Mutual Coupling in the Antennas

Abstract

Mutual coupling refers to the intricate interaction among discrete antenna elements within an array, often causing interference and leading to the deterioration of critical performance parameters. This degradation includes reduced gain, increased side lobe levels, and distorted radiation patterns, significantly impacting the overall system’s capabilities and coverage. With the increasing demand for higher data rates and capacity in next-generation wireless communication systems, such as 5G and the emerging 6G, array antennas are essential for enabling beamforming and spatial multiplexing. However, mutual coupling among antenna elements presents a substantial challenge, affecting the efficiency and effectiveness of these systems. This chapter furnishes a comprehensive exposition on the multifaceted challenges posed by mutual coupling in the domain of array antennas. Furthermore, it undertakes a systematic examination of diverse techniques and strategies meticulously devised to ameliorate the adverse ramifications. In addition, this work undertakes an exhaustive analysis to discern the far-reaching influence of mutual coupling on critical performance metrics, encompassing radiation patterns, efficiency, and channel capacity, all in the context of the dynamic landscape of next-generation wireless communication systems epitomized by 5G and the forthcoming 6G.

1. Introduction

Mutual coupling in the context of antennas presents a substantial and pressing concern within the realm of 5G and 6G wireless communication systems. In light of the profound aspirations of these forthcoming networks, aimed at provisioning elevated data rates, augmented capacity, and enhanced connectivity, the performance of antennas assumes paramount significance. Mutual coupling specifically denotes the interaction that transpires between adjacent antennas arranged within an array configuration, invariably precipitating unwelcome repercussions. These repercussions encompass a distortion of radiation patterns, a diminution in antenna efficiency, and a compromise in channel capacity. In the specific framework of 5G and 6G applications, where the deployment of multiple antennas is indispensable for the realization of advanced techniques such as beamforming and spatial multiplexing, the adversarial influence of mutual coupling looms large over the collective system performance. Notably, it engenders interference among antenna elements, thereby inducing perturbations in the desired directionality of radiation patterns. This, in turn, leads to a dissipation of signal strength, an augmentation of interference, and a curtailment of the extant coverage. Moreover, mutual coupling’s impact reverberates within the realm of antenna efficiency by virtue of the alterations it imposes upon impedance characteristics. The ramifications include power dissipation, a curtailment in signal quality, and an overarching diminution in system efficiency. In addition to these facets, the specter of mutual coupling extends its reach into the arena of channel capacity, effectively introducing correlations among antenna elements. These correlations curtail the system’s ability to concurrently transmit and receive independent data streams. In response to these formidable challenges, rigorous research and development initiatives have been spearheaded to ameliorate the effects of mutual coupling within the domain of 5G and 6G antenna systems. Diverse methodologies, including decoupling structures, optimization of antenna element spacing, and the employment of sophisticated signal processing algorithms, are being meticulously examined and advanced. These endeavors collectively strive to abate mutual coupling’s influence and bolster the performance metrics of the forthcoming generation of wireless communication systems.

2. Unraveling the enigma of wireless interference

In the domain of wireless communication, where rapid data transmission and uninterrupted connectivity have become essential, optimizing antenna performance assumes a central role. Among the factors impacting antenna performance, mutual coupling stands as a significant and intricate phenomenon profoundly influencing the quality of wireless signals. A comprehensive grasp of mutual coupling intricacies becomes parab mount for the effective design of radio frequency (RF) systems, particularly within the context of advanced technologies such as 5G and the forthcoming 6G. Mutual coupling, aptly named, denotes the interaction between two or more closely situated antennas, where one antenna’s performance is affected by the presence of its neighboring antennas. This interaction engenders a spectrum of challenges, including reductions in antenna gain, increased side lobes, distorted radiation patterns, and compromised link quality. Thus, understanding mutual coupling intricacies proves pivotal in ensuring the reliability of wireless communication. Notably, array antenna configurations, widely employed in wireless systems, exhibit heightened susceptibility to mutual coupling. Array antennas offer enhanced directivity and gain through the manipulation of constructive and destructive interference between individual radiating elements. However, their close proximity can induce mutual coupling, leading to undesired consequences. In the context of 5G, where array antenna technology forms the cornerstone of massive multiple-input multiple-output (MIMO) systems, the understanding of mutual coupling takes on heightened importance. To maximize system capacity and spectral efficiency, 5G systems leverage the simultaneous transmission and reception of multiple data streams via a multitude of antennas. Nevertheless, mutual coupling can distort signals, precipitating interference and compromising overall system performance. As the research endeavors for the next-generation wireless technology, 6G, continue to evolve, the issue of mutual coupling assumes even greater prominence. With the aspiration of achieving higher data rates, ultra-low-latency communication, and pervasive connectivity, 6G seeks to redefine the boundaries of wireless communication. However, to realize these ambitious objectives, the challenges posed by mutual coupling must be systematically addressed.

In wireless communication, optimizing antenna performance is crucial for rapid data transmission and uninterrupted connectivity. Mutual coupling, the interaction between closely situated antennas, significantly influences wireless signal quality, especially in advanced technologies like 5G and the upcoming 6G. Array antennas, common in wireless systems, are particularly susceptible to mutual coupling, affecting their directivity and gain. Managing mutual coupling requires a multifaceted approach, including decoupling techniques (passive and active), antenna design optimization, and simulation tools. By addressing mutual coupling, engineers can enhance wireless communication reliability and performance, which is crucial for advancing technologies like 5G and 6G. A schematic illustration in Figure 1 depicts the mutual coupling phenomenon influenced by neighboring antennas’ radiation. Impedance mismatch resulting from mutual coupling can lead to scan blindness or total reflection [1, 2, 3]. In certain extreme scenarios, the impedance mismatch can lead to total reflection, characterized by a reflection coefficient (|Γ|) equal to 1.

Figure 1.

Mutual coupling phenomenon.

Mutual coupling significantly affects the radiation properties of individual elements in an array, altering their radiation patterns and characteristics due to electromagnetic field interactions with neighboring elements. This phenomenon induces various effects:

Beam Steering and Shaping: Neighboring elements influence the direction and configuration of energy beams, altering the beam’s directionality by modifying the effective electrical length of radiating elements.

Gain and Efficiency Adjustment: Mutual coupling influences the gain and efficiency of individual elements, leading to variations in overall array gain due to changes in radiation efficiency.

Side Lobes and Nulls: Mutual coupling introduces undesired side lobes and nulls in radiation patterns due to constructive and destructive interference between proximate elements.

Impedance Matching: Mutual coupling can cause significant impedance mismatch, affecting the input impedance of radiating elements and impacting power transfer efficiency and radiation properties. Understanding and mitigating mutual coupling effects are crucial for achieving desired array characteristics. Various techniques are available for approximating mutual coupling effects in planar antenna arrays:

During initial design phases, mutual coupling influence may be disregarded, but this can lead to unexpected performance degradation and is unsuitable for manufacturing-ready designs.

Comprehensive simulation of the entire array structure considers practical constraints like mutual coupling using methods such as finite element analysis (FEM) or finite difference time domain (FDTD). However, it becomes computationally intensive for larger arrays.

Infinite Array Simulation approach simulates a single antenna element within an infinite array using periodic boundary conditions. It incorporates mutual coupling effects through Floquet modes but may have limitations in modeling nonuniform or sparse arrays and (ultra)wideband scenarios. It is essential to recognize these methodologies’ strengths and limitations to effectively model mutual coupling in antenna array design.

3. Theory of antenna mutual coupling reduction

Arrays have historically been viewed as non-interacting, perfectly matched entities with the feed network. However, in practical settings, interactions among array elements result in mutual coupling, impacting currents, impedances, and element distribution, thus altering the array pattern. This section explores the effects of mutual coupling on impedance and pattern, discussing methodologies for assessing array element impedance and pattern while considering mutual coupling. Hannan’s foundational work [4] provides terminology guidance, although alternative terms exist. Passive arrays use a single generator followed by power dividers and phase adjustment devices, while active arrays employ a separate generator for each element, a more common model. The impedance of an isolated element is termed isolated or antenna impedance, while in the array environment with all elements active, it’s called active or driving impedance. Measuring active impedance requires full array activation, often achieved through simulation. Element impedance is typically characterized by exciting one element while terminating others passively, usually with a reference load like 50 Ω. Passive impedance closely approximates active impedance due to similar coupling and termination conditions, so “active impedance” often substitutes “passive impedance.” For fully active arrays, the term “active impedance in a fully active array” distinguishes cases involving full array activation.

