this frequency. These findings highlight how crucial patch length is in influencing antenna behavior and how carefully it must be considered while enhancing antenna designs. Patch length has a complex relationship with antenna performance results; raising and decreasing the patch length has significant implications on resonance frequencies, bandwidth, return loss, and gain.

Impact of patch length variation on antenna performance (a) Gain; (b) Reflection Coefficient.

We investigate the effect of substrate thickness (st) on antenna performance in this section of the study. Substrate thickness, the fundamental element of antenna design, greatly affects key performance indicators including gain, bandwidth, return loss, and resonance frequencies. Our objective is to reveal the intricate relationship between st and antenna behavior through a methodical analysis, offering insights into its crucial role in optimizing antenna performance. Figure 8b displays the reflection coefficient for various values of substrate thickness (st), while Fig. 8a displays the gain. When “st” was increased from the suggested value, resonance frequencies changed noticeably. In particular, we detected the emergence of a single resonance frequency at 8.21 THz with a 0.34 THz bandwidth. Nevertheless, the configuration’s return loss was a disappointing -15 dB, much below our targeted thresholds. Concurrently, the measured gain—which was 9.4 dBi—did not live up to our expectations about performance. On the other hand, decreasing st produced different outcomes. While there was still just one resonance frequency at 6.2 THz, the bandwidth increased somewhat to 0.36 THz. Even with this slight increase in bandwidth, the return loss—which was measured at—25.42 dB—remained below optimum. In a similar vein, the measured gain of 7.64 dBi fell short of the targeted efficiency limits. These findings underscore the intricate relationship between substrate thickness and antenna performance. Whether increasing or decreasing st, we observe significant alterations in key parameters, emphasizing the critical role of st in shaping antenna behavior. This nuanced understanding highlights the importance of meticulous parameter optimization in achieving optimal antenna performance for real-world applications.

Impact of substrate thickness variation on antenna performance (a) Gain; (b) Reflection Coefficient.

In our quest for optimal antenna performance, we scrutinized the impact of different substrate materials on key performance metrics. Three distinct materials—silicon26, FR427, and polyimide28—were selected for assessment to discern their influence on antenna behavior. Figure 9a presents the gain, while Fig. 9b shows the reflection coefficient for different substrate of the antenna. Firstly, employing FR4 as the substrate material revealed intriguing results. Two resonance frequencies emerged at 6.75 THz, and 7.7 THz, accompanied by bandwidths of 0.33 THz, and 0.34 THz, respectively. However, despite the presence of multiple resonances, the return loss remained suboptimal across all bands, measuring 18 dB, and 14 dB, respectively. The corresponding gains were recorded at 9.94 dBi, and 10.5 dBi, underscoring the challenges encountered with FR4. Subsequently, we turned our attention to silicon as a potential substrate material. Despite the anticipation of favorable outcomes, the results proved disappointing. Four resonance frequencies were observed at 6.08 THz, 7.03 THz, 8.18 THz, and 8.78 THz. However, the bandwidths were alarmingly narrow, ranging from 0.1 THz to 0.14 THz. Moreover, the return loss figures, averaging around 20 dB, fell short of our expectations. The gains were modest, ranging from 7.5 dBi to 8.5 dBi across the four bands, indicating limited suitability for our antenna design. Lastly, polyamide emerged as a promising substrate material, offering compelling performance characteristics. Three resonance frequencies materialized at 6.48 THz, 7.47 THz, and 8.5 THz, accompanied by bandwidths of 0.32 THz, 0.29 THz, and 0.32 THz, respectively. Importantly, the return loss figures were notably superior, reaching −30.6 dB, −30.7 dB, and −36 dB in the respective bands. Correspondingly, the gains exhibited robust performance, ranging from 7.8 dBi to 12.3 dBi, reaffirming polyamide’s efficacy as the optimal substrate material for our proposed antenna design.

Performance of the antennas with different substrate materials (a) Gain; (b) Reflection Coefficient.

The MIMO antenna design originates from the optimization of a single-element antenna. This approach is used to elevate the antenna’s performance by targeting key improvements, including spatial diversity, interference mitigation, capacity enhancement, multipath exploitation, and enhanced security29. By leveraging the strengths of the single-element antenna, the MIMO configuration achieves superior overall performance30.

