Enhancing Gain Through Optimal Antenna Element Distribution in a Thinned Array Configuration

This paper presents an array thinning approach for a 25-element antenna array arranged in a $5\times5$ grid at 5.4 GHz. Our goal is to eliminate a maximum number of antenna elements with minor gain loss and hence reduce the array size, weight, cost, and power requirements. Consequently, the space saved by the thinned array configuration presents opportunities to integrate additional antennas and hardware, allowing for a low-profile antenna-in-package. Our study showed that a 64% array reduction (from 25 to 9 probe-fed patch antennas) achieved an array gain comparable to a full array configuration. As such, various 9-element configurations for testing were generated through the thinning process and optimized using the genetic algorithm. These configurations were then validated using full-wave simulations. Results show that all configurations that preserved the effective area while maintaining symmetry along all axes showed a minimal effect on gain reduction. Specifically, the best thinning configuration resulted in a loss of only 1.82 dB in simulation at broadside compared to a fully populated $5\times5$ array. The exact configuration also showed beam scanning performance from −45° to +45° (viz. 90°). A prototype was fabricated and tested for each of the thinned configurations. The measured gain of the optimal 9-element thinned array configuration showed excellent agreement with the simulations.


I. INTRODUCTION
T HE GROWING need for reliable and efficient data transfer over long distances in modern communication systems has led to the development of high-gain antenna arrays [1], [2], [3], [4], [5].However, these arrays with multiple antenna elements, require complex back-end circuitry to ensure proper feeding.To address this challenge, unconventional antenna designs have been considered, such as thinning and sparse arrays [6] shown in Fig. 1.Antenna array thinning selectively deactivates some elements in a pre-existing antenna array while maintaining the desired performance characteristics.On the other hand, sparse antenna arrays allocate elements more flexibly without restrictions to a grid, resulting in improved cost and physical feasibility compared to traditional antenna arrays.
There have been several studies on how to practically implement sparse antenna array configurations.For instance, in [7], sparse antenna arrays, designed with a separation greater than half-wavelength, were shown to effectively suppress the side lobe levels (SLL) in the focal plane, demonstrating improved performance compared to other antenna array configurations.In [8], a cross-entropy optimization method was used for a sparse antenna array design to measure a target's radar cross-section (RCS).The optimization was subject to constraints on the number of antenna elements, space, and separation distance.Other applications of sparse antenna arrays include unmanned aerial vehicle (UAV) localization [9].In this application, a dome antenna was divided into sections.Each section was optimized using a multiple objective particle swarm optimization (MOPSO) with constraints on the angle of arrival error and peak SLL.In [10], a sparse antenna array with a Fibonacci spiral element, for beamforming network simplification and scalability, achieved less intrusive electronic design for satellite applications.However, sparse antenna arrays are challenging to design, inefficiently utilize space, and precise control over their radiation pattern is even more daunting.
The alternative to sparse array synthesis is antenna array thinning.Given that the thinning consists of deactivating array elements, it is expected for the gain to decrease since the latter depends on the total number of elements in the antenna array [11].Therefore, different techniques have been established to minimize this gain loss after removing active elements.For instance, some research efforts on thinning have focused on the effective area effects, as seen in [12].This work used a modified genetic algorithm (GA) to determine the optimal configuration.It was established that the corner elements of the array are the most influential in preventing significant losses after thinning due to their influence on the effective area.
Despite the gain reduction challenge, antenna array thinning is beneficial for millimeter wave (mmW) applications since it allows for narrower beamwidth and lower SLL.For example, in [13], a 288-element antenna array was gradually thinned to a 128-element array with optimized positions, reducing the design complexity and decreasing the SLL.Notably, parasitic patch antennas were added to improve the overall performance.