3.1 Impedance impact of mutual coupling

The influence of mutual coupling on impedance manifests through three principal mechanisms, illustrated in Figure 2a. The first mechanism involves direct space coupling between the elements within the array, where the proximity of elements results in mutual influence. The second mechanism, indirect coupling, arises from scattering effects induced by nearby objects, such as a support tower. Lastly, the feed network connecting the elements in the array acts as a conduit for coupling. In practical array configurations, measures are taken to mitigate feed network coupling by ensuring proper impedance matching at each individual element. This approach allows the treatment of each element as independent generators, as depicted in Figure 2b. In this representation, the mth element is characterized by an applied generator voltage ($V_m^g$) and terminal impedance ($Z_m^g$). It is crucial to note that the voltage ($V_m$) and current ($I_m$) at the element terminals encompass all the effects of coupling. For the analysis of an array comprising N elements, conventional circuit analysis is employed, treating the array as an N-port network. This methodology facilitates a comprehensive exploration of the impedance effects stemming from mutual coupling, providing valuable insights for both array design and performance evaluation:

Figure 2.

Mutual coupling in a fully excited array antenna. (a) Mechanisms for coupling between elements of an array. (b) Model for mth element in an array.

$$\begin{array}{c}{V}_1=Z_{11}{I}_1+Z_{12}{I}_2+\dots +Z_{1N}{I}_N\\ V_2=Z_{12}{I}_1+Z_{22}{I}_2+\dots +Z_{2N}{I}_N\\ ⋮\\ V_N=Z_{1N}{I}_1+Z_{2N}{I}_2+\dots +Z_{\mathit{NN}}{I}_N\end{array}$$E1

In the examination of array antennas, the delineation of mutual impedance proves to be a pivotal aspect. The impressed current ($I_n$) and voltage ($V_n$) in the nth element, alongside the self-impedance ($Z_{\mathit{nn}}$), when all other elements remain open-circuited, assume a substantial role in this analysis. Additionally, the mutual impedance between the two terminal pairs of elements, denoted as $Z_{\mathit{mn}}$ (equivalently $Z_{\mathit{nm}}$ due to reciprocity), encapsulates crucial information. To establish the definition of mutual impedance, one must consider a scenario where the initial terminal pair is open-circuited, with the remaining terminals similarly open-circuited. In this prescribed configuration, the mutual impedance $Z_{\mathit{nm}}$ is derived by dividing the open-circuit voltage generated at the first terminal pair by the current supplied to the second terminal pair. This formulation facilitates an accurate characterization of the interaction among individual elements within the array, systematically considering the effects induced by mutual coupling. A comprehensive understanding of mutual impedance equips designers with valuable insights into the array’s behavior and performance, thereby facilitating the optimization of its design and radiation properties:

$${\left.Z_{\mathit{mn}}=\frac{V_m}{I_n}\right|}_{I_{i=0}\mathit{\text{for}}\mathit{all}i\mathit{\text{except}}i=n}$$E2

The precise calculation or measurement of mutual impedance between antenna elements poses a considerable challenge. However, the advent of commercial simulation codes grounded in moment methods has significantly streamlined the evaluation of mutual impedance values, particularly in the context of wire antennas. These simulation tools offer a convenient means of acquiring reliable results. In measuring mutual impedance between two antennas, a general approach is adopted, extendable to determine mutual impedance between any two elements within an arbitrary array, denoted as $Z_{\mathit{mn}}$. The specific methodology employed for measuring mutual impedance may vary based on the type of antennas and the experimental setup in use. Leveraging simulation tools and refined measurement techniques enhances the feasibility of determining mutual impedance. This capability provides antenna designers and engineers with invaluable insights into the intricate interactions and coupling effects prevalent among antenna elements.

This knowledge holds paramount importance for the optimization and enhancement of performance in antenna arrays. When an antenna operates in isolation within free space, characterized by a voltage $V_1$​ and a current $I_1$​, the input impedance is a critical parameter to consider for effective system design and integration:

$$Z_{11}=\frac{V_1}{I_1}\mathit{\text{single isolated element}}$$E3

When a secondary antenna is introduced in close proximity to the first, the radiated electromagnetic field from the initial antenna induces currents within the second antenna. Consequently, the second antenna reciprocates by emitting radiation, and this emitted radiation influences the current distribution on the original antenna. The second antenna may be either actively excited or remain unexcited, functioning in a parasitic manner. In either scenario, the second antenna sustains a terminal current denoted as $I_2$. Subsequently, the aggregate voltage at the terminals of the first antenna is influenced by this induced current. This interaction highlights the intricate coupling effects that arise when multiple antennas operate in close quarters. Understanding these effects is crucial for designing antenna systems that operate efficiently and predictably, especially when considering scenarios involving mutual coupling and electromagnetic interference

$$V_1=Z_{11}{I}_1+Z_{12}{I}_2$$E4

Similarly, the voltage at the terminals of the second antenna is expressed by

$$V_2=Z_{21}{I}_1+Z_{22}{I}_2$$E5

Note that (1) is a generalization of (4) and (5). Now, suppose the second antenna has a load impedance $Z_2^g$ across its terminals $\left(V_2^g=0\right)$such that $V_2=-Z_2^g{I}_2$. We can write (5) as

$$-Z_2^g=Z_{21}{I}_1+Z_{22}{I}_2$$E6

Solving for $I_2$ and using $Z_{21}=Z_{12}$, we obtain

$$I_2=\frac{-Z_{21}{I}_1}{Z_{22}+Z_2^g}=\frac{-Z_{12}{I}_1}{Z_{22}+Z_2^g}$$E7

Substituting this into (4) and dividing by $I_1$, we find that

$$\frac{V_1}{V_1}=Z_1=Z_{11}-\frac{{\left(Z_{12}\right)}^2}{Z_{22}+Z_2^g}$$E8

The input impedance of the system can be effectively described by incorporating self-impedances ($Z_{11}$ and $Z_{22}$), (mutual impedance $Z_{12}$), and the load impedance $Z_2^g$ at the unexcited terminals of antenna 2. In light of the preceding discussion, a schematic representation akin to Figure 3 emerges as an apt equivalent circuit for delineating the coupling dynamics between two resonant antennas. In scenarios where a single antenna operates in isolation, with antenna 2 positioned at a substantial distance, the mutual impedance $Z_{12}$ diminishes to zero $Z_{12}=0$Consequently, Eq. (8) simplifies the input impedance to the self-impedance of antenna 1, resulting in $Z_1=Z_{11}$​. Conversely, when antenna 2 is open-circuited in $Z_2^g=\infty$, Eq. (8) indicates $Z_1=Z_{\mathit{oc}}=Z_{11}$​. The act of open-circuiting antenna 2 leads to a cessation of current along its length, a scenario particularly applicable to certain antenna types like half-wave dipoles, where open-circuiting annuls their resonant behavior. However, some antenna types, such as full-wave dipoles, may still exhibit induced current despite being open-circuited, warranting the removal of the second antenna.

Figure 3.

Network representation of the coupling between two antennas.

To analyze the impedance characteristics comprehensively:

1. Open-circuit (or remove) antenna 2 and measure the open-circuit impedance $Z_{\mathit{oc}}=Z_{11}$ at the terminals connected to antenna 1. In cases involving identical antennas, $Z_{22}$ is equivalent to $Z_{11}$

2. Short-circuit antenna 2 and measure the short-circuit impedance $Z_{\mathit{sc}}$​ at the terminals connected to antenna 1.

3. Utilize the obtained values to calculate the mutual impedance $Z_{12}$​.

4. This systematic approach facilitates a thorough understanding of the coupling effects between resonant antennas, enabling precise impedance characterization for effective antenna design and performance optimization:

$$Z_{12}=\sqrt{Z_{\mathit{OC}}\left(Z_{\mathit{OC}}-Z_{\mathit{SC}}\right)}$$E9

The derivation of mutual impedance, as an extension of Eq. (3) with $Z_2^g=0$, involves the introduction of a generator at the input of one antenna. This process entails determining the voltage at the input terminals of the second antenna, followed by the calculation of the voltage-to-current ratio. Scattering parameters emerge as a widely embraced and favored tool due to their direct correlation with measurements, allowing for facile acquisition through network analyzers. The diagonal elements within the scattering matrix align with the reflection coefficients at each port, thereby furnishing valuable insights into the reflected waves at individual ports:

$$S_{\mathit{nm}}={\mathrm{\Gamma }}_m$$E10

In tandem with the impedance matrix, the scattering matrix manifests symmetry in the context of a reciprocal device, signifying that the entry $S_{\mathit{nm}}$ is equivalent to $S_{\mathit{nm}}$​. The non-diagonal components within the scattering matrix furnish essential details pertaining to the coupling between diverse ports. To quantitatively express the coupling between ports m and n in decibels (dB), we introduce $C_{\mathit{mn}}$ as follows:

$$C_{\mathit{mn}}=20log\left|S_{\mathit{mn}}\right|\left[\mathit{dB}\right]$$E11

The entries of the scattering matrix are derived from the impedance matrix, denoted as $Z_{\mathit{mn}}$. Consider a two-element array where the elements are interconnected by transmission lines with a characteristic impedance of $Z_O$​. For the first element of the array, the scattering matrix entries are given by:

$$S_{11}=\frac{\left(Z_{11}-Z_0\right)\left(Z_{22}+Z_0\right)-Z_{12}^2}{\left(Z_{11}-Z_0\right)\left(Z_{22}+Z_0\right)-Z_{12}^2}$$E12

$$S_{12}=\frac{2Z_0{Z}_{12}}{\left(Z_{11}-Z_0\right)\left(Z_{22}+Z_0\right)-Z_{12}^2}$$E13

The validity of these equations can be confirmed through straightforward checks. In the absence of mutual coupling ($Z_{12}=0$), Eq. (12) simplifies to $S_{11}={\mathrm{\Gamma }}_1=\left(Z_{11}-Z_O\right)/\left(Z_{11}+Z_O\right)$​​, which aligns with the conventional formula for the one-port reflection coefficient. Similarly, when there is no mutual coupling, Eq. (13) yields $S_{12}=0$, as expected.

