Unlocking Antenna Performance: Harnessing the Power of the

Hahn-Banach Theorem in Wireless Communication Systems

Muhammad Uzair

1 a

, Sijjad Ali

2 b

, Asad Ali

1 c

, Hamza Amir

3 d

, Rana Zaki Abdul Bari

Hamid Sharif

1 e

, Maryam Jamil

4 f

, M. Hunza

4 g

, Nabel Akram

5 h

and Sharoﬁddin Allaberdiev

2 i

College of Electronics and Information Engineering, Shenzhen University, 518060, Guangdong, China

College of Computer Science and Software Engineering, Shenzhen University, 518060, Guangdong, China

School of Media and Communication, Shenzhen University, 518060, Guangdong, China

College of Physics and Optoelectronic Engineering, Shenzhen University, 518060, Guangdong, China

School of Government, Shenzhen University, 518060, Guangdong, China

Keywords:

Antenna Design, Hahn-Banach Theorem, Optimization, Wireless Communication.

Abstract:

This paper presents a novel approach for improving the performance of the antenna in wireless communication

systems through the utilization of the Hahn-Banach Theorem. With advancements of such standards as 5G and

B5G in design-related issues, traditional methods are typically inadequate. Applying the Hahn-Banach Theo-

rem results in a strong mathematical framework that augments several vital antenna parameters including gain,

efﬁciency, bandwidth, and radiation patterns. The approach takes solutions from limited to large design spaces,

allowing the search for new conﬁgurations within tight constraints. Results show substantial advancement in

antenna performance, creating better, more reliable progressions. This interdisciplinary method connects the-

oretical mathematics with the engineering solutions making a great step forward for practical communication

technologies. This guarantees excellent linearity and overall performance which is very important for wireless

communication signal integrity, impacting future antenna technology and wireless communication research

and development.

1 INTRODUCTION

Antennas are integral to modern wireless communi-

cation systems, supporting diverse applications from

mobile communications to IoT devices (Alexiou and

Haardt, 2004). As we transition to 5G and beyond

(B5G), demand for faster data rates and lower la-

tency intensiﬁes (Hong et al., 2017). Traditional an-

tenna designs struggle to meet the advanced require-

ments of B5G networks, such as multi-band operation

and massive MIMO capacities (Jamil et al., 2010).

Consequently, researchers are turning to mathemati-

cal optimization methods like the Hahn-Banach The-

orem to improve antenna performance (Aharon and

https://orcid.org/0009-0002-6812-7799

https://orcid.org/0000-0002-9141-8837

https://orcid.org/0009-0004-5399-0156

https://orcid.org/0009-0008-6306-9415

https://orcid.org/0009-0006-9695-4600

https://orcid.org/0009-0008-2067-4113

https://orcid.org/0000-0003-3604-7874

https://orcid.org/0009-0002-8815-6124

https://orcid.org/0000-0001-6087-8024

Nemirovski, 2001). These methods offer systematic

frameworks to explore design parameters and con-

straints, identifying optimal conﬁgurations (Alateewe

and Nagy, 2024).

They allow for the evaluation of various intri-

cate performance criteria and trade-offs, resulting in

Pareto-optimal solutions (Wang et al., 2024). In ad-

dition, uncertain reality environment management is

resolved by mathematical design approach (Cheragh-

inia et al., 2024). Many modern antenna techniques

such as metamaterials and reconﬁgurable antennas

are incorporated into it (Kumar et al., 2021), improv-

ing antenna performance in B5G networks.

Our methodology allows for the creation of effec-

tive wireless systems for multiple B5G uses, URIIC,

and big IoT links (Singh et al., 2024). It also guides

development of sophisticated signal processing algo-

rithms and network protocols designed for B5G sys-

tems (Sufyan et al., 2023). In general, utilization of

mathematical optimization strengthens antenna devel-

opment, stimulates innovation, and deﬁnes an infras-

tructure of communication networks.

340

Uzair, M., Ali, S., Ali, A., Amir, H., Bari, R., Sharif, H., Jamil, M., Hunza, M., Akram, N. and Allaberdiev, S.

Unlocking Antenna Performance: Harnessing the Power of the Hahn-Banach Theorem in Wireless Communication Systems.

