Design and optimization of a modified straight-tapered Vivaldi antenna using ANN for GPR system

1 Introduction

Ground-penetrating radar (GPR) has become a widely accepted non-destructive technique for investigating subsurface soil structures over the past five decades. Among the suitable antennas utilized in GPR systems are Vivaldi antennas because they provide directional radiation patterns. This allows high-resolution reflections and deep penetration through various types of soil. Moreover, their directivity is highly appreciated due to ease of integration into systems and low cost, making them ideal for GPR applications [1,2]. However, there is a tradeoff when selecting frequencies for radar scanning – higher ones will result in better resolution but shallower penetration depths, while lower frequencies can give sufficient depth but at lower resolution [3,4].

Traditional soil density and moisture measurements require destructive sampling and time-consuming laboratory analysis that disrupts natural soil layers. While non-destructive GPR techniques have been explored as alternatives, conventional GPR systems produce complex qualitative images that lack direct access to critical quantitative parameters such as phase differences and delay times, essential for accurate soil moisture and compaction evaluation.

Several designs for ultra wide band (UWB) Vivaldi antennas have been suggested in the literature [6,7,8,9] using different approaches to improve the performance, such as high gain, low power, or multi-layer-based ones.

Zerrad et al. proposed the design of a slotted antipodal Vivaldi antenna for various (UWB) applications, including the Internet of Things (IoT). The goal is to maintain good performance across a wide range from 3.29 to 45 GHz for different advanced communication systems [5].

Jaiswal et al. proposed integrating metamaterials and defected ground planes in UWB antennas to increase gain. The proposed UWB antipodal Vivaldi antenna design involves a metasurface with notches that improve the gain and directivity without increasing its size [6].

Yuan et al. designed an all-frequency reconfigurable antenna operating in both single-pole and Vivaldi modes. This flexible device suits a variety of wireless situations, highlighting its usefulness in diverse communication environments. The study describes how this antenna is made, uses examples, and finally presents detailed information on how well it works when used with different types of wireless devices [7].

Guruswamy et al. presented a compact microwave imaging designed ultra wideband Vivaldi antenna featuring hemi-cylindrical slots and directors at its backside due to which this type of feeding structure enhanced directivity along with bandwidth, making it suitable for high-resolution imaging systems. The work comprises extensive simulations and experimental investigations that demonstrate the potential of the antenna as a future imaging modality [8].

Huang et al. [9] proposed a novel method to enhance the gain of antipodal Vivaldi antennas by introducing a V-shaped air slot in the antenna substrate. This technique improves performance without increasing the antenna size or requiring additional components. By modifying the effective permittivity along the radiating conductors, the electromagnetic waves are guided more efficiently within the central dielectric region, resulting in higher gain and better radiation characteristics.

Similarly, Babu et al. [10] developed a compact triband meander line-based antenna with an asymmetric CPW feed, operating at 5.3, 6.6, and 8.1 GHz, which achieved efficiency above 80% and a gain of 7.09 dB, demonstrating suitability for Wi-MAX, public safety, and satellite applications.

In another work, Jahan et al. [11] proposed a dual-band four-port MIMO circular ring plasmonic antenna that provided superior isolation, a low envelope correlation coefficient, and a peak gain of 7.6 dB at 4.3 and 6.1 GHz, confirming its effectiveness for modern wireless communication systems.

Likewise, Lavadiya et al. [12] designed a low-profile multiband frequency-reconfigurable patch antenna using PIN diodes, offering tunability across the S, C, X, and Ku bands with a maximum bandwidth of 1,100 MHz, 700 MHz tunability, and a minimum reflectance response of –28.22 dB, highlighting its application potential in the satellite, military, and sensing domains.

Traditionally, soil compaction (density) is measured by extracting samples for laboratory testing. This method, while widely used, is time-consuming, invasive, and often disrupts the soil’s natural layers. To overcome these limitations, non-destructive testing (NDT) techniques have been explored, with GPR being one of the most common methods. GPR generates subsurface images but typically provides qualitative data, making it challenging to extract critical parameters such as delay times and phase differences that are essential for accurately evaluating soil moisture and compaction.