Now, it becomes feasible to compute the input impedance of an element in the array using mutual impedance values. For the $m$th element, the input impedance $Z_m$can be determined using Eq. (1):

$$Z_m=\frac{V_m}{I_m}=Z_{m1}\frac{I_1}{I_m}+Z_{m2}\frac{I_2}{I_m}+\dots +Z_{\mathit{mN}}\frac{I_N}{I_m}$$E14

The representation of the input impedance, encompassing all constituent elements, denotes the active impedance within a fully excited array. This inclusive characterization takes into consideration the collective influence of coupling effects, wherein mutual impedances are acquired through numerical simulations or measurements employing Eq. (9). The formula explicitly elucidates that the input impedance is shaped not only by the mutual impedances but also by the terminal currents of each individual element. It is essential to underscore that the phase of the terminal currents, meticulously adjusted for pattern scanning, exerts a substantial influence on the input impedance. Consequently, the input impedance of all elements within an array undergoes alterations as the scan angle is adjusted. This dynamic interplay between mutual impedances, terminal currents, and phase adjustments underscores the complexity of the input impedance landscape in array antennas. Understanding these nuances is pivotal for antenna designers and engineers aiming to optimize the performance of array configurations. The intricate relationship between input impedance and scan angle adjustments necessitates a nuanced approach to antenna array design, ensuring adaptability and reliability across a range of operational scenarios.

3.2 Evaluating array pattern with mutual coupling considerations

The examination of mutual coupling’s influence on the radiation characteristics of an array constitutes a crucial facet discussed in this section. While a thorough analysis involving simulations or measurements of individual embedded element antennas can provide a comprehensive array characterization, such an approach is often time-intensive and infrequently employed. In lieu of this, approximate techniques are commonly adopted to encompass the effects of mutual coupling, a methodology we shall delineate. Various approaches exist for modeling arrays, ranging from explicit consideration of all mutual impedances to integrating coupling effects into the isolated-element pattern through current adjustments or into the element pattern using the active-element pattern approach. In this discourse, we espouse the active-element pattern approach.

Within the active-element pattern approach, the total array pattern integrates all coupling effects by adapting the excitations of individual elements. This methodology streamlines the analysis, offering a pragmatic balance between accuracy and computational efficiency in studying the impact of mutual coupling on the radiation characteristics of antenna arrays:

$$F_{\mathit{un}}\left(\theta .\varphi \right)=g_i\left(\theta .\varphi \right)\sum _{m=1}^N{I}_m{e}^{\mathit{j\xi m}}$$E15

In the given context, ${\xi }_m$​ represents the cumulative phase contribution, typically referenced to the center of the array, resulting from spatial phase delay. In the absence of coupling effects, the currents $I_m$ vary proportionally with the excitation voltages:

$$I_m=\frac{V_m^g}{Z_m^g+Z_m}$$E16

This phenomenon is commonly referred to as “unconstrained excitation” because the voltage at the element terminals varies with the scan angle. Instead of using a constant-voltage feed, a constant-incident power feed is employed. For an infinite array composed of identical elements arranged in a uniform grid, where all elements experience the same mutual coupling, each element is exposed to an identical environment. This implies that the active impedances are uniform across all elements, resulting in all $\left\{Z_m\right\}$ being equal to $Z_A$​:

$$I_m=\frac{V_m^g}{Z^g+Z_A}\infty V_m$$E17

This scenario is applicable to large arrays with equal spacing between elements. However, for finite arrays, the conventional implementation of Eq. (15) involves approximating Eq. (17). This approximation neglects variations in terminal currents caused by mutual coupling and only considers variations in the generator voltage. Obtaining accurate current information for evaluating Eq. (15) is challenging, leading to the common usage of the active-element pattern method, which is discussed in the subsequent sections. In the active-element pattern approach, all coupling effects are taken into account through the active element. The active-element pattern $g_{\mathit{ae}}^n\left(\theta .\varphi \right)$ is obtained by exciting only the $n$th element while loading all other elements with the generator impedance $Z^g$. The active-element pattern results from the direct radiation of the $n$th element combined with the fields reradiated from other elements, which receive their power through spatial coupling from element $n$. The formulation of the array pattern in this context is as follows:

$$F_{\mathit{un}}\left(\theta .\varphi \right)=\sum _{n=1}^N{g}_{\mathit{ae}}^n\left(\theta .\varphi \right)I_n{e}^{\mathit{j\xi n}}$$E18

The provided text discusses the correlation between currents and excitation voltages in an array, integrating mutual coupling effects into the active-element patterns. To accommodate potential gain variations, the levels of active-element patterns are referenced to a central element within the array. Although measuring active-element patterns for each array element could be time-intensive, it is often unnecessary. In the context of a large array with uniform elements and equal spacing, each element encounters a similar environment with its nearest neighbors, excluding edge elements. Hence, it is customary to approximate the factorization of the active-element pattern using an average pattern denoted as $g_{\mathit{ae}}^n\left(\theta .\varphi \right)$, representing the normalized pattern for a typical central element in the array:

$$F_{\mathit{un}}\left(\theta .\varphi \right)=g_{\mathit{ae}}\left(\theta .\varphi \right)\sum _{n=1}^N{I}_n{e}^{\mathit{j\xi n}}$$E19

The notable advantage of this approach lies in its utilization of the summation within the equation, based on the array factor derived from basic theory, independent of mutual coupling considerations. Furthermore, all coupling phenomena are encompassed within the average active-element pattern, determinable through a single measurement of the pattern exhibited by a central element within an extensive array.

Within the domain of mathematical approximations, the normalized rendition of Eq. (19) yields a crucial and noteworthy outcome:

$$F\left(\theta .\varphi \right)=g_{\mathit{ae}}\left(\theta .\varphi \right)f\left(\theta .\varphi \right)$$E20

Undoubtedly, this formulation adopts a semblance to the pattern multiplication formula, denoted as Formula (20), yet intricately interwoven within it are the ramifications of mutual coupling. This approximation is frequently employed in practical applications. The average pattern of the active element assumes a pivotal role in the construction of arrays. Prior to the creation and testing of the grand array, replete with active elements, the pattern of an individual active element surrounded by passive elements undergoes measurement and evaluation. If the pattern of the active element proves to be irregular, so too will be the grand array. It has been demonstrated that the active input impedance can be deduced from the data of the active-element pattern [5]. The pattern of the isolated element differs from those of the active elements within the array. However, in an array of sufficient magnitude, the average pattern of the elements represents the majority of the active-element patterns within the array. The question of how extensive an array must be before (20) can be applied holds great significance and is addressed through guidelines and examples. As the size of the array increases in magnitude (ideally, an infinite multitude of elements), the active-element patterns of individual elements tend toward becoming identical and aligned with the average pattern of the active element. Elements near the borders of a finite array bear patterns that deviate from the pattern of the central elements, which should closely adhere to the average-element pattern. This is evident in the patterns depicted in Figure 4, illustrating the active-element patterns of each element in an array of eight microstrip patch antennas spaced apart by 0.57λ. The polar -dB patterns displayed for selected elements were measured while that element was excited and all others inactive. The patterns of elements 2 through 7 (only pattern 5 is shown) are nearly indistinguishable and symmetrical. The patterns of the edge elements ((1) and (8)) are distorted owing to the asymmetrical environment of the array and the finite effects of the ground plane’s borders. Note that the greatest distortion in the patterns occurs on the side away from the array. Similar findings have been reported concerning dipoles above a ground plane.

Figure 4.