DOI: 10.5220/0012795100003758

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 14th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2024), pages 340-347

ISBN: 978-989-758-708-5; ISSN: 2184-2841

2 ANTENNA DESIGN METHODS

2.0.1 Empirical and Numerical Methods

Methods are practical for antenna designers who will

work with these designs on and on, reﬁning them in

the process through experience. On the other hand,

for complex antenna structures and detailed electro-

magnetic analysis requirements, numerical methods

such as Finite-Difference Time-Domain (FDTD) sim-

ulations (Thaher et al., 2020) are invaluables. They

offer accurate and rapid analyses, supplementing em-

pirical approaches and extending the toolkit of the de-

signer for best performance.

∇ × E = −

∂B

∂t

, ∇ × B = µ

J + µ

∂E

∂t

(1)

Numerical methods, illustrated in (Zhu et al.,

2023), take standard antenna conﬁgurations such as

dipoles and Yagi-Uda arrays as the basic geome-

tries for further modiﬁcation. FDTD simulations dis-

cussed in (Zhu et al., 2023) enable analytical accu-

racy through discretization of space and time domains

for solving Maxwell’s equations to present a thor-

ough modeling of antenna performance parameters on

a computational grid;

∇ × E = −

∂B

∂t

(2)

This equation presents the curl form of electric

ﬁeld (E), which is equal to the negative rate of change

of the magnetic ﬂux density (B). It demosntrates how

a time-varying magnetic ﬁeld gives rise to an electric

ﬁeld, which is a basic principal of electromagnetic in-

duction.

∇ × H = J +

∂D

∂t

(3)

The magnetic ﬁeld of the curl (H) is created

among electric current (J) and the rate of change of

the electric displacement ﬁeld (D). This equation

generalizes Ampere’s Law to include displacement

current, which considers changes in the electric

ﬁeld (Mittra, 2018). FDTD iterative updates electric

and magnetic ﬁelds at discrete points to model

wave propagation and electromagnetic phenomena,

making it indispensable in modern antenna design.

For instance, updating electric and magnetic ﬁelds

relies on their respective curls. This discretization is

typically represented as:

(i, j, k)

n+1

= E

(i, j, k)

− ∆t



(i, j+1,k)

−H

(i, j,k)

∆y

−

(i, j,k+1)

−H

(i, j,k)

∆z



(i, j, k)

n+1

= H

(i, j, k)

+ ∆t



(i, j+1,k)

−E

(i, j,k)

∆y

−

(i, j,k+1)

−E

(i, j,k)

∆z



(4)

where E

and H

is the electric ﬁeld component

and magnetic ﬁeld component, n is the time step in-

dex, and i, j, k are the indices of the grid points in the

x, y, and z directions, respectively. Where ∆t is the

time step increment, and ∆x, ∆y, and ∆z are the step

increments in each direction in space.

The empirical methods lay solid basis for antenna

design, particularly for conventional types of anten-

nas. The power of numerical methods, such as FDTD

in solving Maxwell’s equation in practically any ge-

ometry, is crucial in designing the modern complex

antenna systems(Alexiou and Haardt, 2004).

2.0.2 Genetic Algorithms (GA)

GA are modeled after biological evolution, using

mechanisms like selection, crossover, and mutation.

Population of potential designs in the antenna design

is evolved for several generations until the optimal so-

lutions are found.

Fitness Function in GA:

f (x) = Performance(x) (5)

where x represents the antenna parameters.

2.0.3 Particle Swarm Optimization (PSO)

PSO simulates the social behavior of birds or ﬁsh to

optimize a problem. Particles move through the so-

lution space, adjusting their trajectories based on per-

sonal and communal experiences(Sehrai et al., 2020).

PSO Equations:

Position Update:

(t + 1) = x

(t) + v

(t + 1) (6)

Velocity Update:

(t + 1) =w · v

(t) + c

· r

· (p

best

− x

(t))

+ c

· r

· (g

best

− x

(t))

(7)

we considered the case where i is a particle in-

dex, x

an d v

are positions and velocities, p

best

and

best

are best known positions, r

, r

are two random

numbers, and c

, c

are learning factors. They are es-

pecially efﬁcient in regards to problem spaces which

consist of several dimensions for example than tradi-

tional methods could not be so practical (Thaher et al.,

2020).

