High-Performance Sub-6GHz 5G Antenna with Frequency Selective Surface Integration: Design, Optimization and Experimental Validation

The proposed antenna configuration consists of a single-element square antenna implemented on an FR4 substrate with dimensions of 25mm×25mm. The substrate has a thickness of 1.6mm and a dielectric constant (εr) of 4.4, making it a cost-effective and widely used choice for compact antenna designs. To enhance the antenna's performance, a Frequency Selective Surface (FSS) array is integrated into the structure. The FSS features either a 3×3 or 5×5 square-shaped arrangement, comprising 9 or 25 unit cells, respectively, each with square slot shapes. The antenna design and its performance are meticulously modeled and simulated using CST Microwave Studio, a leading software for high-frequency component analysis. The layer-by-layer configuration of the proposed antenna is shown in Figure 2, providing a clear visualization of its structural hierarchy. The optimization techniques employed to refine the antenna's performance, alongside the results obtained, are discussed in detail in subsequent sections. Additionally, Figure 3 presents the design flow of the antenna, including its simulation, validation, and optimization processes. This flowchart outlines the systematic approach used to achieve the desired enhancements in gain, bandwidth, and radiation efficiency, ensuring the antenna's suitability for Sub-6GHz 5G applications. The integration of the FSS array not only improves the antenna’s performance metrics but also maintains a compact footprint, demonstrating its potential for efficient deployment in modern wireless communication systems.

Figure 4 illustrates the geometric design of the proposed antenna configuration without the Frequency Selective Surface (FSS). A 25×25mm monopole element, with a copper thickness of 0.035mm, is mounted on a 1.6mm thick FR4 substrate. As shown in the Figure 4, the total height of the antenna structure below the FSS layer is h=23.4mm. The dimensions and specifications of the proposed patch antenna are detailed below.

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Figure 2. Layer-wise representation of proposed antenna

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Figure 3. FSS-integrated antenna design process

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(a) Squared patch (Front side)

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(b) Ground plane (Rear side)

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(c) FSS-unit cell geometry

Figure 4. Geometrical representation of proposed antenna

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Figure 5. Equivalent circuit of proposed FSS unit cell

The proposed antenna configuration employs a single-element square antenna built on an FR4 substrate with dimensions of 25mm×25mm. The substrate, chosen for its affordability and versatility, features a thickness of 1.6 mm and a dielectric constant (ε_r) of 4.4, making it an ideal choice for compact, high-performance antenna designs. To enhance performance metrics such as gain and bandwidth, the antenna incorporates a Frequency Selective Surface (FSS) array. Figure 5 shows the equivalent circuit of proposed unit cell. This array consists of either a 3×3 or 5×5 configuration of square slot-shaped unit cells, comprising 9 or 25 elements, respectively, which are periodically arranged for optimized electromagnetic response. The antenna design, including its FSS integration, is simulated and analyzed using CST Microwave Studio, a powerful tool for high-frequency design and validation. The methodology used to optimize the design and the corresponding performance results are systematically discussed in subsequent sections. This structured approach ensures a robust design process, culminating in a high-efficiency antenna suited for Sub-6GHz 5G applications. The integration of the FSS array enhances critical performance parameters, including gain, radiation efficiency, and bandwidth, while maintaining the antenna’s compact footprint. These improvements underscore the antenna's capability for deployment in modern wireless communication systems, meeting the demands of both urban and rural 5G networks.

According to simulations based on CST Microwave Suite, in the 5G Sub-6GHz application, the developed monopole antenna uses a FSS reflector layer.

${{\varphi }_{FSS}}-2\beta h=2N\pi $                   (1)

$\frac{{{B}_{c}}}{{{Y}_{0}}}=\omega C=\frac{\pi }{2}4{{\epsilon }_{eff}}\frac{V}{U}F\left( U,n,\lambda ,\theta  \right)$           (2)

$\frac{{{X}_{L}}}{{{z}_{0}}}=\omega L=\frac{\pi }{4}\frac{V}{U}F\left( U,2m,\lambda ,\theta  \right)$                    (3)

where, $F\left( U,n,\lambda ,\theta  \right)$ and $F\left( U,2m,\lambda ,\theta  \right)$ can be computed from the