Determining the optimal MIMO antenna configuration is a critical step in achieving high-performance wireless communication systems. The orientation of antenna elements plays a pivotal role in this process, as it directly impacts factors such as signal reception quality, interference mitigation, and overall system capacity31. In this instance, Fig. 10 displays three different configurations, designated Ant. 1, Ant. 2, and Ant. 3, each of which provides a different orientation scheme. This thorough analysis seeks to clarify the optimal configuration that optimizes performance measures including gain, transmission coefficient, and reflection coefficient in different frequency ranges. The design procedure aims to fully utilize the capabilities of the MIMO antenna system by methodically examining various orientations, guaranteeing stability and dependability in a variety of communication contexts32.

Comparative Analysis of MIMO Antenna Configurations, (a) Ant 1; (b) Ant 2; (c) Ant 3.

In comparison to the first element, the two elements are orientated 180 degrees upside-down in the first configuration (Ant. 1). The two elements are positioned side by side in the second configuration (Ant. 2), with a 0-degree orientation with respect to the first member. Finally, the two elements are positioned side by side with a 180-degree orientation with respect to the first element in the third configuration (Ant. 3). The effects of each arrangement on variables like gain, reflection coefficient, and transmission coefficient are compared, as illustrated in Fig. 11a,b, and Fig. 11c, in that order. Initially, Antenna-1's performance is evaluated, revealing reflection coefficients of −38 dB, −20 dB, and −17 dB across three bands. However, the antenna exhibits low isolation (−18 dB) and relatively low gain (9.1dBi, 8.2dBi, and 10.2dBi) across these bands. Modifications are then made to enhance performance, resulting in the development of Antenna-2.

Comparative Analysis of Performance Across Three MIMO Antenna Configurations, (a) S11; (b) S21; (c) Gain.

Antenna-2 shows some improvement in reflection coefficient, with values of −25 dB, −46 dB, and −28 dB across the bands. However, isolation remains relatively low (−25 dB), and the gain sees only slight improvement compared to Antenna-1.

Antenna-3 was developed as a result of additional adjustments, and it shows significant performance gains. With notable advancements over Antenna-1 and Antenna-2, Antenna-3 stands out as the most promising option for a MIMO antenna design. Antenna-3 exhibits impressive performance in a number of critical measures after careful modifications to improve performance parameters.

Antenna-3 is a noteworthy improvement in terms of reflection coefficient, with values of −37.5 dB, −45 dB, and −60 dB in all three frequency bands. These numbers indicate lower energy reflection and improved signal-receiving capabilities. In addition, Antenna-3 shows notable improvements in isolation performance over Antenna-2, with remarkable values of −31.99 dB, −44 dB, and −45 dB recorded over the three frequency bands. Furthermore, Antenna-3 has better gain characteristics than any of its predecessors. Antenna-3 enables stronger and more dependable communication linkages by providing enhanced signal amplification capabilities with gains of 11.53 dBi, 11.38 dBi, and 13.53 dBi in each of the three frequency bands. Antenna-3 is the best option for the MIMO antenna design as a result of these combined performance improvements. Its success in achieving the intended design objectives, such as improved signal reception, interference reduction, and capacity enhancement, is highlighted by its superior performance in terms of reflection coefficient, isolation, and gain. Antenna-3 is the most practical option for meeting the demanding specifications of contemporary wireless communication systems since it is the result of iterative design revisions focused on attaining the highest levels of performance.

The amount of electromagnetic energy that is reflected back from an antenna as a result of impedance mismatches along its transmission line is measured by the reflection coefficient, which is commonly expressed in decibels (dB). Given that it directly affects the antenna’s performance and efficiency, it is an essential design parameter. Better impedance matching between the antenna and its feeding network is indicated by a lower reflection coefficient value, which leads to less power being reflected and more being radiated33. A reflection coefficient of −10 dB or less is generally regarded as appropriate.

