Global navigation satellite systems (GNSS) have been widely utilized in various wireless communication applications, such as automotive vehicles, unmanned aerial vehicles, military electronics, consumer electronics, and diverse Internet of Things devices. The global positioning system (GPS), the Russian GLONASS, the Chinese BeiDou, and the EU’s Galileo are fully functioning and provide positioning, navigation, and timing services around the world, with GPS being the most famous of these services. The demand for high-precision satellite positioning techniques and services is growing rapidly, as is evident in the automotive world and next-generation mobility. The new generation of GNSS receiver and correction data services are enabling truly high-precision GNSS solutions ready for the mass market. However, due to their complexity, size, and power as well as cost restrictions, these solutions are not suitable for mainstream use cases. In contrast, receiving-antenna-related solutions are becoming important and attractive and can maximize precision at the lowest price. The receiving antenna is expected to capture stable signals from GNSS satellites, so a high-performance receiving antenna is critical in enhancing the signal strength and reliability of the overall communication link. Total isotropic sensitivity (TIS), upper hemisphere isotropic sensitivity (UHIS), and signal-to-noise ratio (SNR) are important figures of merit to evaluate the performance of the receiving antenna and are all closely related to the receiver’s and antenna’s performances. Accordingly, as regards the antenna, the improvement of antenna efficiency, especially the upper hemisphere efficiency, is the simplest and most efficient solution to achieve high-precision satellite positioning [1, 2].

In the literature, various kinds of GNSS antennas have been studied for high-precision satellite positioning by either creating circularly polarized (CP) waves [3–9] or by improving antenna efficiency and bandwidth [10, 11]. Generally, CP-receiving antennas have higher reception performance than linearly polarized antennas due to reduced polarization loss. However, a conventional terminal antenna can only produce linearly polarized waves, and CP waves can be produced only by deploying multiple radiators or coupling elements [3, 5, 6], which increases design complexity and required volume. Besides, it is difficult to achieve CP radiation in the upper hemisphere toward the sky [3–9]. For these reasons, the abovementioned CP antennas are rarely adopted in practice.

More importantly, in terminal devices, especially the popularly used smartphones, the antenna elements are usually placed at the top or bottom due to space limitations and location restrictions (Fig. 1(a)) as well as to prevent the user from interacting with the liquid crystal display (LCD) (Fig. 1(b)) [12–15]. Moreover, terminal antennas must be low-profile, miniaturized, and low-cost. For these reasons, slot-type, loop-type, or monopole-type antennas are particularly popular [12–15]. Accordingly, a high-precision receiving antenna with a simple structure, low profile, and miniaturization is extremely sought-after in the industry.

The upper hemisphere efficiency, as well as the CP property, is a significant figure of merit for receiving antennas to obtain high-precision satellite positioning. According to characteristic mode theory [16], the ground modes play an important role in determining the radiation beam, while antenna types and design methods are important considerations [3–6]. Therefore, a compact and simple antenna solution with higher upper hemisphere efficiency is an attractive candidate for high-precision receiving antennas. To the best of the authors’ knowledge, the commonly used conventional antennas in terminals suffer from low upper hemisphere efficiency and cannot satisfy the increasing need for high-precision receiving antennas.

In this study, we propose a novel receiving antenna to improve the upper hemisphere efficiency for GPS applications. The proposed receiving antenna has two capacitive ends loaded by lumped capacitors to achieve antenna miniaturization and simple resonance control simultaneously. This special structure enables radiation-pattern alteration, thereby radiating more energy into the upper hemisphere. Both simulation and measurement are conducted to verify the performance of the proposed antenna. It is shown that the proposed antenna design produces 1.5 dB higher upper hemisphere efficiency and 2 dB higher SNR than the reference antenna.