Recent advancements in antenna design have addressed the increasing demand for efficient, compact, and dual-band structures suited for applications such as wireless sensor networks, the IoT, and International Telecommunication Union (ITU) standards. Saikumar et al. [13] developed a miniature MIMO antenna with patterned surface enhancements, achieving improved isolation and high radiation efficiency. Similarly, Kundu et al. [14] proposed a compact wideband trapezoidal-stepped patch antenna for dual-band operation with enhanced gain and bandwidth. Aras et al. [15] introduced a dual-resonant crescent-moon-shaped antenna using concentric circular rings, offering compact geometry and strong impedance matching.

Abbas et al. [16] proposed a high-efficiency, dual-moon-printed antenna using a triangle slot to enhance matching at 1.1 GHz, for measuring sand gradation.

More recently, Srinivas et al. [17] designed a slotted T-shaped patch antenna with CPW feed for IoT/ITU applications, achieving low return loss and high gains (up to 6.5 dBi) at 6.2 and 8.3 GHz.

In addition, a dual-band Vivaldi antenna with an electrical size of (0.424 × 0.429 × 0.013) λ ₀, functioning in the dual bands of 2.6–3.46 and 4.16–5.35 GHz, was proposed by Chaabane and Guerroui. This antenna offers 1–3.8 dBi of gain, and its efficiency is in the region of 62–85%. This is a large-sized, high-frequency antenna [18].

These studies underscore the significance of innovative miniaturized and multiband antenna structures – principles that directly align with the goals of this work in developing a compact straight-tapered Vivaldi antenna (STVA) antenna for soil sensing.

This study used two identical antennas instead of a conventional single-antenna GPR setup. This approach allows for calculating the delay time and S21 parameters to assess the soil moisture content and density compaction. Signals transmitted through the soil are received by a second antenna connected to a vector network analyzer (VNA), enabling precise measurement and analysis.

The objectives of this study are to develop a compact STVA with dual-band operation suitable for in situ soil parameter sensing and to measure soil moisture and density compaction using a VNA, unlike traditional methods that rely on images captured by GPR. An artificial neural network (ANN) will be employed to map these parameters to accurately predict soil density and moisture, overcoming the limitations of conventional GPR techniques.

This article is structured as follows: Section 2 covers the STVA antenna design and analysis, Section 3 presents simulation results, Section 4 provides experimental validation, Section 5 describes the VNA-based soil sensing methodology and ANN implementation, Section 6 discusses performance analysis, and Section 7 concludes the work.

2 STVA

The methodology of the proposed STVA consists of three main phases: antenna design, antenna testing, and developing a model for soil compaction measurement.

2.1 Design and fabrication of an antenna

The substrate used is FR4 with relative permittivity equal to 4.3, a thickness of h = 1.6 mm, and loss tangent equal to 0.027. Figure 1 illustrates a rectangular substrate with side lengths La = 115 mm and Wa = 100 mm.

Figure 1

The proposed antenna: (a) front view and (b) back view.

The design of the proposed antenna involves optimization of the microstrip main feed line, coupler, and radial bowtie stub to radiate power in the triangular pattern over a symmetrical slot line. A feed width of 3.1 mm is selected to realize a reference impedance of Z ₀ = 50 Ω for correct coupling with the SMA connector and the coaxial cable. The parametric analysis reveals how resonance can degrade when transitioning from curved to linear tapering, which complicates impedance matching in specific frequency bands, as illustrated in Figure 2. In the optimized configuration, the curved profile was replaced by a straight edge, and the circular slot was repositioned and resized, thereby yielding the improved performance observed.

Figure 2

Simulated S11 responses of the proposed antenna with linear and taper slots.