$F\left( U,\omega ,\lambda ,\theta  \right)=\frac{U}{\lambda }cos\theta \left[ ln\left( cosec\frac{\pi \omega }{2U} \right) \right]+G\left( U,\text{ }\!\!\omega\!\!\text{ },\text{ }\!\!\lambda\!\!\text{ },\text{ }\!\!\theta\!\!\text{ } \right)$          (4)

$G\left( U,\text{ }\!\!\omega\!\!\text{ },\text{ }\!\!\lambda\!\!\text{ },\text{ }\!\!\theta\!\!\text{ } \right)=\frac{{{\left( 1-{{\delta }^{2}} \right)}^{2}}\left[ \left( 1-\frac{{{\delta }^{2}}}{4} \right)\left( \frac{{{A}_{+}}+{{A}_{-}}}{2} \right)+2{{\delta }^{2}}{{A}_{+}}{{A}_{-}} \right]}{\left( 1-\frac{{{\delta }^{2}}}{4} \right)+{{\delta }^{2}}\left( 1+\frac{{{\delta }^{2}}}{2}-\frac{{{\delta }^{4}}}{8} \right)\left( {{A}_{+}}+{{A}_{-}} \right)+2{{\delta }^{6}}{{A}_{+}}{{A}_{-}}}$                    (5)

${{A}_{\pm }}={{\left[ 1\pm \frac{2Usin\theta }{\lambda }-{{\left( \frac{2Usin\theta }{\lambda } \right)}^{2}} \right]}^{-\frac{1}{2}}}-1$

And $\delta =sin\left( \frac{\pi \omega }{2U} \right)$.

The proposed antenna system demonstrates a high efficiency of 82% and operates effectively within the frequency range of 3.2GHz to 3.8GHz, achieving a measured impedance bandwidth of 500MHz. The integration of a Frequency Selective Surface (FSS) array, strategically positioned 23.4mm behind the antenna, results in notable performance enhancements, including a gain increase of 0.33dBi, culminating in a peak gain of 7.93dBi. Performance evaluations confirm excellent results across key metrics such as the radiation pattern, S-parameters, and Voltage Standing Wave Ratio (VSWR), establishing the system's suitability for Sub-6 GHz 5G applications. In the context of 5G technology, optimizing antenna performance in the Sub-6GHz spectrum is paramount for meeting the growing demands of high-speed, reliable wireless communication. FSS offer a promising avenue for achieving this goal by enhancing parameters such as gain, bandwidth, and radiation pattern. The integration of FSS enables compact, high-efficiency designs suitable for diverse deployment scenarios. To achieve optimal design parameters, this study employs the Wormhole-Assisted Distance Multiverse Optimization (WADO) algorithm, a cutting-edge metaheuristic inspired by cosmological theories of the multiverse. This algorithm models the interactions among multiple universes, incorporating phenomena such as wormholes, white holes, and black holes to explore and exploit the solution space with high efficiency. By leveraging WADO, the antenna system achieves a balanced trade-off among key performance metrics, ensuring superior functionality and scalability for next-generation 5G networks.

3.1 WADO multiverse algorithm for antenna design optimization

The Wormhole-Assisted Distance Optimization (WADO) algorithm presents an innovative solution for addressing the complex demands of Sub-6GHz 5G antenna design, emphasizing strategic optimization through cosmologically inspired mechanisms.

3.2 Key features and mechanisms

1) Exploration and Exploitation Balance:

• The WADO algorithm excels in maintaining a balanced approach between exploration (searching new areas of the solution space) and exploitation (refining existing solutions).
• Black Holes: These mimic strong gravitational pull, drawing poteial solutions toward promising areas while avoidi prature convergence by preventing entrapment in local optima.
• White Holes: These iroduce new, diverse solutions into the search space, enhancing global exploration and ensuring coverage of the entire design spectrum.
• Wormholes: Acting as shortcuts, they enable instantaneous transitions between high-quality solutions, accelerating the search trajectory toward the global optimum and facilitating rapid convergence.

2) Adaptive Parameter Tuning:

• The algorithm dynamically adjusts two critical parameters:
  
  • Wormhole Existence Probability (WEP): Governs the frequency of shortcut paths, enhancing exploration during initial iterations and favoring exploitation in later stages.
  • Traveling Distance Rate (TDR): Controls the step size of the search, adapting as the optimization process progresses to ensure precision in refining solutions.
• This adaptive mechanism ensures that the algorithm is well-suited for tackling high-dimensional and precision-sensitive problems, such as the optimization of Sub-6 GHz 5G antennas.