As depicted in Fig. 2, both the reference and proposed antenna designs are mounted on a rectangular ground plane measuring 161 mm × 75 mm, with the ground plane fabricated on a 1-mm-thick FR4 substrate (ɛ_r = 4.4, tan δ = 0.02). A conventional inverted-F antenna, a popularly used antenna type in both academia and industry [11, 12, 15], is presented as a reference for comparison to validate the advancement of the proposed antenna. Fig. 2(a) and 2(b) illustrate that both the reference and proposed antennas occupy an identical volume of 28 mm × 5 mm × 2 mm and are strategically placed at the top edge of the ground plane. This positioning is the most prevalent method for installing GPS antennas in commercial devices. The reference antenna is first shown in Fig. 2(a), as a comparison, where the right side of the antenna is open, and the left side is shorted to the ground plane. In Fig. 2(b), the proposed antenna consists of a series capacitor C_F for input impedance control and dual capacitors C_R1 and C_R2 at the two ends for the resonant frequency control. The optimized values of C_F, C_R1, and C_R2 are 0.7, 0.76, and 0.9 pF, respectively. The proposed antenna differs from the reference design in featuring two open ends equipped with loaded lumped capacitors, a novel structural approach that has yet to be reported in the literature. It is important to note that the modeling of all the antennas was performed using Ansys HFSS (High-Frequency Structure Simulator) version 19.

Fig. 3 showcases the reflection coefficients of both antennas, illustrating that they are tuned to operate within the 1,575 MHz frequency band. The reference antenna exhibits a −6 dB impedance bandwidth of 200 MHz, while the proposed antenna has a bandwidth of 80 MHz. This impedance bandwidth is intrinsically linked to the antenna element’s quality factor (Q-factor), with the proposed antenna structure displaying a higher Q-factor than the reference antenna. Despite its narrower bandwidth, the proposed antenna is specifically designed to enhance radiation efficiency toward the upper hemisphere without compromising overall radiation efficiency. Furthermore, the impedance bandwidths for both antennas meet the requirements for industrial applications, given that the desired frequency band is quite narrow.

The radiation patterns produced by both the reference and proposed antennas are displayed in Fig. 4. The realized gain of the proposed antenna in the +z direction is measured at 2.08 dBi, in stark contrast to the reference antenna’s −2.29 dBi. Additionally, the proposed antenna achieves realized gains of 2.85 and 2.53 dBi at θ−= ±30°, whereas the reference antenna recorded lower gains of −1.11 and −0.61 dBi at the same angles. Consequently, the proposed antenna significantly enhances radiation strength within a 60° beamwidth directed toward the sky, marking a notable improvement over the reference antenna.

In mobile handsets, antenna elements are electrically small, and their radiation characteristics are predominantly determined by the excitation of ground modes. The most commonly invoked ground modes for this purpose are the vertical ground mode, which operates along the z-axis, and the horizontal mode, functioning along the y-axis [5, 6]. The proposed antenna is designed to enhance upper hemisphere efficiency specifically by exciting the horizontal ground mode. This approach is supported by the reaction theorem, which posits that the interaction between the antenna element and the ground mode can be expressed by an integral form [5, 6, 16].

where J_a and M_a denote the electric and magnetic current densities generated by the antenna element, respectively. These densities represent the external forces (i.e., the antenna element) acting on the ground mode. E_g and H_g symbolize the electric and magnetic fields emanated by the ground mode, which are contingent solely on the ground plane’s configuration and dimensions as per characteristic mode theory [16]. Meanwhile, the volume integral in (1) is taken within a finite region enclosing the antenna element and the ground plane. Eq. (1) elucidates that the coupling between the antenna and the ground mode can be either electric or magnetic, allowing for the strategic selection of the ground mode to optimize radiation.

As shown in Fig. 5(a), activating a vertical ground mode would lead to a radiation beam around the horizontal perimeter of the ground plane (or smartphone), with notable radiation nulls in the upper hemisphere. Conversely, exciting the horizontal ground mode would enhance radiation toward the upper hemisphere, thereby improving reception for GNSS applications. Given the placement of the antenna at the top edge of the ground plane, an antenna element characterized by a magnetic current is better positioned to facilitate strong coupling with the horizontal ground mode, ensuring that a greater proportion of radiation is projected into the upper hemisphere. Consequently, the antenna element is optimized as a magnetic coupler (M-type coupler) as opposed to an electric coupler (J-type coupler). Unlike the common J-type coupler, which is akin to a linear impressed electric current found in dipole or monopole currents, an M-type coupler is represented by an electric current loop, offering a distinct advantage in this context [17–19].