Unlocking Antenna Performance: Harnessing the Power of the Hahn-Banach Theorem in Wireless Communication Systems

341

3 METHODOLOGY

3.1 Hahn-Banach Theorem

The Hahn-Banach theorem extends bounded linear

functionals from subspaces to the entire space while

preserving their norms, playing a crucial role in math-

ematics and various ﬁelds (Ben-Tal and Nemirovski,

2021). Its signiﬁcance lies in functional analysis and

ﬁnds applications in optimization, information trans-

mission, and antenna design. This ensures continuous

operationalization of metric functions on normed vec-

tor spaces without altering their norms, a characteris-

tic vital for numerous applications;

| f (x)| ≤ C||x||, ∀x ∈ U (8)

F(x) = f (x), ∀x ∈ U (9)

|F(x)| ≤ C||x||, ∀x ∈ V (10)

here, f denotes the functional on U, F is its exten-

sion on V , and C is a constant. Provide the descrip-

tion of the antenna design problem with speciﬁcations

(directivity, bandwidth, radiation pattern, interference

rejection); use the Hahn-Banach Theorem for strate-

gic extension in order to overcome performance lim-

itations with the design constraints (Abdullah et al.,

2019).

3.2 Problem Formulation

Design a compact antenna for portable 5G devices,

optimizing gain, bandwidth, linearity, and adhering to

strict weight constraints;

• Gain (G): Aim for a high gain to ensure robust

signal reception and transmission over distances,

targeting a minimum gain of 6 dBi.

• Bandwidth (BW ): The antenna must support

a wide bandwidth to accommodate the 5G fre-

quency range, speciﬁcally from 3.3 GHz to 3.8

GHz, to cover various 5G bands.

• Linearity: Ensure high linearity to reduce signal

distortion, which is crucial for maintaining the in-

tegrity of high-speed data transmission in 5G net-

works.

• Weight (W ): Due to the portable nature of the

device, the antenna’s weight should not exceed 20

grams.

3.3 Solution Approach Using the

Hahn-Banach Theorem

Proposing a novel approach using the Hahn-Banach

Theorem to tackle design challenges in compact,

high-performance antennas for portable 5G devices,

optimizing gain, bandwidth, linearity, and adhering to

weight constraints.

3.3.1 Deﬁning Design Space and Performance

Metrics

Let V represent the vector space of all possible an-

tenna designs, and U ⊆ V the subspace (Ben-Tal and

Nemirovski, 2021) of initially feasible designs. The

performance metrics are deﬁned as functions map-

ping designs to real values representing gain (G),

bandwidth (BW ), linearity (L), and weight (W ).

The theorem is applied to extend performance

evaluation functionals (Jamil et al., 2010) from U to

the entire space V , facilitating the exploration of in-

novative designs. This extension ensures that:

| f (x)| ≤ p(x), ∀x ∈ U → ∀x ∈ V

The expression | f (x)| ≤ p(x), ∀x ∈ U → ∀x ∈V sig-

niﬁes that the condition imposed by p(x) on f (x) in

the subspace U is preserved as f (x) is extended across

the entire space V . where as,

• f (x): Represents a functional that evaluates the

performance of an antenna design x, such as its

gain, efﬁciency, or bandwidth.

• U: Denotes the initial subspace of feasible de-

signs, satisfying basic performance criteria or

constraints.

• V : Represents the entire design space, includ-

ing more innovative or unconventional designs be-

yond those in U.

• p(x): Deﬁnes a bound for the performance eval-

uation functional f (x), ensuring that the evalua-

tion does not exceed certain physical, regulatory,

or performance-related limits.

The Hahn-Banach Theorem expands antenna de-

sign optimization possibilities while maintaining per-

formance within speciﬁed bounds (Banks and Ku-

nisch, 2012). Systematic search enables the identiﬁ-

cation of enhanced performance measures within set

constraints (Jiang et al., 2019).

4 MATHEMATICAL MODELING

The mathematical modeling of antenna graph consists

of the example of the antenna’s electromagnetic char-

acteristics through various mathematical equations.

Key factors of this modeling included radiation pat-

tern, impedance, beneﬁt, and efﬁciency.

SIMULTECH 2024 - 14th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

342

Radiation Pattern. The radiation pattern is repre-

sented by means of:

E(θ, φ) = f (θ, φ) (11)

where E(θ, φ) denotes the electric ﬁeld intensity at an-

gles θ and φ.