Figure 12 shows the simulated Reflection Coefficient for the suggested MIMO antenna. When the planned microstrip patch antenna achieves 6.51 THz, 7.48 THz, and 8.46 THz with corresponding return loss values of −37.5 dB, −45 dB, and −60 dB, respectively, at the relevant resonant frequencies, the obtained values indicate excellent impedance matching. This implies that electromagnetic energy is efficiently absorbed and radiated by the antenna over a wide frequency range. Furthermore, the bandwidths of 0.7 THz, 0.69 THz, and 0.89 THz attained by the antenna demonstrate its adaptability and fit for applications needing a broad frequency range. Overall, the wide bandwidths and low return loss values show how well the developed microstrip patch antenna works for high-frequency sensing and communication applications.

Reflection Coefficient of the proposed MIMO antenna.

An antenna’s capacity to reduce unwanted coupling or interference between various antenna elements or ports is referred to as its isolation34. The transmission coefficient, which calculates the power transferred from one antenna port to another, is commonly used to quantify it35. Better separation between antenna elements and less mutual coupling are denoted by a greater isolation value, which is represented by a lower transmission coefficient36. The transmission coefficient for the recommended MIMO antenna is shown in Fig. 13. Strong performance in reducing mutual coupling between ports is demonstrated by the developed microstrip patch antenna, which achieved isolation of −31.99 dB, −44 dB, and −45 dB throughout the three frequency bands. In order to evaluate the antenna’s effectiveness in mitigating interference and maintaining signal integrity, the achieved isolation value is used, lower values indicate improved isolation and less cross-talk across ports.

Transmission Coefficient of the proposed MIMO antenna.

Gain is an important parameter in multiple-input multiple-output (MIMO) systems because it affects the communication system’s coverage and overall performance37. The ability of the antennas to concentrate radiation in a certain direction, so boosting the power of the broadcast or received signal in that direction, is referred to as antenna gain in a Multiple-Input Multiple-Output (MIMO) system38. The proposed MIMO antenna’s simulated gain is shown in Fig. 14. As seen in the figure, the antenna’s peak gain was 13.53 dBi, and it continuously outperformed 11 dBi over the whole range. This high gain number shows that the antennas can focus energy, either transmitted or received, in a specific direction. By doing so, the antennas can reduce interference from undesired signals that are coming from other directions. This helps improve the reliability and efficiency of communication systems in crowded or noisy environments.

Efficiency and Gain of the proposed MIMO antenna.

Efficiency on the other hand refers to its ability to convert input power into radiated electromagnetic energy effectively. It is a measure of how much of the input power supplied to the antenna is radiated as useful electromagnetic waves, compared to how much is lost as heat or dissipated in the antenna structure39. Figure 14 demonstrates that the antenna achieved a high efficiency of 99.91% consistently exceeding 96.5% throughout the range. This high value of efficiency indicates that the antenna contributes to better system performance by maximizing signal transmission or reception capabilities, leading to improved data rates, range, and reliability.

The Envelope Correlation Coefficient (ECC) is a metric used to assess the correlation between the envelope of signals received by multiple antennas in a MIMO (Multiple Input Multiple Output) system. It quantifies the similarity between the envelopes of the signals received by different antenna elements. Generally, ECC values close to zero are preferred as they suggest minimal correlation and maximum diversity gain40. The subsequent equation can calculate the value of ECC:

In the context of the presented MIMO antenna design, achieving an ECC of 0.00006 (as depicted in Fig. 15) indicates excellent spatial diversity and signal separation performance. This low ECC value signifies that the antennas in the MIMO array are effectively capturing distinct signal characteristics, enhancing the system’s ability to mitigate fading and improve overall reliability and capacity. Therefore, the observed ECC value underscores the effectiveness of the proposed MIMO antenna design for high-performance wireless communication applications.

ECC of the proposed MIMO antenna.

Diversity Gain (DG) in MIMO (Multiple Input Multiple Output) systems refers to the enhancement in signal quality obtained by utilizing multiple antenna elements to exploit spatial diversity. The value of DG is related to the value of ECC41. The subsequent equation can calculate the value of DG in a MIMO system:

The simulated DG value of 9.9997 for the proposed MIMO antenna, as shown in Fig. 16, signifies a substantial improvement in signal reliability and quality achieved through spatial diversity. Such a high DG value suggests that the MIMO antenna configuration effectively leverages spatial diversity to mitigate fading effects and enhance the robustness of the communication system. Overall, the obtained DG value exceeds typical standards for MIMO systems, demonstrating the effectiveness of the proposed antenna design in improving signal reliability and quality in challenging propagation environments.