Measured active-element patterns for three elements, an interior element (5) and the end elements ((1) and (8)), of a linear array of eight microstrip patch elements spaced 0:57lapart.

The overarching pattern of the array undergoes perturbation due to the inherent coupling within. Arrays are crafted with excitation voltages tailored to our specifications and modeled with voltage generators. In the absence of coupling, the currents at the terminals maintain proportionality to the excitation voltage, and the desired pattern emerges, as implied by Formula (17). However, when coupling emerges, the pattern undergoes deformation. It often occurs that the terminal currents deviate significantly from the desired excitation, yet the pattern remains largely unaffected. Coupling not only influences the pattern but also impacts the gain and polarization of the entire array pattern. Mutual coupling does not alter the distribution of currents on elements within the array, but it does change the complex currents at the terminals. Compensation schemes can anticipate how coupling will alter the terminal currents and adjust the excitation voltages to elicit the desired currents. Moreover, physical methods exist to directly mitigate mutual coupling, such as the insertion of conductive baffles and resembling fences, among the elements.

4. Methods of reducing mutual coupling

Mutual coupling reduction refers to techniques and methods employed to minimize the effects of mutual coupling in antennas and other electronic systems. Here are a few common methods used to reduce mutual coupling: Increased spacing: One of the simplest ways to reduce mutual coupling is by increasing the physical distance between antennas or components. By spacing them further apart, the coupling effect diminishes, resulting in reduced interference. Alternating structures: Alternative structures are two or three-dimensional arrays of elements that are alternately placed together. Types of these structures include frequency-selective surfaces, crystal photonics, and metamaterials. The analysis of these structures is done using simple Floquet analysis. EBG (electromagnetic bandgap): EBG structures are highly desirable in modern antenna and microwave designs. In essence, EBG structures are artificial periodic arrangements of dielectric materials and metallic conductors. They exhibit the unique property of preventing radiation and facilitating the propagation of electromagnetic waves within a specific frequency range and for all angles. EBG structures can effectively suppress unwanted radiation and support desired polarization modes. Mutual coupling reduction involves techniques to minimize its effects in antennas and electronic systems. Common methods include:

• Increased spacing: Widening the physical distance between antennas reduces coupling and interference.

• Alternating structures: Using structures like frequency selective surfaces (FSS), crystal photonics, and metamaterials can reduce coupling effects.

• EBG (electromagnetic bandgap) structures: Artificial periodic arrangements of dielectric materials and conductors, EBGs prevent radiation and facilitate electromagnetic wave propagation within specific frequency ranges.

• FSS (frequency selective surfaces): Made of alternating patches on a grounded dielectric layer, FSS act as specialized filters, absorbing specific frequencies.

• PBG (photonic bandgap) structures: These reduce surface waves, improving antenna efficiency, bandwidth, and reducing interference.

• Fractals: By exploiting space-filling properties, fractals reduce size and cross-coupling in microarrays.

• DGS (Defected Ground Structure): Meandering techniques in the ground plane reduce mutual coupling by creating gaps perpendicular to the feeding point.

• Resonator rings: Used for protection and enhancing radiation, resonant levels create frequency gaps, reducing cross-coupling.

• Geometric changes to the patch: Altering patch geometry, like using fractal patches, reduces mutual coupling. The choice of technique depends on factors like frequency range, available space, cost, and performance objectives. Future methods for mutual coupling reduction will be explored.

4.1 Reduction of mutual coupling with liquid dielectric

Numerous techniques implemented thus far aimed at mitigating mutual coupling have resulted in the isolation of sizable elements, unwieldy structures, intricate numerical computations, and irreversible structural modifications. The focal point of this research lies in the design of array antennas tailored for contemporary, practical, and multidisciplinary applications. Consequently, this study proposes a pragmatic approach for segregating antennas through the utilization of water. This innovative and controllable method circumvents the need for complex numerical equations, validating the structural efficacy via the wave scattering method. The procedure involves minimizing mutual coupling between two elements by introducing a liquid dielectric, specifically distilled water, between the components of an antenna array. The future potential of this technique to suppress crosstalk holds promise for diverse applications such as the integration of solar panels and energy harvesting with electromagnetic structures [6, 7], transparent electromagnetic structures [8], and low radar cross-section (RCS) devices [9, 10, 11]. The ensuing sections outline the primary specifications of this device, emphasizing its applicability in air and marine environments:

• Utilize liquid water to mitigate cross-coupling between diffusing components.

• The method is fully implementable due to the confined glass plexiglass structure.

• Strongly recommend optically transparent solar panel integration solutions.

• The proposed structure enhances the characteristics of the primary antenna.

Following this, a comprehensive discussion ensues, covering the presented structure, including a summary of water characteristics concerning electromagnetic (EM) waves, the design of a simple microstrip antenna array, and a cross-coupling reducer featuring a confined water device. The subsequent section presents the results obtained from numerical, experimental, and analytical solutions.

4.1.1 Wave propagation in water

Owing to the elevated conductivity loss of seawater in the mid-RF range’s propagation of EM waves, the normal conductivity is established to be 4 S/m [12]. In contrast, freshwater exhibits a conductivity of 0.01 S/m, which is 400 times lower than that of seawater. Consequently, EM wave propagation in freshwater may prove more effective than in seawater. This section delves into the theoretical aspects of water absorption ability. As EM waves transition from open air to freshwater, two types of losses warrant investigation:

• Connection loss, arising from air reflection and water interference.

• Propagation loss of EM waves in water, explored based on water material properties.

This loss is harnessed as a novel technique to diminish undesirable coupling between two propagation components. Both loss mechanisms are analytically defined in this section, drawing from the scattering presentation depicted in Figure 5. Eq. (1) is used to measure total propagation loss of the structure where (${\alpha }_p$) and (${\alpha }_t$) give the propagation and transmission losses:

Figure 5.

Penetration plan of EM waves into freshwater.

$${\alpha }_{\mathit{\text{total}}}={\alpha }_t+{\alpha }_p=10log\left(\frac{P_t}{P_i}\right)$$E21

$$T=\frac{2{\eta }_1}{\left({\eta }_0+{\eta }_1\right)}$$E22

where a, d, T, η0, and η1 denote the imaginary component of the wave propagation constant, depth of propagation in water, transmission coefficient, and air and water characteristic impedances, respectively. In addition, EM wave interaction with water can be modeled with the Debye dispersive dielectric constant, as in Eq. (7):

$$\overline{{\epsilon }_r}\left(f\right)={\epsilon }_{\infty }+\left(\frac{{\epsilon }_s-{\epsilon }_{\infty }}{1+\left(i\frac{f}{f_{\mathit{ref}}}\right)}\right)-\frac{\mathit{i\sigma }}{2\mathit{\pi f}{\epsilon }_0}$$E23

It can be understood that the propagation losses are determined by the propagation depth and water permittivity. Therefore, the surface current transmission from one patch to another may be prevented by applying a proper material and geometry. According to the total loss equation, the water depth is chosen so that it only blocks the transmission of surface currents from the first to the second patch while causing no interference with the propagation of antenna. As a theoretical proof of concept, the wave dissipation value from Eq. (1) can be used to propose water as a novel mechanism for mutual coupling reduction.

4.1.2 Antenna structure description

This section introduces a novel approach aimed at mitigating mutual coupling in a microstrip antenna array through the utilization of a liquid dielectric, specifically distilled water. The proposed antenna array is configured as a two-element microstrip patch array, engineered for operation at 7 GHz, corresponding to the C-frequency range. The foundational antenna structure employs a typical geometry, serving as a baseline to illustrate the coupling characteristics inherent to an array antenna. To further explore the potential of reducing antenna mutual coupling, a structured water medium is introduced into the array. This serves as a demonstrative application of a transparent dielectric, strategically employed to diminish mutual coupling within the antenna system. This innovative integration of a structurized water element represents a promising avenue for enhancing the performance and applicability of microstrip antenna arrays, particularly in scenarios where mutual coupling reduction is critical.

4.1.3 Base antenna configuration

The base array antenna is fed by two coaxial Sub-Miniature version A (SMA) connectors. These coaxial cables exhibit an outer conductor linked to the ground plane, with a center conductor routed through a hole in the ground plane, establishing electrical connectivity with the patch element. The antennas within the array are strategically spaced at a distance of 0.4λ₀. Among various array configurations, the adjacent 1 × 2 array stands out with the highest coupling value, rendering it highly compatible with circuit board technology. Figure 6 provides a visual representation of the planned array, while Table 1 outlines the specific specifications of the antennas. The substrate’s thickness, relative permittivity, and loss tangent are designated as 1.6 mm, 4.8, and 0.025, respectively. A comprehensive analysis of the scattering parameters diagram is conducted both before and after the incorporation of the coupling reduction structure involving a liquid dielectric. This analysis aims to quantify the coupling effect between the two antenna components. Moreover, the simulation yields a maximum radiation gain of 10.7 dB for the antenna without a liquid dielectric at the resonance frequency of 7 GHz. This information contributes to a thorough understanding of the antenna’s performance characteristics in the absence of the proposed coupling reduction mechanism.