Impedance. Antenna impedance, combining resis-

tance and reactance, is given by:

Z = R + jX (12)

where Z is the impedance, R is resistance, and jX is

reactance.

Gain. The gain of an antenna is deﬁned as:

G =

4πU(θ, φ)

(13)

where G is the gain, U(θ, φ) the radiation intensity,

and P

the input power.

Efﬁciency. Efﬁciency is the ratio of the power radi-

ated to the power input:

η =

rad

(14)

where η is efﬁciency, P

rad

is radiated power, and P

is input power.

Bandwidth. The bandwidth of an antenna is ex-

pressed as:

BW = f

− f

(15)

where BW is bandwidth, and f

, f

are the lower and

upper frequency limits, respectively. Mathematical

modeling is crucial in antenna design, providing in-

sights into performance and aiding in the optimiza-

tion of antenna characteristics. This modeling forms

the basis for simulation and analysis in the antenna

design process.

4.1 Performance Speciﬁcations

The antenna design must meet the following speciﬁ-

cations:

• Desired Gain: Minimum of 06 dBi.

• Bandwidth: Operate effectively from 3.3 GHz to

3.8 GHz.

• Radiation Pattern: Ensure consistent perfor-

mance across orientations, focusing on omni-

directional or directional patterns.

• Interference Rejection: Incorporate features to

minimize electromagnetic interference.

The main challenge is optimizing antenna gain

within size and weight limits(Abdullah et al., 2019),

demanding a delicate balance between performance

and dimensions, necessitating innovative design and

strategic optimization techniques.

4.2 Functional Analysis

Apply the Hahn-Banach Theorem to extend a

bounded linear functional from a subspace (e.g., spe-

ciﬁc antenna conﬁguration) to the entire vector space

(e.g., design space)(Ben-Tal and Nemirovski, 2021).

This extension facilitates advanced optimization of

key antenna characteristics, enabling efﬁcient utiliza-

tion of complex design spaces.

4.3 Functional Extensions Using

Hahn-Banach Theorem

4.3.1 Radiation Pattern

Simpliﬁed Functional in U:

(x) = Integration(E(θ, φ;x)) (16)

Extended Functional in V:

(y) = ExtendedIntegration (E(θ, φ; y)) (17)

4.3.2 Impedance

Simpliﬁed Functional in U:

(x) = CalculateImpedance(x) (18)

Extended Functional in V:

(y) = ExtendedCalculateImpedance(y) (19)

4.3.3 Gain

Simpliﬁed Functional in U:

(x) = CalculateGain(x) (20)

Extended Functional in V:

(y) = ExtendedCalculateGain(y) (21)

4.3.4 Efﬁciency

Simpliﬁed Functional in U:

(x) =

rad

(x)

(22)

Extended Functional in V:

(y) =

rad

(y)

(23)

The objective is to ﬁnd an antenna design y

∗

in V that

optimizes the extended functional, considering real-

world constraints.

Unlocking Antenna Performance: Harnessing the Power of the Hahn-Banach Theorem in Wireless Communication Systems

343

4.4 Mathematical Formulation for

Optimizing y

∗

in V

We aim to ﬁnd an optimal antenna design y

∗

in V ,

which involves solving the following optimization

problem:

4.4.1 Extended Functional Formulation

Find y

∗

in V such that: (24)

maxF

total

(y) (25)

subject to:

(y) ≥ Threshold

, (26)

(y) ≈ Desired Impedance, (27)

(y) ≥ Threshold

, (28)

(y) ≥ Threshold

, (29)

and other real-world constraints.

Where:

• F

total

(y) is a combined functional representing

overall performance.

• F

, F

are extended functionals for radi-

ation pattern, impedance, gain, and efﬁciency re-

spectively.

• Thresholds and desired values are set based on

real-world requirements.

4.4.2 Optimization Criteria

• The optimization seeks to maximize F

total

(y)

while meeting all individual functional require-

ments.

• This process involves balancing various antenna

characteristics within the constraints of the com-

plex design space V .

Through advanced mathematical equations and the

application of the Hahn-Banach Theorem, the pro-

cess of optimizing antenna design in a complex space

V addresses both theoretical and practical aspects,

leading to the determination of an optimal design y

∗

(Banks and Kunisch, 2012).

Implement numerical simulations to validate the

results obtained through the Hahn-Banach-based op-

timization.