3) Application in Frequency Selective Surface (FSS) Integration:

• The WADO algorithm demonstrates significant capability in optimizing antenna designs integrated with FSS, enabling:
  
  • Enhanced frequency selectivity for precise band targeting.
  • Improved radiation efficiency and gain.
  • Effective miniaturization of antenna structures while maintaining high performance.
• By leveraging a Pareto front-based multi-objective optimization approach, WADO efficiently balances trade-offs between conflicting performance metrics, such as bandwidth, gain, and miniaturization, ensuring an optimized and scalable design.

3.3 Significance to Sub-6 GHz 5G applications

The combination of exploration/exploitation balance, adaptive parameter tuning, and FSS integration makes WADO a powerful tool for addressing the stringent requirements of 5G antenna systems. Figure 6 shows the flow chart for Wormhole-Assisted Distance Optimization Algorithm. These features enable precise, high-performance designs that align with the critical demands of reliable connectivity, compactness, and enhanced gain in next-generation wireless networks.

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Figure 6. Flow chart for wormhole-assisted distance optimization algorithms

Step 1: Set up the population

• Initialize the population of universes (N) within the search space.
• Let 'y' represent the number of universes, and 'O' represent the number of parameters.

$N=\left[ \begin{matrix}   x_{1}^{1} & x_{1}^{2} & \cdots  & x_{1}^{0}  \\   x_{2}^{1} & x_{2}^{2} & \cdots  & x_{2}^{0}  \\   \vdots  & \vdots  & \vdots  & \vdots   \\   x_{y}^{1} & x_{y}^{2} & \cdots  & x_{y}^{0}  \\\end{matrix} \right]$

Step 2: Initialize Parameters

• Initialize the WEP and TDR

Step 3: Examine Universes

• Evaluate the fitness of each universe.
• Normalize the fitness values.
• Sort the universes according to the inflation rate to determine the best universe.

Step 4: Exploration Phase (White/Black Hole Tunnelling)

• The white/black hole tunnel mechanism allows universes to exchange objects.
• Use the roulette wheel mechanism to select white holes based on the following condition:

$x_{a}^{b}=\left\{ \begin{matrix}   x_{1}^{b}~~~~~~~~rn1<M\left( Na \right)  \\   x_{a}^{b}~~~~~~~~rn1\ge M\left( Na \right)  \\ \end{matrix} \right.$

where,

• $x_{a}^{b}$ is the b^th parameter of the a^th universe.
• M_a is the a^th universe.
• N(Ma) is the normalized inflation rate of the a^th universe.
• rn₁ is a random number between [0, 1].
• $x_{1}^{b}~$is the b^th parameter of the best universe.

Step 5: Exploitation Phase (Using Wormholes)

• Randomly move objects between a universe and the best universe using wormholes, ignoring the inflation rate:

                   $x_{a}^{b}=\left\{ \begin{matrix}   \left\{ \begin{matrix}   {{x}_{b}}+TDRX\left( \left( {{u}_{b-}}{{l}_{b}} \right)Xr{{n}_{4}}+{{l}_{b}} \right)~~~~~~r{{n}_{2}}<WEP  \\   {{x}_{b}}+TDRX\left( \left( {{u}_{b-}}{{l}_{b}} \right)Xr{{n}_{4}}+{{l}_{b}} \right)~~~~~~~~~~~~~~~~~~~~~~~~~~~~  \\ \end{matrix} \right.  \\   x_{a}^{b}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r{{n}_{2}}\ge WEP  \\ \end{matrix} \right.$

where,

x_b is the b^th parameter of the best universe.

l_b and u_b are the lower and upper bounds of the b^th variable.

$x_{a}^{b}$ is the b^th parameter of the a^thuniverse.

rn₂, rn₃, rn₄ are random numbers between [0, 1].

Step 6: TDR and WEP updates

Update WEP as follows:

$WEP=min+lX\left( \frac{max-min}{L} \right)$

The minimum and maximum values are min and max, respectively.

The number of iterations and the time for the current iteration are given by l and L, respectively.