Moreover, various GA modifications for sparse and thinned antenna array designs have been suggested to solve particular optimization problems related to sparse rectangular [14] and concentric ring arrays with circular boundaries [15].Aside from the GA, other algorithms, including Social Network Optimization (SNO), Particle Swarm Optimization (PSO), Stud-Genetic Algorithm (Stud-GA), Boolean PSO with velocity mutation (BPSO-vm), iterative convex optimization, iterative fast Fourier transform (FFT), GA based and sparse sub-arrays, and binary SNO (bSNO), have also been used to design thinned and sparse arrays [13], [16], [17], [18], [19], [20].Particular to sparse arrays, some synthesis methods can also be based on tapering power.As shown in [21], optimal spacing is proportional to the reference tapering power.These optimization methods are beneficial for synthesizing sparse antenna arrays but face challenges with prolonged convergence times.
To solve the convergence time issue, [22] used the GA to split the array into zones for a better convergence time.Similarly, in [23], an iterative Fourier technique demonstrated a high computational speed for SLL synthesis in periodically spaced arrays.However, the thinning percentage is not high enough in these optimizations to consider using the saved space for additional hardware or applications.
Furthermore, most of these optimizations do not consider realized gain.Rather, they focus on optimizing the realized gain through directivity.In [24], a generalized expression for the directivity is derived to overcome the computing time constraint for large arrays.The authors considered element type, array geometry, complex excitation, mutual coupling, scan angle, and embedded element pattern in the study.Also, in [25], an array dilation technique is proposed for array thinning.The results show a lower SLL without tapering.They also achieved wide scanning and were able to consider the gain through a simplified directivity equation.In [26], Bayesian Compressive Sensing and Array Dilation are combined to improve tapering efficiency.The optimization places constraints on aperture length and thinning levels, achieving wide scanning and low losses in directivity.While thinned and sparse array syntheses have been thoroughly investigated in previous research efforts, a 50% thinning percentage was only achieved.In addition, the previously mentioned designs do not save enough space for additional hardware, posing a challenge for space-constrained applications like cube satellites (CubeSat).
This paper presents a novel optimization strategy for a 25element microstrip patch antenna array utilizing the antenna array thinning concept.Our optimization process objective is to minimize the number of elements while retaining a high realized gain.Notably, our thinned antenna array configuration saves space for additional hardware or other frequency bands, making it ideal for future CubeSats.We start with a fully populated 5 × 5 patch antenna array and gradually thin the array while preserving the effective area.In particular, we remove 4, 8, and 12 elements, then stop at removing 16 elements while the rest of the antenna elements are left active in the array, as shown in Fig. 2. Keeping 9 active antenna elements allows us to satisfy our criteria of a symmetrical configuration with one central element.Simulated and measured results show that, despite having an equivalent number of elements, configurations that have more elements located along the border of the array exhibit minimal changes in gain compared with the fully populated antenna array (25 elements).Using the same configuration, we checked the scanning performance from −45 • to +45 • (viz.90 • ).Results show excellent gain bandwidth (≤ 3 dB compared to broadside) within the scanning range.To validate our result, we used a GA-based optimization to compare 4 configurations of equal effective area.We verified that our presented configuration had the best-realized gain performance.A prototype was fabricated and tested to verify our designs.
This paper is divided as follows.Section II discusses the theoretical basis for our array thinning technique.Section III explains how the GA generated different 9element configurations and presents the simulation results obtained for each thinned antenna array configuration.The measurement results and the corresponding measurement setup used to validate the presented technique are provided in Section IV along with a discussion of our results.Finally, in Section V, the paper summarizes the key findings and their implications.