5 RESULTS ANALYSIS

Applying the Hahn-Banach Theorem to antenna de-

sign and optimization has yielded signiﬁcant im-

provements. This mathematical framework has been

leveraged to observe beneﬁts through advanced sim-

ulations, enhancing the helical signal’s creation, dis-

tortion correction, and overall performance.

Figure 1: Radiation Pattern of a Nonlinear Antenna Array.

Magnitude in Decibels.

Figure 1, illustrates the enhancement process for

two distinct 5G frequency bands—Sub-6 GHz and

mmWave—showcasing signal optimization,A statis-

tical analysis comparing signal-to-noise ratio (SNR)

and mean squared error (MSE) before and after opti-

mization demonstrates the effectiveness of the Hahn-

Banach theorem in reducing interference and enhanc-

ing signal quality. Table 1, lists the unique time and

frequency settings used within the evaluation.

In signal processing (Table 3) linearity ensures the

output remains proportional to input, critical for sig-

nal integrity and avoiding nonlinear distortions which

can alter signal quality. The enhancement process

aims to minimize such distortions, enhancing linear-

ity as demonstrated by improved SNR and reduced

MSE in the enhanced signal, indicating a closer align-

ment to the original signal.

Figure 2: Comparison of Original and Distorted Signals for

a Dipole Antenna at Third Harmonic Order.

Figure 2 shows the original signal (blue line) and

the noise signal (red dashed line) before optimization.

The stable, undisturbed signal is represented by the

consistent helical shape of the blue line, while the red

dashed line indicates signiﬁcant deviation, signaling

distortion. As signal order increases, distortion and

randomness worsen, directly impacting antenna efﬁ-

ciency and causing receiver lag, resulting in increased

SIMULTECH 2024 - 14th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

344

Table 1: Summary of Signal Characteristics Before and After Enhancement for Sub-6 GHz and mmWave 5G Frequencies.

Parameter Value Description

Frequencies (f) {’Sub-6 GHz’: 3.5 x

, ’mmWave’: 28 x

}

Frequency bands for 5G in GHz, including Sub-6

GHz and mmWave frequencies.

Time (t) np.linspace(0, 1, 1000) Time vector used for signal simulation, spanning from

0 to 1 second with 1000 points.

distortion frequency

(fz)

2 x 10

Frequency of the distortion signal in Hz.

distortion level

(Lmin)

Random (0.3 to 0.6) Level of the distortion added to the original signal,

adjusted for visibility.

Table 2: Comparison of Original and Distorted/Optimized Signals for a Third-Order Harmonic.

Parameter Value Description

Time (t) 0.1 to 100 A vector representing time from 0 to 1 second with

1000 sample points.

Frequencies (f) [1, 2, 3] A list of frequencies (in Hz) for which the signals will

be simulated.

distortion level

(Lmin)

Random (0.3) The level of distortion applied to the original signal.

Order (Harmonics) 3 The harmonic order used to modify the frequency

component of the original signal.

interference. Higher signal order complexity poses

optimization challenges, with the distorted signal de-

viating signiﬁcantly from the original signal, leading

to degraded efﬁciency.

As indicated in Table 2, Figure 2 illustrates the

contrast between the pre-optimization noisy signal

(red dashed line) and the stable original signal (blue

line). The chaotic pattern of the red line signiﬁes dis-

tortion, while the constant helix of the blue line de-

notes an unchanged signal. This distortion degrades

antenna performance, exacerbating interference and

receiver delay, particularly as signal order increases,

set to 3 according to Table 2. Python simulations

conﬁrm that higher order signals present greater chal-

lenges to signal ﬁdelity during optimization.

Figure 3: Radiation Pattern comparison of the Baseline and

Enhanced Antenna Array.

The Figure 3, shows a blue curve for the clean sig-

nal and a red dashed curve for the same signal after it

has been enhanced. The optimization, inﬂuenced by

the Hahn-Banach Theorem, effectively reduces noise,

bringing the red signal closer to the original blue one,

demonstrating the theorem’s utility in improving sig-

nal clarity at receiver end.

Figure 4: Signal Distortion in a Dipole Antenna Across

three Orders.

The Figure 4, depict 3D plots showing how the

signal amplitude of a dipole antenna changes over

time, labeled as ”Time” and ”Signal Amplitude.”