Figure 6.

Top and side views of the antenna before inserting the coupling reduction structure.

Ls	Ws	h	d	Lp	Wp	Ls	Ws
100 mm	80 mm	1.6 mm	23.25 mm	28.75 mm	28.75 mm	100 mm	80 mm

Table 1.

Dimensions of the antenna are shown in Figure 6.

4.1.4 Mutual coupling reduction mechanism

In order to mitigate mutual coupling, a novel approach involving a confined water structure on the base antenna is presented. Plexiglass material is employed to construct the structure, exhibiting specific characteristics suitable for mounting the liquid dielectric between the two antenna components. The choice of plexiglass for this project is motivated by its high resilience to diverse climatic conditions, ready availability in terms of thickness and dimensions, cost-effectiveness, transparency, and minimal impact on wave propagation. For the intended configuration, plexiglass sheets are meticulously assembled into a hollow container capable of accommodating the liquid dielectric, as illustrated in Figure 7(a) and (b). Notably, the bottom of the container covering the antenna remains exposed, allowing the liquid dielectric to make direct contact with the surface of the microstrip antenna substrate. When a surface current emerges on the antenna substrate plane, it is absorbed by the liquid dielectric before being radiated. The hollow containers crafted from plexiglass are filled with distilled water, characterized by ε_r, μ_r, and σ values of 90, 1, and 1.59 [S/m], respectively. The pivotal operation for coupling reduction is executed by the first segment with a ⊏ shape strategically positioned between the two radiating elements of the microstrip antenna array. It is imperative to note that substantial changes in the medium’s temperature may impact the effectiveness of this approach under stable coupling reduction conditions. The introduction of water into the array mirrors the principles observed in meander line structures designed to reduce mutual coupling between patch antennas [13]. It is essential to highlight that any alteration in the overall structure of water confinement for coupling reduction would be necessitated if there are new frequency goals to be achieved.

Figure 7.

Illustrates the proposed design for mutual coupling reduction, providing a sectional view of the structure installed over the antenna (a) and depicting the entire plexiglass structure (b).

4.1.5 Characterization results

In the transmission of surface current from the first patch to the second, it encounters a semiconductive state within the water medium, incurring some losses. This distinctive feature plays a pivotal role in diminishing the coupling within the antenna array by mitigating the detrimental effects of the surface current transmitted between the two patches. To detail these characteristics, the CST-Microwave Studio software is employed to execute all three stages of design and simulation, as expounded by previous works [14]. The mutual coupling reduction structure, incorporating a liquid dielectric, is strategically inserted between two microstrip patch antennas, as depicted in Figure 8.

Figure 8.

The structure was designed by applying the air gap. (a) Step 1; (b) step 2; (c) step 3.

Stage 1: As previously mentioned, the proposed structure comprises two distinct sections in ⊏ and I forms. An air gap exists between the two ⊏ − form segments. The impact of this air gap is significant, as neglecting it results in the transmission of electromagnetic (EM) waves and surface currents from the left to the right, effectively behaving as a conductor of waves (refer to Figure 8a). The scattering parameters are initially evaluated before the introduction of the air gap, as illustrated in Figure 9.

Figure 9.

S11 and S21 scattering parameters of the antenna of sample 3 for different lengths ln.

Stage 2: The dimensions of the ⊏ − section are substantiated through parametric simulations. In the second stage, the structure, excluding the I-form section, undergoes examination. A 4.4 mm air gap is introduced, as presented in Figure 8b.

Stage 3: The final stage incorporates the antenna’s I-form structure (Figure 8c). Scattering diagrams for various I-form dimensions are depicted in Figure 9. A comparative analysis of the scattering parameters for Sample 3 (Figure 8c), featuring different lengths (Ln), along with the antenna’s radiation pattern, is detailed in Table 2. Notably, an increased length of the I-form structure (Ln) correlates with an enhanced radiation pattern. The optimum length of the I-form section that yielded optimal results was determined to be 59 mm. All dimensions of Figure 8 are listed in Table 3, and The comparison of the radiation parameters of the antenna Sample 3 with Ln(c) in the measurement and simulation stages is shown in Figure 10.

Stage 3; Ln (mm)	Frequency (GHz)	S11 (dB)	S12 (dB)	Directivity (dB)
Ln(a) = 30	7	−24	−30	8
Ln(b) = 44	7	−30	−28	7.8
Ln(c) = 59	7	−31	−30	10

Table 2.

Variations in S11, S21, and radiation pattern for different ln values.

La	Lb	Lc	Ld	Le	Lf	Lg	Lh
57.2 mm	50.19 mm	39.6 mm	19.8 mm	6.05 mm	4.54 mm	2.83 mm	5.4 mm

Table 3.

Dimensions of the antenna are shown in Figure 8.

Figure 10.

The diagram radiation parameters as compared in antenna of sample 3 with ln(c) in measure and simulation stages.

All stages of the structure design have been thoroughly examined in the preceding sections. The culmination of these investigations, as evidenced in the last section and elucidated in the analysis presented in Table 4, reveals that the most effective configuration for coupling reduction is achieved in Sample 3 with Ln(c). Subsequent analyses delve into the scattering of waves and the dynamics of surface current movement. As previously outlined, this approach mitigates mutual coupling through the absorption and confinement of surface currents. The design methodology involves establishing equilibrium in dielectric coefficients and determining suitable water height and depth. In Figure 11(a), the surface current distribution on the antenna is depicted without the insertion of the coupling reduction structure, while Figure 11(b) explicitly illustrates the absorption and confinement of the surface current facilitated by the designed structure. Furthermore, Figure 12(a) elucidates the direction of electric field propagation in the antenna lacking the coupling reduction structure. Contrarily, in Figure 12(b), the inhibitory effect of the designed structure on the transmission of electric fields from the first patch to the second patch is evident, effectively creating an obstruction. These visualizations provide valuable insights into the efficacy of the coupling reduction mechanism in redirecting and mitigating surface currents within the microstrip antenna array.

Parameter	Dimensions (mm)	Parameter	Dimensions (mm)
a	14	G	5
b	12	H	1
c	12	K	0.5
d	9	M	2
e	9	N	5
f	1

Table 4.

Dimensions of the proposed antenna (Figure 14).

Figure 11.

Distribution of surface current on the designed antenna. (a) the prototype antenna without inserting the coupling reduction structure, (b) the prototype antenna with inserting the coupling reduction structure as sample 3 with ln(c).

Figure 12.

Distribution direction of electric field propagation in the designed antenna. (a) the prototype antenna without inserting the coupling reduction structure, (b) the prototype antenna with inserting the coupling reduction structure as sample 3 with ln(c).

The constructed prototype of the antenna, featuring the integration of the mutual coupling reduction structure with a liquid dielectric (distilled water), is presented in Figure 13. This specific configuration is labeled as Sample 3 with Ln(c), and it is depicted from various viewpoints to provide a comprehensive understanding of its physical attributes.

Figure 13.

The antenna sample fabricated with mutual coupling reduction structure with liquid dielectric (distilled water) as sample 3 with ln(c).

4.2 Reduction of mutual coupling with graphite materials, MTM, and EBG design

This method introduces a specialized approach to mitigate cross-coupling by integrating graphite materials, metamaterials (MTM), and electromagnetic bandgap (EBG) design. The proposed antenna is configured as part of an array, with a specific pair intended for testing the structural performance. The array antennas are tailored for use in extensive screens, a crucial consideration for large-scale applications. In dimensions spanning several hundreds, the incorporation of a graphite structure contributes to a reduction in antenna weight due to its inherent lightweight properties. This design not only significantly minimizes mutual coupling losses but also enhances fundamental antenna parameters such as gain and radiation efficiency. These improvements signify an overall enhancement in antenna performance, highlighting the efficacy of the proposed concept for various applications. The investigation begins by examining the relationship between graphite and the propagation of electromagnetic waves. Subsequently, the array antenna is meticulously designed, incorporating the coupling reduction structure. In the final step, the performance of the multiple-input multiple-output (MIMO) antenna is analyzed to validate the effectiveness of the proposed method.