II. ARRAY THINNING TECHNIQUE
The radiation pattern S(θ, φ) of a uniform planar array is computed using where G is the gain of a single element and AF is the array factor.For an N × M element array, AF is expressed as: e jk(md x sin θ cos φ+nd y sin θ sin φ) ( where d x and d y are the inter-element spacing between the elements in the x and y directions, respectively.κ is the wave number.The elevation and azimuth angles are θ and φ, respectively.The weighting matrix (W mn ) represents the excitation magnitude for each element in the m by n antenna array.W mn is unitary in uniformly fed arrays.Conversely, sparse/thinned antenna arrays exhibit varying mutual coupling effects between elements, resulting in nonuniform gain distributions.As a result, most antenna array optimizations focus only on optimizing the array factor, neglecting physical gain optimization by considering each antenna element to be a point source.Optimization methods utilize (2) as an objective function and W mn as part of the optimization process.
In the context of antenna arrays, the goal is to maximize the overall gain of the array, considering limited aperture dimensions.As such, reducing the physical size and weight of the array through thinning is a crucial step toward achieving higher performance while minimizing the system's footprint.
In this work, our thinning strategy: 1) Preserves effective area.
3) Preserves the center antenna element.
To achieve this, we systematically remove elements that contribute minimally to the effective area while maintaining a symmetrical configuration, as shown in Fig. 2. The importance of symmetry in the thinned antenna array cannot be overstated.It is a critical factor for achieving a symmetrical radiation pattern and reducing the occurrence of grating lobes.Specifically, a symmetrically spaced and excited thinned antenna array ensures predictable and reliable performance, simplified manufacturing, and faster signal processing.The symmetric radiation pattern is particularly advantageous in applications that require a uniform response, such as radar and communication systems.Furthermore, it should be noted that the central antenna element exhibits the highest mutual coupling effects among all the elements in the array, making it a key contributor to the overall gain of the antenna system.Therefore, our study seeks to provide a detailed understanding of how removing antenna elements affects the gain pattern of a thinned antenna array while emphasizing the fundamental importance of maintaining certain factors, including a symmetrical structure and central elements.

III. SIMULATION OF THINNED CONFIGURATIONS
We designed a uniform planar array with probe-fed patch antennas at 5.4 GHz using a full-wave simulator.The centerto-center distance between each patch is λ/2, where λ is the wavelength at 5.4 GHz.Each patch has dimensions of 17.25 mm × 17.25 mm.Each unit cell of the array is a square of 27.6 mm × 27.6 mm and printed on Rogers RT/Duroid 5880.The total size of the 25-element array is 138 mm × 138 mm.According to antenna theory, an antenna's gain is proportional to the effective aperture of the antenna.Therefore, by removing the elements from the antenna array while simultaneously preserving the effective area, a similar gain pattern can be obtained as in a fully populated antenna array.We are employing patch antennas for simulation purposes, but it is important to note that the methodology can be applied to any directional antenna array with a confined aperture.Furthermore, as the element spacing is frequency-dependent, the design can be proportionally adjusted when working with different frequencies.

A. ARRAY THINNING PROCESS
We gradually removed antenna elements shown in Fig. 2, where N is the number of removed elements (N = 4, N = 8, N = 12, and N = 16 indicate 4, 8, 12, and 16 elements removed, respectively).As shown in Fig. 3, removing 4 elements leads to 0.76 dB gain reduction, 8 elements to 1.35 dB, and 12 elements to 1.74 dB gain reduction compared with the full antenna array (N = 0).As N = 12 removes almost half of the antenna elements, we expected about a 3 dB of loss, but there was only a 1.74 dB loss in the total gain.Therefore, we continued removing antenna elements beyond N = 12 to check the optimum difference in realized gain.However, removing more than 16 elements from the antenna array prevents us from maintaining symmetry while keeping a central element.Therefore, we proceed with a study on 3 different N = 16 configurations, where each configuration has 9 elements but covers different effective areas, as shown in Fig. 4. The first configuration (C1) is a conventional 3-by-3 antenna array, the second configuration (C2) has more central elements, and  the third configuration has more elements populated along the border of the array (C3).
The simulated results show a realized gain of 14.61 dBi, 16.42 dBi, and 17.27 dBi for configurations C1, C2, and C3, respectively, as shown in Fig. 5. Notably, configuration C3 exhibits the highest gain despite having equivalent elements to C1 and C2.Contrary to expectations based on the radiation pattern equation, we observe that we can achieve greater gains and more directive beams by spacing the array elements in configurations C2 and C3.This instance is attributed to the larger spacing and increased effective area resulting from more elements around the edges of the original array.Foremost, the superiority of C3 over C2 can similarly be explained by the former's larger number of elements located at the edge compared to the latter's more centralized clustering.Our use of full-wave simulations allows us to account for mutual coupling without using an optimization algorithm.These findings have significant implications for designing and optimizing antenna arrays and underscore the importance of carefully considering the element placement and spacing in achieving optimal performance.Compared with the fully populated array (N = 0), configuration C3 has 64% fewer elements, yet, it only loses 1.82 dB of realized gain.With this saved space, C3 provides symmetric spacing to integrate different band antennas or hardware.The maximum allocated spacing is 130 cm 2 .This result shows that a trade-off can be made between the 1.82dB of realized gain and the saved space.However, to further validate this conclusion, the next section focuses on GAgenerated configurations with the same effective area.