Each plot contrasts an original signal in solid lines

with a noise added signal version in dashed lines

across three orders:

Order 1: The blue lines indicate a clear deviation

of the distorted signal from the original, highlighting

noticeable distortion.

Order 2: The green lines show less deviation than

Unlocking Antenna Performance: Harnessing the Power of the Hahn-Banach Theorem in Wireless Communication Systems

345

Table 3: Comparison of SNR and MSE Metrics for Different Frequency Bands.

Frequency Band Metric Original Distorted Enhanced

Sub-6 GHz SNR (dB) 16.96 8.70 13.12

MSE - 0.0675 0.0244

mmWave SNR (dB) 16.96 8.88 13.19

MSE - 0.0648 0.0240

Order 1, suggesting less distortion.

Order 3: The orange lines display the greatest

deviation, implying the most signiﬁcant distortion.

These visualizations illustrate the signal’s degradation

with increasing order, providing insight into the an-

tenna’s performance and signal degradation when it

was receive at receiver ends. The original signals in-

formation is missing or undetectable at this distortion.

Figure 5: Signal processing of an antenna at three harmonic

orders, showing original (solid), distorted (dashed), and en-

hanced (dotted) signal states.

The Figure 5, displays curves for original, dis-

torted, and enhanced signals across three frequency

levels, known as orders. With each order representing

a higher frequency, the distortion grows more severe

and severe that cause for the mismatched information

at receiver ends, yet the enhanced signal—improved

using the Hahn-Banach Theorem that will enhance

the signal at higher frequencies and mitigate the noise

and closely mirrors the original curve, indicating ef-

fective noise reduction for clearer communication.

Figure 6: 3-D Visualization of Antenna response: tracking

input vs. Output alerts over time.

The Figure 6, is a 3D plot that compares the input

and output signals of an antenna. The solid blue line

represents the consistent input signal, while the red

dashed line shows how the antenna has altered this

signal, indicating the antenna’s response over time.

The vertical gaps between the lines suggest changes

in signal strength due to noise/distortion, and the hori-

zontal spread may point to timing or phase shifts. This

visualization helps assess the antenna’s performance.

Figure 7: Enhancing sign Integrity: Hahn-Banach

Theorem-driven Optimization of Antenna Output.

The second Figure 7, titled ”Optimized Antenna

Response” shows a 3D plot with a solid blue sur-

face for the input signal and a larger, more varied

red dashed surface for the output signal, indicating

signiﬁcant changes made during optimization. The

culmination of results given in Table 3 highlights the

proposed method’s substantial enhancement of signal

linearity, marked by reduced distortion and noise, af-

ﬁrming the technique’s proﬁciency in preserving sig-

nal integrity across diverse 5G frequencies. Using the

Hahn-Banach Theorem inside the signal optimization

process targets to limit these variations enhancing the

antenna’s performance by way of making the output

more carefully ﬁt the input.

6 CONCLUSION, LIMITATIONS

AND ISSUES, FUTURE WORK

The Hahn-Banach Theorem offers a functional analy-

sis approach that enhances antenna design, accelerat-

ing 5G development and broadening application hori-

zons from eMBB to URLLC and mMTC. This break-

through calls for an evolution in wireless communi-

cation, elimination of the current hurdles, and setting

SIMULTECH 2024 - 14th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

346

of new connectivity standards. Such designs are inte-

gral to supporting key 5G applications including au-

tonomous vehicles, smart manufacturing, and exten-

sive IoT networks, underscoring their importance in

future wireless technologies.

6.1 Limitations and Issues

• Complexity: Implementing Hahn-Banach

Theorem-based designs requires advanced math-

ematical expertise, potentially limiting practical

application.

• Scalability: Adapting designs to real-world sce-

narios, especially in urban environments, may

pose challenges.

• Resource Demands: Computational requirements

could hinder deployment in resource-constrained

settings.

6.2 Future Work

• Optimization: Develop tailored optimization al-

gorithms to streamline design processes.

• Machine Learning Integration: Explore integrat-

ing machine learning for adaptive antenna sys-

tems.

• Experimental Validation: Conduct real-world val-

idation to ensure performance across environ-

ments.

ACKNOWLEDGEMENTS

We sincerely thank each author, participant, and col-

league for their invaluable contributions to this article.

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