4.2.1 Properties of graphite in the propagation of electromagnetic waves

Graphite sheets are compressible, porous, and electrically conductive materials extensively used in diverse applications, including fuel cells, flow batteries, and electromagnetic shields. The sheet density, a critical parameter influencing electrical conductivity, exhibits a linear relationship with electrical conductivity [15, 16]. Researchers have shown interest in utilizing graphite compounds as effective electromagnetic absorbers due to their electrical conductivity, chemical stability, and ease of manufacturing at a low cost. Recent attention has been directed toward graphene and carbon nanotubes for their remarkable properties, although their impact on electromagnetic wave absorption may be influenced by factors like room temperature carrier mobility [17]. Graphite compounds, characterized by low density, large surface area, high-temperature resistance, oil absorption, and excellent electrical conductivity, present a viable and cost-effective solution for industrial applications. The microwave current behavior in graphite compounds is governed by carrier transfer within the graphite layers, leading to high electrical conductivity and reduced resistance [18]. In line with transfer theory, computational formulas for single-layer adsorbents are expressed in the following equations. These properties make graphite a compelling material for applications requiring effective electromagnetic wave absorption [19, 20]:

$$z_{\mathit{\text{in}}}=\sqrt{\frac{{\mu }_r}{{\epsilon }_r}tanh}\left(j\frac{2\mathit{\pi fd}}{c}\right)\sqrt{{\mu }_r{\epsilon }_r}$$E24

$$\mathrm{\Gamma }=\frac{\sqrt{\frac{{\mu }_r}{{\epsilon }_r}tanh}\left(j\frac{2\mathit{\pi fd}}{c}\right)\sqrt{{\mu }_r{\epsilon }_r}-1}{\sqrt{\frac{{\mu }_r}{{\epsilon }_r}tanh}\left(j\frac{2\mathit{\pi fd}}{c}\right)\sqrt{{\mu }_r{\epsilon }_r}+1}$$E25

where ${\epsilon }_r$ and ${\mu }_r$ represent the relative permittivity and the relative permeability of the adsorbents, respectively. $z_{\mathit{\text{in}}}$ is the input impedance normalized because it relates to the impedance in the free space, d is the thickness of the absorber, c is the speed of light, and f is the frequency of the microwave in the free space.

4.2.2 Antenna design

The antenna structure proposed in this study is depicted in Figure 14. This microstrip multiple-input multiple-output (MIMO) antenna comprises two identical rectangular radiation patches designed on an FR4 substrate. The substrate has dimensions of 81.7 × 52.85 mm and a thickness of 1.6 mm, possessing a dielectric constant of 4.3. Both antennas are connected to a 50 Ω SMA port. The separation between the two patches is set at 20 mm, a relatively small distance chosen to minimize coupling effects. Increasing this distance excessively could result in a reduction of coupling, but such adjustments are deemed beyond the scope of this study. Table 5 provides the specific dimensions of the proposed antenna.

Figure 14.

Sample of the proposed microstrip MIMO antenna.

Parameter	Dimensions (mm)	Parameter	Dimensions (mm)
Wa	53.85	Lc	20.42
Wb	26.93	Xa	7.03
La	81.7	Ya	13.46
Lb	20.43	H	1.6

Table 5.

Dimensions of the proposed antenna Figure 14.

4.2.3 Structure description utilizing graphite for mutual coupling reduction in Array antennas

In this research, we propose a structure designed with graphite to alleviate mutual coupling among array antennas, as illustrated in Figure 14. Building upon the principles outlined in Section II, where expanded graphite’s resistive absorbent nature was detailed, we employ a graphite sheet, a compressible, porous, and electrically conductive material, as the substrate for the proposed structure. To enhance the graphite structure, we incorporate a perfect electric conductor (PEC) electromagnetic bandgap (EBG) layer. The specific graphite utilized in this study has a dielectric constant (ɛr) of 12, magnetic permeability (μ) of 1, and a thickness of 1 mm. Figure 15 presents diverse perspectives of the graphite and EBG composite structure.

Figure 15.

Schematic of the combined unit structure of graphite and EBG to reduce mutual coupling: (a) general and top view, (b) three-dimensional view back, (c) three-dimensional view of the front of the structure, and (d) side view.

EBG structures offer versatility in configuring stop-bands, pass-bands, and bandgaps. They effectively impede the propagation of electromagnetic surface waves across different frequencies. The EBG structure is composed of periodic elements, either dielectric or metallic, arranged as a single cell and repeated. By adjusting the unit cell’s repetition shape and resonance value, bandgaps can be tailored. To analyze the designed structure in Figure 15 and ascertain the magnetic bandgap, we employ the eigenmode method, considering alternation in both the X and Y axes.

One method for inducing capacitive properties involves placing a rectangular ring around the structure. In our approach, we create capacitive properties in the EBG by encircling the internal structure with a loop and introduce inductive properties by incorporating cuts in the center. By adjusting the structure’s dimensions, we determine the optimal values for creating a magnetic bandgap at the desired frequency. Table 4 provides the dimensions of the proposed graphite structure in Figure 15.

Two noteworthy considerations arise: firstly, the utilization of the inner region of the light cone to determine the bandgap, and secondly, the exclusion of the mode 1 curve in the bandgap calculation, as depicted in Figure 16. The latter is specific to mode 1, and its exclusion is justified by examining the electric field vectors’ symmetry inside the substrate.

Figure 16.

Showing the range of the magnetic gap band structure from the output of the dispersion diagram.

As shown in Figure 16, the yellow area represents the magnetic bandgap of the structure, ranging from 3.1 GHz to approximately 3.75 GHz. This denotes a magnetic forbidden band within this frequency range, where electromagnetic waves are impeded from passing through the structure. The graphite sheet’s structure inhibits surface currents from entering the graphite layers, reducing surface currents at the output. Figure 17 illustrates the reduction of mutual coupling within the graphite structure and the attenuation of input surface waves, aligning with the schematically designed EBG structure to induce inductance and capacitive properties. The incoming surface currents enter the graphite structure, vibrating between layers and suppressing surface currents, consequently diminishing the outgoing surface current. The designed EBG structure further aids in reducing mutual coupling between antenna radiating patches by creating inductor and capacitor properties and establishing an electromagnetic forbidden band at the desired frequency. The physical properties of graphite and its interaction with electromagnetic waves were discussed in Section II, emphasizing graphite’s conductivity and the impact of dimensions and thickness on the magnetic bandgap frequency, as described by Eq. (1).

Figure 17.

Showing the effect of graphite structure in reducing mutual coupling.

4.2.4 Analysis of results

This section delves into the examination and scrutiny of outcomes arising from the integration of the designed electromagnetic bandgap (EBG) structure with graphite amid the radiating elements of the designated antenna. The antenna, featuring coupling reduction structures positioned between the two radiating elements, is visually represented in Figure 18. The surface disparity between the antenna ground and the meticulously designed graphite structure is determined to be 0.6 mm, as evident from Figure 18a and b. This was achieved by strategically cutting the substrate and ground part of the antenna structure, allowing for the insertion of graphite between the two radiator elements. Upon analysis, it is discerned that the proximity of antenna patches influences the destructive effects, with a more pronounced impact when the antenna patches are in close proximity. Conversely, as the patches are situated farther apart, the impact diminishes. Consequently, a lower LC (line-of-centers) results in higher mutual coupling, whereas a higher LC leads to diminished mutual coupling. The fundamental objective of the structural design is to curtail mutual coupling within the compact structure, particularly focusing on minimizing the mutual coupling between the two radiation patches positioned at the shortest distance from each other.

Figure 18.

Antenna with coupling reduction structures between two radiating elements: (a) top view and (b) bottom view.

In the assessment of the coupling effect between the two elements of the array antenna, a thorough analysis was conducted through the examination of scatter plots of S21 both before and after the incorporation of the graphite structure. Figure 19 illustrates the comparative diagram, categorizing the graphite structure arrays into four modes: single, double, triple, and quadruple. Notably, the quadruple array emerges as the most suitable configuration, exhibiting the highest degree of mating. For comprehensive insight, the comparative diagram of scattering parameters in Figure 19, representing the antenna before and after the integration of the graphite structure, reveals a substantial reduction of 30 dB in coupling. In the context of multiple-input multiple-output (MIMO) systems, achieving a coupling reduction exceeding 15 dB is deemed highly commendable. The synergy between electromagnetic bandgap (EBG) and the graphite substrate is pivotal. The graphite plate contributes significantly to mutual coupling reduction, leveraging its inherent properties that impede the propagation of electromagnetic waves. Simultaneously, the EBG structure plays a complementary role in reducing mutual coupling. The combined utilization of these two structures in this study yields a more pronounced reduction in mutual coupling. Figure 19 presents a comparative analysis of the graphical representations, distinguishing between the structure with graphite alone and the structure incorporating both graphite and EBG. The radiation pattern of the antenna, specifically designed for mutual coupling reduction among array elements, is elucidated in Figure 20. The comparison chart therein indicates a notable increase in gain, escalating from 8.1 to 9.3 dB, underscoring the efficacy of the integrated structures in enhancing antenna performance.