B. VALIDATION USING GENETIC ALGORITHM
The comparison made between C1, C2, and C3 shows how effective area plays a role in our gain.However, since each of these configurations is of a different aperture size, we also need to check other configurations with equal aperture.To do so, we needed to select an optimization algorithm and optimize our array while maintaining 8 elements along the edge, symmetry, and one antenna element at the center.Many optimization algorithms have been used for sparse array optimization, but the GA works best for our optimization due to its robustness, global optimization capability, and its ability to handle nonlinear problems.
Using (3) as the fitness function, the genetic algorithm arrived at 8 different 9-element configurations: Our fitness function aims to minimize the difference in the array factor.Therefore, we calculated the area under the curve for the full array and the area under the curve for the thinned array.We then normalized each based on the maximum value from −180 • to 180 • .We can then take the difference between the full and sparse antenna array and work to minimize it.
The algorithm produced 6 different configurations with equal fitness values.Out of the 6 configurations, we chose the 4 best-performing configurations.The algorithm generated our configuration C3 as well as the 3 configurations shown in Fig. 6.Each configuration meets our criteria and maintains 8 elements along the edge of the array.
From Fig. 6 we can see that the configuration C3 was generated from the GA as well as being the resultant configuration after our thinning process.We find that out of the 4 configurations shown in the figure, C3 is still the best-performing configuration regarding the realized gain.After confirming that C3 achieves the highest realized gain, other performance parameters, such as scanning, were analyzed.Fig. 7 and Fig. 8 show the scanning performance for configuration C3 along the x-axis and y-axis, respectively.As can be seen, we achieved scanning from −45 • to +45 • (viz.90 • ).The thinning process does not significantly impact the scanning performance of the proposed array configuration.The primary variation in scanning performance arises from the peak realized gain value, which is an expected outcome of the thinning process.Subsequently, the next focus is the power divider design to test the configuration's practical implementation and physical validation.

C. POWER DIVIDER DESIGN
To minimize the complexity of the measurement setup and facilitate the testing process, we opted to fabricate a single power divider with a 1-to-32 split.The substrate is RT/Duroid 5880 ( r = 2.2 and tanδ = 0.009), with a thickness of 0.79 mm.An equal 1-to-32 corporate power divider is designed using a T-junction to feed the antenna elements.The power divider is designed with 50 ohmsmatched ports and operates from 4 GHz to 6.7 GHz.To avoid complexities and save space, the output ports of the power divider are placed in planar orientation and optimized, as shown in Fig. 9.The maximum insertion loss (S 21 ) is approximately equal for all of the output ports, showing as −15.8 dB indicating only 0.8 dB loss in the power divider, as shown in Fig. 10.Only half of the output ports (16 ports) are shown for symmetry because the other half is symmetrical.The simulated S 21 phases for all output ports are constant, as shown in Fig. 11.This power divider is an excellent choice for the antenna configuration of N = 0, N = 4, N = 8, and N = 12.We de-embedded the realized gain to measure these configurations using a 1-to-32-way power divider as a few output ports need to be terminated with a 50 ohms matched load.The 1-to-32-way power divider is then connected to the 25-patch antennas.We terminated the unused ports with matched loads for configurations with fewer elements.In Fig. 12, the simulated active S 11 for a single element in a 25-element antenna array shows excellent agreement with the simulation of the antenna array connected to the power divider with 7 matched loads.