DG of the proposed MIMO antenna.

The Channel Capacity Loss (CCL) is a vital metric used to assess MIMO antenna performance. Measuring the Channel Capacity Loss (CCL) provides an indication of how well a channel can transfer data or signals. A MIMO system’s channel capacity directly rises with the number of antenna elements in the system42. The correlation between the MIMO channels causes capacity losses. When there is a correlation, the Channel Capacity Loss, or CCL, is a crucial metric for estimating the MIMO channel capacity. Equation 8 can be utilized to compute it43.

Equation 9 can be utilized to calculate the two-port correlation matrix at the receiver.

The symbols (x) and (y) represent the coefficients for ports 1 and 2, respectively. The CCL standard recommends a value of less than 0.5 bps/Hz. Figure 17a shows the Channel Capacity Loss (CCL) of the suggested antenna. On average, a CCL of less than 0.4 bps/Hz is preferred. Simulated results validate that the suggested antenna’s Channel Capacity Loss (CCL) is less than 0.3 bits per second per Hertz (bps/Hz) over the whole operating frequency range.

(a) CCL & (b) TARC of Proposed MIMO Antenna.

Total Active Reflection Coefficient, or TARC, is an important measure for four-port antennas because it shows how transmitted and received power are related to one another44. This can be determined using Eq. 10.

An ideal Total Active Reflection Coefficient (TARC) for a Multiple-Input Multiple-Output (MIMO) antenna would be  < 0 dB45,46. The simulated outputs of TARC for the proposed antenna are displayed as < −15 dB, in Fig. 17b.

Antenna current distribution can change due to design, operating frequency, environmental conditions, and impedance matching, among other things. Antennas of various varieties, like dipoles, loops, and patches, display different current distributions47. The surface current distribution, consisting of only one element, reaches its maximum value of 33,945 A/m at a frequency of 5 THz. This is illustrated in Fig. 18a. The surface currents are strongest along the feedline and the upper section adjacent to the slots. One stimulated port, and matching loads at the other ports make up the MIMO antenna, as shown in Fig. 18b for the expected distribution of surface currents. No antenna in Fig. 18c shows a surface current unless we take Ant.1, activated by a surface current, out of the picture. The other antennas do not produce any surface current except for Antenna 2, as shown in Fig. 18c.

Surface Current (a) Single Element Antenna; (b) MIMO Antenna (port 1); (c) MIMO Antenna (port 2).

An antenna’s radiation pattern can be understood by considering both its electric field (E-field) and its magnetic field (H-field). Antenna polarization is a common partner for the electric field vector. Component of the electromagnetic wave, the H-field vector is perpendicular to the E-field vector48. Figure 19 displays the 2D radiation patterns that were simulated at 6.5 and 7.48 THz, respectively. At 6.5 THz, the main lobe magnitude at φ = 0 degree is 17 dBV/m in the E-field at the initial operating frequency, and the 3 dB angular beam width at φ = 90 degree is 34.10. According to H-field, the main lobe magnitude at φ = 0 degrees is −49.6 dBA/m, and the 3 dB angular beam width at φ = 90 degrees is 47.50 at 6.5 THz. In the E-field, at the second operating frequency, the prime lobe magnitude at φ = 0 degree is 16.7 dBV/m, and the 3 dB angular beam width at φ = 90 degree is 34.2∘ at 7.48 THz. Under the H-field condition, the main lobe magnitude at φ = 0 degree is −48.6 dBA/m, and the 3 dB angular beam width at φ = 90 degrees is 14.60 at 7.48 THz.

Simulated Radiation Pattern of recommended MIMO Antenna.

In our quest to advance antenna technology, we undertook an in-depth analysis of the antenna’s electromagnetic behavior through the formulation of an R-L-C (Resistance-Inductance-Capacitance) circuit model. The goal of this project was to clarify the intricate relationships between the electrical parts of the antenna structure so that its performance properties could be accurately represented. We carefully extracted the R-L-C characteristics from our antenna simulations using sophisticated simulation tools like CST Studio, guaranteeing accuracy in our circuit representation. Through circuit modeling in Agilent ADS, we were able to further improve our study and conduct a thorough analysis of the behavior of the antenna.49.