Changing the curve to linear enables matching at bandwidths of 0.85 and 2.5 GHz. The reflection response of an antenna, S11, indicates bandwidths of 0.74–1.00 and 2.2–2.85 GHz with return losses of −35 and −23 dB at resonant frequencies of 0.85 and 2.5 GHz, respectively. The results demonstrate significant performance improvements achieved through slot geometry modification, which effectively altered the antenna’s electrical size and electromagnetic characteristics.

Figure 3 presents the physical prototype of the antenna, fabricated using a laser printer (LPKF S-103). The front view displays the copper-clad design with a circular slot, while the back view illustrates the feedline structure and the semi-circular matching stub.

Figure 3

The fabricated antenna: (a) front view, and (b) back view.

The proposed antenna is supposed to be printed on a compact FR-4 substrate with a relative permittivity of 4.3 and dimensions of 115 × 100 × 1.6 mm³. All related parameters are shown in Figure 2, and the physical dimensions are presented in Table 1.

Table 1

Parameters of the proposed antenna

Parameter	Value (mm)	Parameter	Value (mm)
Wa	100	d	11.36
La	115	L coplar	25.32
Wf	3.1	W coup	1
h	1.6	r-stub	25.84
Lf	47.7	Ø-stub	80

2.2 Measurements and simulation results

The impedance bandwidth of the Vivaldi antenna is illustrated in Figure 4, highlighting its operation across two frequency bands. There is a remarkable agreement between the simulated and measured reflection coefficients.

Figure 4

Comparison between the simulated and measured S-parameters for the fabricated antenna.

It can be noted that both curves display sharp dips at specific frequencies, indicating good antenna performance in these frequency bands. The differences between the measured and simulated results show that, in the upper band, the simulated resonant frequency is 2.50 GHz, while the measured resonant frequency is 2.49 GHz. This discrepancy is likely due to an unspecified value of ε _r. Additionally, the variation in the bandwidth can be attributed to losses in the SMA connector.

Figure 5 displays the simulated realized gain and radiation efficiency for the proposed STVA antenna across the frequency range of 0.7–2.8 GHz. The antenna demonstrates dual-band characteristics with distinct performance regions. In the lower operational band (0.74–1.00 GHz), the gain reaches approximately 3 dBi with radiation efficiency exceeding 99%. A significant gain reduction is observed in the stopband region (1.0–2.2 GHz), where the gain drops to approximately 2 dBi, which is typical behavior for dual-band antenna designs. In the upper operational band (2.2–2.85 GHz), the antenna achieves peak gain values of 6.5 dBi with a radiation efficiency of 98.2%. The efficiency remains consistently high (>98%) across both operational bands, demonstrating the antenna’s effective electromagnetic energy conversion.

Figure 5

Simulated gain and efficiency of the resulting antenna vs frequency.

The gain variation between the two bands can be attributed to the different electrical lengths and current distribution patterns at the respective frequencies, which is characteristic of tapered slot antenna behavior.

Three-dimensional patterns at two frequencies, 0.8 and 2.5 GHz, clearly show that an antenna’s beam steering property is retained irrespective of its actual operating frequency over a range of values, as shown in Figure 6.

Figure 6

Simulated 3D radiation patterns: (a) 0.85 GHz and (b) 2.5 GHz.

3 Soil density compaction and moisture measurement

Two antennas were placed inside a wooden box filled with soil to investigate soil compaction and moisture levels. The signals were then transmitted by one antenna while the other received them using a VNA, from which MATLAB was used to analyze the data obtained. Figure 7 shows the two antennas located in the soil for parameters such as the received power, S21 phase, and delay time to realize how an antenna interacts under different soil conditions. The antenna’s responses are measured for each case of variation in the sand moisture content and density compaction.

Figure 7

The two antennas with a soil sample in between are connected to the VNA.

4 ANN training

The ANN model used in this study was developed in MATLAB and comprises three layers:

• An input layer utilizing five parameters – moisture, normalized peak power, delay time (ns), maximum S21 (dB), and the phase of S21 (deg).

• A hidden layer.

• An output layer designed to predict soil compaction.