IV. FABRICATION AND MEASUREMENT
To validate the performances of different thinned configurations, we fabricated a 1-to-32-way equal split power divider, as shown in Fig. 13.We also devised a new methodology for measuring different thinned array configurations of patch antennas.We created a 3D-printed housing to hold the patch antennas and the power divider feeding them, as shown in Fig. 14.Using this structure, we can fabricate 25 separate patch antennas and arrange them in any configuration on the top layer.Then, we can use coax cables to connect them to the power divider on the bottom layer.We measured the antenna's S 11 using a vector network analyzer, and both the measured and simulated results are shown in Fig. 15.The resonance frequency of the measured antenna shifted slightly towards a lower frequency near 5.2 GHz from 5.4 GHz due to fabrication inaccuracy.
The far-field measurement setup in an anechoic chamber is shown in Fig. 16.The simulated and measured realized gains are shown in Fig. 17    the maximum realized gain in simulation and measurement compared to C1 and C2.However, the measured realized gain difference between N = 0 and C3 is 2.6 dB, as shown in Fig. 24.We also found that configuration C3 was also generated by the GA and still has the highest realized gain out of all the generated configurations.Although C3, C4, C5, and C6 each have 8 elements along the edge, C3 is still the best-performing configuration due to its symmetry along all axes and aperture efficiency.The losses associated with power dividers, connectors, dielectric, and copper loss are the main reasons for the discrepancy between the simulated and measured results.Table 1 shows all antenna configurations' simulated and measured realized gain and half power beam width (HPBW).A comparison table comparing our work to prior literature is shown in Table 2.It is evident that high gain leads to low HPBW.Configuration C3 (9 elements) shows only 0.5 degrees more HPBW despite 64% reduction of antenna elements compared with N = 0 (25 elements).Hence, our presented antenna configuration is suitable for various applications requiring a pencil beam with low HPBW.

V. CONCLUSION
This paper presented an optimization technique through array thinning for a 25-element microstrip patch antenna to achieve size, weight, and power reduction.Different thinned array configurations were analyzed in full-wave simulation to find the best possible gain after elements reduction.Our works showed that as long as the thinned array's aperture area is kept intact, removing 64% of the elements only results in a 1.82 dB gain loss in simulation and 2.6 dB gain loss compared to the fully populated array.To validate our findings, we generated configurations using the GA and found that our presented configuration performed the best in terms of realized gain while achieving a beam scanning performance from −45 • to +45 • (emplviz.90 • ).The optimal  positioning of the remaining 9 elements results in an enhanced gain when compared to the other configurations generated by the GA.Moreover, our configuration shows a practical solution to use the saved spaces inside the array more efficiently than the traditional sparse or thinned arrays.Hence, this configuration is suitable for various modern communication and can be implemented for any frequency that will reduce hardware complexities while  high gain.Our next steps include creating a compact design for practical implementation as well as co-planar feeding and a multi-band design within the saved space.

FIGURE 1 .
FIGURE 1.A sparse antenna array (left) compared to a thinned antenna array (right).

FIGURE 2 .
FIGURE 2. Gradual removal of antenna elements, where N is the number of elements removed from the 25-element (5 × 5) array.

FIGURE 3 .
FIGURE 3. Full-wave simulation results show the realized gain of gradual array thinning (N = 0 to N = 12).

FIGURE 6 .
FIGURE 6. Best-performing configurations generated by the GA optimization process using our fitness function in (3).

FIGURE 7 .
FIGURE 7. Simulation of the beam scanning performance along the x-axis for configuration C3.

FIGURE 8 .
FIGURE 8. Simulation of the beam scanning performance along the y-axis for configuration C3.

FIGURE 11 .
FIGURE 11.Simulated S21 phase of 1-to-32 way power divider (showing the result of 16 output ports of the power divider).

FIGURE 12 .
FIGURE 12. Active S11 for a single element in a 25-element antenna array compared to the simulation of the antenna array connected to the power divider with 7 matched loads.

FIGURE 15 .
FIGURE 15.Simulated and measured S11 of the center element in the antenna array.

FIGURE 16 .
FIGURE 16.Far-field measurement setup in an anechoic chamber.