We disassembled the antenna construction into its basic electrical components and built a thorough circuit model in order to accurately depict it. A parallel circuit configuration consisting of resistance (R1), capacitance (C1), and inductance (L1), as well as a parallel circuit with R2, C2, and L2, contains the frequency, which is essential for antenna operation. Furthermore, the circuit model correctly depicted the antenna structure’s slots: a parallel circuit of C4 and L4 described the V-shaped slot at the top middle, while a series circuit of L3 and C3 defined the slot at the antenna’s center. A series circuit of C6 and L6 was used to simulate the slot on the right half of the antenna, while a series circuit of C5 and L5 was used to model the slot on the left.

The circuit model appropriately captured the electrical properties of the feedline, a crucial part of the antenna system, by including parameters like resistance (R3), capacitance (C12), and inductance (L9). These factors were essential in determining the antenna system’s overall impedance and transmission characteristics. Through the careful integration of these discrete circuit components, we were able to create a detailed model that accurately replicated the performance of our single element antenna. By utilizing a parallel circuit consisting of (L7 + C10) and (L8 + C11) in addition to an extra circuit with C7, C8, and C9, we were able to incorporate mutual impedance between antenna elements when we extended this model to a MIMO (Multiple Input Multiple Output) configuration. Figure 20, which illustrates the MIMO antenna’s equivalent circuit, shows how this configuration optimized performance evaluation by precisely capturing the interaction between multiple antenna parts. We verified the R-L-C circuit model’s equivalency to our antenna design by simulating it in Agilent ADS. To ensure the precision of the Agilent ADS simulation, a comparative analysis was performed by juxtaposing the outcomes of the CST simulation with the results of the parallel circuit simulation, explicitly focusing on the S11 parameter. Figure 21 illustrates a comparison between the results of the circuit simulation and the CST simulation, providing a thorough assessment of the accuracy and reliability of our R-L-C circuit model in representing the antenna’s behavior. All parameters of RLC are shown in Table 2

Equivalent Circuit of the Proposed MIMO antenna.

Reflection Coefficient Analysis: CST and Equivalent Circuits in ADS.

Machine learning is a highly successful tool for optimizing and predicting antenna performance, especially in antenna design and performance analysis. The objective is to optimize the parameters of the antenna to get the desired performance metrics, including gain, bandwidth, and radiation pattern. To meet specified performance objectives, machine learning can optimize characteristics such as antenna dimensions, feed placements, and material properties. Machine learning algorithms can utilize design characteristics to forecast antenna performance indicators, resulting in time savings compared to conventional simulation methods50.

The approach can be categorized into two main constituents, both of which will be elucidated in the following sections. Initially, it is important to create the MIMO antenna using CST, a simulation programmed. Subsequently, it is necessary to extract the dataset that was produced by doing a parametric sweep, as illustrated in Fig. 22. Currently, the initial phase will be completed. While analyzing the dataset, it is necessary to train a machine-learning model to determine the most effective technique for achieving optimal results51. To determine the gain of the proposed antenna, we begin by conducting a simulation using CST MWS. We then collected 105 data points and proceed to estimate the gain using a range of regression machine-learning approaches as shown in Fig. 23.

Data acquisition workflow for Machine Learning.

Schematic depicting the steps required to develop machine learning.

Supervised regression machine learning models forecast a continuous outcome variable by considering one or more predictor factors. The technique entails instructing a model using a dataset that has been labeled, meaning the outcomes are already known. Subsequently, the trained model is utilized to make predictions on fresh data.

Decision tree regression is a technique employed to forecast continuous values using input data collection. The process involves dividing the data into smaller groups depending on the values of specific features to reduce the variability within each group52.

Regression and classification applications both use the well-known and incredibly effective machine learning technique known as Extreme Gradient Boosting, or XGBoost. A machine-learning technique called XGBoost combines decision trees to create an ensemble model. It has become well-known and widely used in the area because to its effectiveness, capacity to handle large datasets, and competitive performance in machine learning competitions.53.