Update TDR as follows:

$TDR=1-\frac{{{l}^{\frac{1}{q}}}}{{{L}^{\frac{1}{q}}}}$

where,

• During iterations, q indicates the exploitation accuracy.

Step 7: Reinitialize Universes

• Reinitialize the universes that fall outside the search area.

Step 8: Check Termination Criteria

• Repeat steps 3 to 7 until the termination criteria are met, which could be either the minimum error between subsequent inflation rates or reaching the total number of iterations.

Step 9: Identify Global Optimum Solution

• The global optimum solution is represented by the best universe found.

3.4 WADO-based FSS optimization

The WADO algorithm was employed to optimize the FSS array configuration (3×3 and 5×5) by balancing multiple performance objectives while adhering to physical constraints. The optimization process involved the following key steps:

The primary objectives for optimization were:

• Maximizing Gain: Achieve the highest possible gain at the target frequency (3.5GHz).
• Maximize the transmission coefficient (S₂₁) in the desired frequency band.
• Minimizing Return Loss (S₁₁): Ensure impedance matching below -10dB across the operating band (3.2-3.8GHz).
• Objective Function (F) is formulated as:

F=w₁(1-|S₁₁(f_center)|) + w₂(1-|S₂₁(f_center)|)

where,

• w₁, w₂ are the weight factors to prioritize transmission or reflection performance (e.g., 0.4 and 0.6),
• f_center is the centre frequency of operation.
• Enhancing Bandwidth: Maintain a bandwidth of at least 500MHz.
• Improving Radiation Efficiency: Target efficiency >80%.

These objectives were formulated into a multi-objective optimization problem, where WADO sought Pareto-optimal solutions.

3.5 Design variables

The key parameters optimized included:

• Unit cell dimensions (W×L): Ranged from 20mm to 30mm (constrained by the 25mm×25mm antenna size).
• Spacing between unit cells (d): Varied between 5 mm and 15mm to minimize mutual coupling.
• FSS layer height (H): Optimized between 20mm and 30mm for phase alignment (Eq. (1) in the manuscript).

3.6 Constraints

• Physical size constraints: L,W<λ/2,
• Avoiding mutual coupling degradation (spacing>0.3λ),
• Fabrication feasibility and standard substrate availability.
• Physical footprint: Total FSS size≤125mm×125mm.
• Fabrication limits: Minimum copper trace width =0.5mm.
• Substrate limitations: FR4 dielectric constant (ε_r=4.4) and thickness (1.6mm).

3.7 WADO optimization flowchart

Below is a flowchart summarizing the WADO-based optimization process for the FSS array:

key Steps:

1. Initialization:
   
   • Generate a population of candidate solutions (universes) with randomized unit cell dimensions, spacing, and FSS height.
   • Define bounds for variables (e.g., 20mm≤W≤ 0mm).
2. Fitness Evaluation:
   
   • Simulate each candidate design in CST Microwave Studio to evaluate S₁₁, gain, bandwidth, and efficiency.
   • Normalize performance metrics into a composite fitness score.
3. Exploration (White/Black Hole Phase):
   
   • Replace underperforming designs ("black holes") with high-performing ones ("white holes") via roulette wheel selection.
4. Exploitation (Wormhole Phase):
   
   • Refine top solutions using wormholes to accelerate convergence.
   • Adjust WEP (Wormhole Existence Probability) and TDR (Traveling Distance Rate) adaptively:
     • Early iterations: High WEP (0.9) for global exploration.
     • Late iterations: Low WEP (0.1) for local refinement.
5. Termination:
   
   • Stop when improvement in fitness <1% over 50 iterations or after 200 iterations.

Sensitivity Analysis of Key Parameters

The impact of design variables on performance, a sensitivity analysis was conducted as:

(a) Unit Cell Size (W×L)

• Larger unit cells (≥28mm) reduced resonant frequency but increased mutual coupling.
• 25mm×25mm (balanced gain and bandwidth).

(b) Spacing (d)

• Smaller spacing (<8mm) degraded gain due to coupling; larger spacing (>12mm) reduced reflectivity.
• d 10mm (3×3), 8mm (5×5).

(c) FSS Height (H)

• H=23.4mm maximized constructive interference (Eq. (1): ϕ_FSS−2βh=2Nπ).