The network is a feed-forward backpropagation neural network. Specifically, this study utilizes two distinct feed-forward backpropagation networks. One is dedicated to measuring soil compaction, featuring a hidden layer with 20 neurons and employing the TANSIG (tangent-sigmoid) transfer function, as shown in Figure 8. The data were divided into two sets: 30% for training the neural network and 70% for validation. During the training phase, the five main parameters, along with the compaction level, are fed into the network to enable learning. The remaining 70% of the data are then used to test the network, which showed good predictive accuracy. Once training is complete, only five parameters are needed for the neural network to predict soil compaction.

Figure 8

The ANN model for measuring soil compaction.

These configurations enable the networks to effectively model non-linear relationships within the data, which is crucial for accurate, real-time assessment of soil properties.

Data were collected with these antennas, which recorded the soil’s electrical response to different soil compaction levels for both soil moisture and compact measurements. A second neural network was trained on these data to relate electromagnetic parameters such as S21, delay time, power, and phase to the percentages of soil compaction. Neural network models were trained iteratively by optimizing the number of neurons, epochs, and learning rates to distinguish training data from testing dataset sets for accuracy and reliability. The rigorous process of training and optimization involving neural networks showed that they have the potential to estimate density efficiently while being reliable in defining water content in soils; hence, they can be considered an effective tool for practical applications in geotechnical and civil engineering.

Table 4 shows the performance of the neural network in predicting dry density and soil compaction based on the collected data. The “measured” columns represent the actual measured values for dry density and compaction, while the “ANN” columns indicate the predictions made by the neural network. The error between the true and predicted values is calculated, and the performance index (PI) is used to measure the accuracy of the predictions, as shown in Figure 9.

Figure 9

Actual and measured ANN network of compaction.

The trained ANNs produced very accurate soil compaction indices with PIs above 99%. This system provides real-time information without having elaborate gadgets, making it an asset for field-based agricultural monitoring, civil engineering works, or even environmental evaluation due to its quickness and accuracy at the site.

The close overall tracking between the actual and predicted curves demonstrates the physical viability of using phase and delay measurements as reliable indicators for soil compaction analysis.

5 Comparison with previous work

In this section, a comparison is presented between the proposed antenna and previously published antennas, as well as with previous research that examined soil properties using GPR.

6 Conclusions

The antennas used in this study are compact, planar STVA fabricated on a single substrate with an electrical size of (0.266 × 0.306 × 0.003) λ ₀ ³. The tapered section of the traditional Vivaldi antenna is modified with a straight side instead of the traditional curved shape, simplifying the fabrication, improving specific characteristics, and downshift of the desired frequency.

The antenna demonstrates excellent dual-band performance with resonant frequencies at 0.74–1.00 GHz (31% bandwidth) and 2.2–2.85 GHz (26% bandwidth), with gains of 2–6.5 dB and radiation efficiency exceeding 98%. The straight-tapered slot geometry modification significantly improved impedance matching compared to traditional curved Vivaldi designs, with S11 values reaching −35 dB at resonant frequencies. These compact antennas are designed for measurements of soil properties.

The compact size and low profile of the antennas make them easy to deploy, reducing costs and system complexity. Additionally, their design enables direct soil insertion without requiring supplementary components or elaborate setups, enhancing their practicality and reliability for field measurements.

The study establishes clear physical relationships between soil electromagnetic properties and mechanical characteristics. Increased soil compaction reduces air voids (εᵣ = 1) and increases water content (εᵣ = 81), resulting in higher effective dielectric constants that cause measurable increases in signal delay time and phase shifts. This fundamental understanding enables reliable soil property prediction through electromagnetic wave propagation analysis. By extracting these parameters using a VNA, the compaction level can be accurately predicted.

This approach offers a reliable, non-destructive alternative to traditional testing methods. Furthermore, the underlying mechanism can be extended to detect voids and defects in other materials, such as concrete or foam. The proposed system also shows promise for related applications, including sand gradation analysis. Based on this principle, the system can also be used as an effective tool for non-destructive detection of internal defects and voids within materials.