Figure 19.

Antenna scattering parameters: Diagram of without and with graphite structure: (a) S11 and (b) S21 diagram.

Figure 20.

Diagrams of antenna radiation structure: Comparison without and with graphite structure: (a) H-plane and (b) E-plane.

The assessment of the antenna’s radiation efficiency before and after the integration of the graphite structure is presented in Figure 21. The comparative analysis in Figure 21 reveals a substantial improvement of nearly 24% in the antenna’s radiation efficiency following the incorporation of the graphite structure. The primary contributor to mutual coupling is the transition of surface currents from the first patch to the second patch. Figure 22 illustrates the distribution of surface currents in the antenna, showcasing the impact of the coupling reduction structure between the two radiating elements. Upon stimulating one of the patches, Figure 22 demonstrates the designed structure’s efficacy as a barrier, effectively impeding the transition of surface current from the first patch to the second patch. Further insight into the dynamics of electric fields is provided in Figure 23, where the graphite structure positioned between the two elements creates a vortex, effectively preventing the transition of electric fields from the first patch to the second patch. This visual representation emphasizes the role of the graphite structure in disrupting the flow of electric fields between the radiating elements, thereby contributing to the reduction of mutual coupling in the antenna system.

Figure 21.

Comparative diagram of radiation efficiency of the antenna without and with graphite structure.

Figure 22.

Antenna surface current distribution: (a) without graphite structure and (b) with graphite structure.

Figure 23.

Distribution of antenna electric fields: (a) without graphite structure and (b) with graphite structure.

In the realm of communication channels, the transmission of electromagnetic waves encounters various obstacles, leading to signals reaching the receiver from diverse directions. Direct waves differ from those reflected in terms of amplitude and phase, introducing interference at the receiver, commonly referred to as “tach.” Circular polarization antennas play a pivotal role in mitigating these challenges. When electromagnetic waves reflect, circular polarization antennas induce a change in the direction of polarization. For instance, if waves are initially upright, they turn left after reflection, and vice versa. This phenomenon significantly diminishes multi-directional interference. Unlike their linear polarization counterparts, circular polarization antennas do not require precise alignment for a reliable connection between the transmitter and receiver. Circular polarization antennas can send and receive signals with both horizontal and vertical components simultaneously. Consequently, the orientation of antennas in the receiver and transmitter becomes less critical. This research employs a structural approach designed to meet necessary specifications while ensuring simplicity and cost-effectiveness in the antenna manufacturing process. The utilization of circular polarization antennas aligns with the goal of streamlining mass production, making it both simple and economically feasible within the available facilities.

4.3 Mitigating mutual coupling through DGS and EBG integration

In the realm of communication channels, obstacles abound, and electromagnetic waves encounter various directions before reaching the receiver. The waves directly received differ from those reaching the antenna via reflection, leading to disparities in amplitude and phase, causing interference known as “tach.” Circular polarization antennas play a pivotal role in addressing these challenges. Reflection induces a change in the direction of polarization, significantly reducing multi-directional interference compared to linear polarization antennas. Unlike their linear counterparts, circular polarization antennas can send and receive both horizontal and vertical components, eliminating the need for precise alignment between the transmitter and receiver antennas. In this research, we introduce a structure designed to meet specifications while ensuring a straightforward and cost-effective antenna manufacturing process conducive to mass production within available facilities.

4.3.1 Description of the designed antenna

Circular polarization proves advantageous due to its ability to overcome the multi-way phenomenon, eliminate the need for intricate tuning of transmitter and receiver antennas, and facilitate frequency band reuse with left and right polarization. This property, crucial in various telecommunication systems, extends to military and industrial applications. To achieve circular polarization, a square patch with two cut corners is employed, fed by a probe through a coaxial line. The coaxial line power supply offers several advantages over micro-line alternatives, including lower power line losses, prevention of undesirable power line radiation, and the ability to adjust input impedance without requiring a quarter-wavelength line. The antenna patch is crafted on a 6035 RT microwave substrate with a dielectric coefficient (εr) of 3.6 and a 1 mm thickness, courtesy of the Rogers Company. Operating in the C-frequency band at approximately 6.39 GHz, the antenna is powered by a 50-ohm coaxial SMA probe. All dimensions adhere to standard formulas outlined in Refs. [21, 22]. Figure 24 illustrates the structure of the designed antenna, fed by a probe through the coaxial line, with radiant fields exhibiting right circular polarization. Altering the cut placement to the other two corners generates left circular polarization and Table 6 shows the antenna dimension values.

Figure 24.

Initially designed antenna view without placement of the coupling reduction structure: (a) top view and (b) side view.

Parameter	Dimensions (mm)	Parameter	Dimensions (mm)
X	70.7	L1	10.6
Y	35.4	D	23.5
c	11.7	A	5.8
f	11.7	b	3.3
W1	10.6	θ	135°
L1	10.6	h	1
X	70.7	L1	10.6

Table 6.

Values of designed antenna dimensions Figure 24.

In line with the resonator model, the square patch’s predominant mode is 10TM. To induce circular polarization, cuts in the two corners along the patch’s diameter are essential. Properly selecting square dimensions and cut amounts create two modes with equal amplitude and a 90-degree phase difference, intensifying at frequencies close to each other.

To comprehensively assess the impact of mutual coupling between two array antenna elements, a thorough analysis of the scattering parameters (S12) is imperative for both the pre and post application of the reduction structure. Figure 25, in the initial step, presents the schematic representation of the antenna’s scattering parameters before implementing the coupling reduction structure, focusing on S11. Observing the S11 diagram in Figure 25 reveals the antenna’s resonant frequency to be 6.35 GHz, positioning it within the C-frequency band spanning 4 to 8 GHz. This frequency range holds significance as the primary allocation for Earth-satellite communication, particularly prevalent in commercial communication satellites. To delve into the polarization characteristics of the antenna, scrutiny of the axial ratio diagram becomes essential. Figure 26 illustrates the axial ratio of the designed antenna concerning frequency. When the axial ratio value at the antenna’s resonance frequency is below 3 dB, it signifies circular polarization, as depicted in Figure 26.

Figure 25.

Diagram of antenna scattering parameters without EBG and DGS structure.

Figure 26.

Axial ratio diagram of the antenna without EBG and DGS structure.

The antenna bandwidth, calculated using Eq. (7), is determined to be 0.5%:

$$\%\mathit{FBW}=\frac{f_{\text{high}}-f_{\mathrm{low}}}{f_{\text{center}}}$$E26

The radiant pattern characteristics of the initially designed antenna are expounded in Figure 27. The simulated E-plane radiation pattern, showcased in Figure 27, captures the antenna’s behavior at the resonant frequency of 6.35 GHz without the mutual reduction structure, attaining a maximum value of 10.4 dB.

Figure 27.

Antenna radiation pattern diagram without EBG and DGS structure.

4.3.2 Description of the designed structure for mutual coupling reduction

Electromagnetic bandgap (EBG) structures have emerged as a promising paradigm for innovative antenna designs, offering insights into dispersion diagrams, surface impedance, and reflection phase characteristics. EBG structures enable the specification of stop-bands, pass-bands, and bandgaps. Essentially, an EBG structure comprises repeated elements of dielectric or metallic materials organized as a unit cell, strategically placed with specific repetitions. Conventionally, EBG structures find placement between antenna arrays, playing a crucial role in mitigating mutual coupling and enhancing reflected radiation [23, 24]. To achieve a targeted electromagnetic forbidden band, designers can introduce gaps in the ground plane with diverse shapes and configurations. This method employs a synergistic approach, integrating EBG and Defected Ground Structure (DGS) methods to craft a novel structure aimed at reducing mutual coupling. The EBG structure features multiple nested circles, while the DGS structure encompasses a section of the ground plate with two circular rings, as illustrated in Figure 28, showcasing the unit cell view of the designed structure. The structural analysis, including the extraction of the dispersion diagram to delineate the magnetic bandgap, utilizes the eigenmode method. Figure 29 depicts the yellow region symbolizing the magnetic bandgap of the structure, with the horizontal diagram denoted as ΓXΜΓ. The interval [0,1] or [ΓX] correlates to the electrical phase spanning [0,180] degrees. Notably, the exclusion of one of the modes warrants consideration. This qualitative omission is addressed by scrutinizing the electric field vectors at a specific kx value (first Brillouin region (ΓX)) within the inner region of the light cone and the YZ plane, as determined by the structure’s orientation. Given that this study explores the combined EBG and DGS structure for coupling reduction in flat array antennas, recognizing that electric field vectors inside the substrate align in the ±Z direction with a predominant vector direction (e.g., all vectors in the −Z direction), it becomes evident that the first mode deviates from this pattern and should be excluded from the bandgap calculation (Figure 29). Table 7 also shows the dimensions of the designed structure in Figure 28.