One popular ensemble learning strategy for regression applications is the Random Forest regression technique. By merging the forecasts of multiple distinct decision trees, it generates a prediction that is more dependable and precise (decision trees)54.

An ensemble learning technique known as "Extra Trees Regression," or "Extremely Randomized Trees Regression," involves building multiple decision trees and averaging their predictions. Although it is similar to Random Forests, its method of choosing splits during tree growth sets it apart. More unpredictability is prioritized by Extra Trees Regression than by Random Forests, which leads to a more efficient variance reduction and faster training periods55.

Gradient Boosting in Practice Regression is a powerful machine learning technique used to predict continuous data. The algorithm builds a series of weak prediction models, typically decision trees, one after the other. In order to minimize a predefined loss measure, each tree in the sequence that comes after it corrects the errors committed by the trees that came before it.56.

Regression models can be assessed for their ability to predict the target variable using a range of performance indicators. Every indicator offers a unique viewpoint on the model’s performance and measures several regions of prediction accuracy. The degree of agreement between the model’s predictions and the actual results is displayed in this visual analysis. Moreover, the accuracy and prediction power of the model may be quantitatively evaluated using statistical measures as R-squared (R2), Explained Variance Score, Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE).

The MAE is a commonly used statistic for assessing regression models due to its simple interpretation and user-friendliness. The average difference between the two sets of data is displayed to evaluate how well the model predicts future occurrences. A lower MAE number indicates better performance when comparing models or modifying hyperparameters.57.

Here is the given expression:

where, n = number of errors \(\left|{y}_{i}- {\widehat{y}}_{i}\right|\) = error absolute.

Mean Squared Error (MSE) is a commonly employed statistic in the assessment of regression models. Smaller numbers indicate that the model is performing better. The average squared deviation between the actual and projected values is assessed. Outliers are more noticeable because MSE squares the errors, which causes its units to differ from the target variable’s initial units.58.

When evaluating regression models, the Root Mean Squared Error (RMSE) is a commonly used statistic that measures the average magnitude of errors in the same units as the target variable. Higher values of the RMSE indicate better model performance, but it’s important to compare it to other models or benchmarks and interpret it within the context of the specific issue area.59.

R-squared (R2) is a useful metric for evaluating how well regression models fit the data. It provides insight into how much of the variance in the dependent variable may be attributed to the independent factors. However, in order to properly analyze the model’s overall performance, R-squared must be used in conjunction with other assessment metrics and domain expertise60.

"Explained Variance Score" is a numerical metric used to evaluate regression models’ performance. The metric measures how much of the target variable’s variability the model can explain. It gauges how well the model captures the range of values found in the dependent variable61.

Table 3 describes the advantages of several regression techniques, such as decision tree regression, XGB Regression, extra tree regression, random forest, and gradient boosting regression. Furthermore, Fig. 24 utilizes a bar chart to depict the comparative performance of these models. These metrics include R-squared, variance score, mean squared error (MSE), mean root-mean-square error (RMSE), and mean absolute error (MAE). The gradient-boosting regression model, on the other hand, stands out because it displays minor disparities in terms of Mean Absolute Error (MAE) (4.94%), Mean Squared Error (MSE) (6.60%), and Root Mean Square Error (RMSE) (4.13%). The accuracy of the variance score is reported to be 98.47%, and the R-squared value is discovered to be 98.42% when applied to the context of gradient-boosting regression.

Performance Comparative Bar Chart.

Figure 25 shows the predicted and simulated isolation for twenty test samples run using Gradient Boosting Regression. We altered the isolation for the study from −10 dB to −40 dB. Table 4 shows a little difference between the expected and simulated benefits for gradient boosting regression. Figure 25 shows that the predicted result and the results of the simulation are very similar. The remarkable skill of this ML model in predicting future benefits led to its selection: gradient boosting regression.

Simulated vs. Predicted isolation Using Gradient boost Regression.

The proposed THz MIMO antenna exhibits excellent simulated performance; however, practical limitations and scalability challenges must be considered for real-world deployment.

Fabricating THz antennas requires precision techniques like photolithography or 3D printing due to the small dimensions involved. These methods are costly and not widely available. Emerging fabrication technologies, such as nanoscale manufacturing, can help address this limitation while maintaining performance accuracy.