Figure 28.

View of the cell structure of the combined DGS and EBG unit to reduce mutual coupling, (a) DGS bottom view, (b) top view of EBG, (c) side view, and (d) three-dimensional view.

Figure 29.

Dispersion diagram output diagram in order to obtain the magnetic bandgap of the structure.

Parameter	Dimensions (mm)	Parameter	Dimensions (mm)
n	14	s	3
m	12	o	0.8
t	0.6	u	1.6
j	0.8	i	2
p	2	v	2.4
q	2

Table 7.

Unit cell values of Figure 28.

The output dispersion diagram (Figure 29) reveals that the magnetic bandgap of the structure crafted in this investigation spans from 6 GHz to approximately 7.8 GHz. This signifies the presence of a magnetic band within this frequency range, indicating the exclusive application of coupling reduction during this specific span. Consequently, the designed structure remains inactive in frequencies outside this specified range. However, considering the antenna’s operational frequency and acknowledging the inverse correlation between frequency and structural dimensions, diverse operational frequencies can be attained by modifying the structure’s dimensions. By diminishing the structure’s dimensions, a higher operational frequency can be achieved, whereas increasing the dimensions facilitates operation at a lower frequency. Consequently, it is imperative to recognize that a tailored design approach is necessary for each distinct frequency range. This nuanced strategy ensures optimal performance and targeted coupling reduction for specific operational frequencies.

4.3.3 Conclusive outcomes

In this segment, an examination of the mutual coupling between array antenna elements is undertaken, guided by the principles and configurations elucidated in Sections 2 and 3. The implementation of the synergistic EBG and DGS structure is a focal point in this analysis. Figure 30 provides a visual representation of the antenna featuring coupling reduction structures positioned between its two radiating elements. This strategic integration is pivotal for assessing and quantifying the impact on mutual coupling within the array antenna system.

Figure 30.

Placement of the structure designed for mutual coupling, (a) underside view of the DGS structure antenna. (b) Upper view of EBG structure antenna.

In this context, a comprehensive examination of the antenna’s performance is presented through Figures 31 and 25, delineating the contrasting scenarios before and after implementing the devised structure aimed at mitigating mutual coupling among array antenna elements. Figure 31 specifically explores the influence of varying the repetitions of the unit cell within the antenna patches, scrutinizing three distinct stages. The dispersion parameter S12 is instrumental in this analysis, revealing that the optimal configuration, denoted as STEP3 (involving 4 unit cell repetitions), achieves a remarkable 36.5 dB reduction in mutual coupling. Figure 32 shows the comparison diagram of the radiation pattern. Additionally, Figure 33 offers a comparative illustration of the axial ratio for the antenna, both in its original state and with the integrated EBG and DGS structure. This comparative assessment, as depicted in Figure 33, provides valuable insights into the impact of the devised structure on the antenna’s axial ratio, offering a holistic view of its polarization characteristics in the presence of the coupling reduction strategy. Also, Figure 34 shows the comparative diagram of antenna efficiency.

Figure 31.

Diagram of antenna dispersion parameters without and with EBG and DGS structure in three STEP with different unit cell arrangement.

Figure 32.

Comparative diagram of unstructured antenna radiation pattern with EBG and DGS structure. (a) H-plane and (b) E-plane.

Figure 33.

Comparative diagram of axial ratio antenna without and with EBG and DGS structure.

Figure 34.

Comparative diagram of radiation efficiency of antenna without and with EBG and DGS structure.

4.3.4 Surface current distribution and magnetic field analysis

The primary determinant of mutual coupling lies in the transmission of surface currents from the first antenna patch to the second one. Illustrated in Figure 35 is the surface current distribution in an antenna, both with and without a coupling reduction structure positioned between the two radiation elements. This visualization (Figure 35) elucidates how the devised structure, intended for mutual coupling reduction, functions as a barrier when one of the patches is stimulated, effectively impeding the transfer of surface current from the first patch to the second. Furthermore, Figure 36 provides insight into the magnetic fields of the antenna, comparing scenarios with and without the coupling reduction structure between the two radiating elements. The magnetic field analysis offers a comprehensive view of the electromagnetic behavior, highlighting the efficacy of the coupling reduction structure.

Figure 35.

Distribution of antenna surface currents (a) without EBG and DGS structure (b) with EBG and DGS structure.

Figure 36.

Antenna magnetic fields (a) without EBG and DGS structure (b) with EBG and DGS structure.

5. Conclusion

In the first part of the book, an introduction to mutual coupling is explained, and in the second part, wireless interference is explained. In the third part, the theory of antenna cross-coupling reduction is investigated. In the third part, we have analyzed different methods of reducing mutual coupling. These methods include reduction of mutual coupling with liquid dielectric, reduction of mutual coupling with graphite materials, MTM, and EBG design, and reduction of mutual coupling through the integration of DGS and EBG, which was first proposed by Mohammadreza Rohaninezhad and his colleagues in 2023. and 202 were presented. Section 4.1 focuses on a specific application of water as a dielectric material to improve antenna performance, with aerial and naval applications in mind. For the first time, a method for lowering surface currents between the antenna array’s two radiators has been proposed based on water. The liquid dielectric was inserted into hollow plexiglass containers. Pure water is used, and it has the ability to absorb and reradiate EM waves in partial proportions. To consider environmental variables, an ambient temperature of 4 to 40°C is assumed for both water and glass containment. EM waves from the first patch to the second patch collide with semiconductive water during coupling, which absorbs the waves. Using this method, the coupling was reduced by 15 decibels. The mutual coupling reduction in the extended operating frequency is one of the advantages of this method. According to the measurements, the coupling has been reduced in an extensive band. Furthermore, when compared to traditional methods, the amount of metal pieces used in this method has been reduced. The method presented here can be used in any antenna array, but it is especially useful for multidisciplinary communication. The proposed instrument is invaluable for integrating the antenna with solar panels for the mentioned application due to the optical transparency of the water and the contained material. Furthermore, the use of water rather than other dielectric materials allows for applications in naval communications. In Section 4.2, the application of graphite in reducing the mutual coupling of electromagnetic waves by combining the structure of EBG was investigated. This structure is one of the practical methods to reduce mutual coupling in array antennas. Considering that EBG and graphite substrate are complementary to each other, therefore, the graphite sheet is responsible for a part of reducing the mutual coupling, and the other part is responsible for the EBG structure. This structure can be applied to all antennas with a working frequency between 3.1 and 3.75 GHz, and there is no limit to its use. It was possible to further reduce mutual coupling by combining these two structures. Also, in the composition design, graphite should be placed in a place that reduces the overall weight of the antenna due to the lightness of graphite. This feature can significantly reduce the weight of the antenna in larger dimensions and more arrays. The results showed that the mutual coupling between the two elements is reduced by 30 dB, which in the MIMO system, the coupling reduction of more than 15 dB is a very good value. Also, the antenna’s radiation efficiency was increased by nearly 24%, and the gain of the antenna was improved from 8.1 to 9.3 dB. By analyzing and also confirming the good performance of the structure in the antenna outputs, the basic parameters of the MIMO antenna, such as envelope correlation coefficient (ECC), diversity gain (DG), mean effective gain (MEG), total active reflection coefficient (TARC), and channel capacity loss (CCL), in the operating frequency band of the antenna showed that the obtained values show the positive effects of a graphite structure on antenna components. In Section 4.3, first, a circular array antenna was designed with the technique of cutting the corners of the patches. Then, by combining EBG and DGS methods, a single cell was designed to reduce mutual coupling. This is because, in previous studies, the combination of the two methods did not reduce the coupling in the antenna with circular polarization at a frequency of 6.3. Therefore, by applying a combination of EBG and DGS methods, the reduction of mutual coupling by 36.5 dB was calculated, which is an acceptable value compared to previous studies. The advantages of this structure include improved antenna gain, antenna radiation efficiency, and antenna envelope correlation coefficient. This structure can be used in all transmitter and receiver systems to send waves from the ground to the satellite in telecommunication and military satellites in the C-frequency band. In less research, all antenna components have been improved together, and by designing this combined structure, the characteristics of all antenna components have been improved. This structure can be used in aperture array antennas and wherever there is a need to suppress surface waves in the frequency range of 6 to 7.8 GHz. Also, by changing the dimensions of the main elements of the designed unit cell, its bandgap frequency can be changed and this structure can be used in other frequencies.

Acknowledgments

The authors extend their sincere appreciation to the NAK Company Research Laboratory for providing the invaluable opportunity to carry out research in a real-world setting and for granting access to specific components for examination. The generous support from NAK Company has been instrumental in the successful completion of this study.

Conflict of interest

The authors declare no conflict of interest.