Measuring THz antennas demands specialized equipment like THz vector network analyzers and anechoic chambers, which are limited globally. To address this, the antenna performance was validated through CST and ADS simulations, along with machine learning techniques, providing reliable and comparable results.

THz signals suffer high atmospheric attenuation, limiting their range. This makes the antenna more suitable for short-range applications. Future solutions, such as beamforming and adaptive arrays, can help mitigate these issues and enhance robustness.

Scaling the design for large MIMO systems introduces challenges like increased mutual coupling and spatial constraints. While the anti-parallel arrangement achieves high isolation, advanced techniques like defected ground structures or decoupling networks can be explored for massive MIMO integration.

This article introduces a high-performance THz MIMO antenna and details the integration of simulation, the development of the RLC equivalent circuit model, and the application of machine learning techniques to assess the antenna’s performance. It highlights the use of Graphene for the patch and copper for the ground element, resulting in significant performance enhancements, a 13.1 dBi gain, isolation better than −31 dB across the entire operating band, efficiency over 96%, ECC below 0.0005 dB, and DG exceeding 9.99 dB. Additionally, the CST-simulated antenna design and the RLC equivalent circuit model, both created with ADS Agilent, show similar results. Machine learning techniques have been employed to estimate isolation, with Gradient Boosting Regression outperforming other models. It achieved an impressive R-squared value of 98.42%, a variance score of 98.47%, a mean absolute error (MAE) of 4.94%, and a root mean squared error (RMSE) of 4.13%. Future work will involve collecting extensive data samples and using deep learning models like ANN and CNN to further improve results. The proposed MIMO antenna has been successfully validated for Terahertz (THz) frequency band applications in Wireless Communication and the Internet of Things (IoT), based on simulations, the RLC equivalent circuit, and projected outcomes.

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

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This research was supported by Princess Nourah bint Abdulrahman University, Researchers Supporting Project number (PNURSP2025R51), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. The authors would also like to thanks Prince Sultan University for their valuable support.

This research was funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2025R51), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

Department of Electrical and Electronic Engineering, Daffodil International University, Dhaka, 1207, Bangladesh

Md Ashraful Haque, Kamal Hossain Nahin, Jamal Hossain Nirob & Md. Kawsar Ahmed

Faculty of Data Science and Information Technology, INTI International University, Persiaran Perdana BBN, Putra Nilai, 71800, Nilai, Negeri Sembilan, Malaysia

Narinderjit Singh Sawaran Singh

Department of Electrical, Electronic and Communication Engineering, Pabna University of Science and Technology, Pabna, Bangladesh

Liton Chandra Paul

Department of Information Technology, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, 11671, Riyadh, Saudi Arabia

Abeer D. Algarni

EIAS Data Science Lab, College of Computer and Information Sciences, Prince Sultan University, 11586, Riyadh, Saudi Arabia

Mohammed ElAffendi, Ahmed A. Abd El-Latif & Abdelhamied A. Ateya

Department of Electronics and Communications Engineering, Zagazig University, Zagazig, 44519, Egypt

Abdelhamied A. Ateya

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M.A.H: Methodology, Investigation, Conceptualization. K.H.N: Writing—original draft, review & editing, Software, Conceptualization. J.H.N: Writing—original draft, review & editing, Formal analysis, Conceptualization. M.K.A: Methodology, Validation, Investigation. N.S.S.S: Resources, Investigation. L.C.P: Writing—review & editing, Resources. A.D.A: Validation, Funding acquisition. M.E: Validation, Visualization. A.A.A.E.L: Writing—review & editing. A.A.A: Supervision, Project administration.

Correspondence to Abdelhamied A. Ateya.

The authors declare no competing interests.

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Haque, M.A., Nahin, K.H., Nirob, J.H. et al. Multiband THz MIMO antenna with regression machine learning techniques for isolation prediction in IoT applications. Sci Rep 15, 7701 (2025). https://doi.org/10.1038/s41598-025-89962-6

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Received: 13 August 2024

Accepted: 10 February 2025

Published: 05 March 2025

DOI: https://doi.org/10.1038/s41598-025-89962-6

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