To further verify the operation mechanism of the proposed antenna, the simulated surface current distributions are shown and compared in Fig. 6. As can be observed in Fig. 6(a), the reference antenna produced a monopole-type current mode (J-type current mode) in the antenna structure, and the induced current distribution over the ground plane is directed diagonally, which means the horizontal ground mode is sufficiently excited. In contrast, the proposed antenna in Fig. 6(b) produced a loop-type current mode (M-type current mode), and the induced current distributions over the ground plane are directed along the y-axis, which means the horizontal ground mode is operating. This is a fundamental difference between the reference and proposed antennas that determines the higher radiation gain on the z-axis. This difference can be explained by the formula of the total current distribution over the surface of the ground plane, which is a summation of a series of modes, as follows:

where m is the mode index. The eigenvalue λ_m is 0 at the resonance of a certain ground mode J_m. ∫∫∫(E_i · J_m)dτ represents the coupling between the impressed field E_i (produced by the antenna element) and a modal current J_m in the ground plane. Accordingly, the surface current distribution of the reference antenna (J_t1) can be approximately written as

where J_v is the vertical ground mode. ∫∫∫(E_i · J_v)dτ represents the electric coupling between the impressed electric field E_i (produced by the reference antenna) and the vertical ground plane J_v. In contrast, the surface current distribution of the proposed antenna (J_t2) can be represented by

where J_h is the horizontal ground mode. ∫∫∫(E_i · J_h)dτ represents the magnetic coupling between the impressed electric field E_i (produced by the proposed antenna) and the horizontal ground plane J_h. In this context, the surface current distribution of the proposed antenna (J_t2) dominantly flows in the horizontal direction, which may be more likely to direct the radiation beam into the upper hemisphere, contributing to the radiation difference in Fig. 4.

In this study, dual capacitance ends are important features, so the capacitor effect is discussed in this subsection. Fig. 7 shows the results in the reflection coefficient and Smith chart with the variation of C_R1 and C_R2. As shown in Fig. 7(a) and 7(c), an increased value of C_R1 or C_R2 can lower the resonant frequency of the antenna. However, C_R1 and C_R2 have a different effect on the input impedance. As can be observed in Fig. 7(b) and 7(d), an increase in C_R1 decreases the impedance locus, whereas an increase in C_R2 increases the impedance locus.

Fig. 8 shows the effect of the ratio of C_R1 and C_R2 on the antenna radiation pattern at the GPS L1 bands (1,575 MHz). Fig. 8(a) shows the radiation gain pattern when a larger C_R1 (1.6 pF) and a smaller C_R2 (0.5 pF) are used, and Fig. 8(b) shows the radiation gain pattern when a smaller C_R1 (0.4 pF) and a larger C_R2 (1.6 pF) are used. When the ratio of C_R1 is larger, as shown in Fig. 8(a), the radiation gain is 1.06, 1.9, and 1.8 dBi in the +z direction and θ = ±30°, respectively. When the ratio of C_R1 and C_R2 is smaller, as shown in Fig. 8(b), the radiation gain is 1.6, 1.65, and 1.73 dBi in the +z direction and θ = ±30°, respectively. Therefore, the highest upper hemisphere efficiency could be obtained when the values of C_R1 and C_R2 are similar, as indicated in Fig. 4.

The reference and proposed antennas were tested using a network analyzer and measured in a 6 m × 3 m × 3 m three-dimensional (3D) Cellular Telecommunications and Internet Association (CTIA) over-the-air (OTA) anechoic chamber. The measured total efficiencies are presented in Table 1, where the total efficiencies of the reference and proposed antennas are almost the same, but the upper hemisphere efficiency of the proposed antenna is 1.5 dB higher than that of the reference antenna.

Fig. 9 shows the measured 3D radiation pattern of both the reference and proposed antennas. It is seen that the proposed antenna has a higher beam pattern toward the +z direction than the reference antenna. The measured radiation gains of the proposed antenna are 0.82, 1.18, and 1.36 dBi in the +z direction and θ = ±30°, respectively, and those of the reference antenna are −2.28, −0.75, and −2.05 dBi, respectively. Accordingly, the proposed antenna has a higher gain (of over 2 dB) than the reference antenna. Therefore, the proposed antenna has a significant superiority over the reference antenna in both radiation gain and upper hemisphere efficiency, and it is expected that the proposed antenna could obtain excellent active test performance, including TIS, UHIS, and SNR.

To further assess the viability of the proposed antenna, both the reference and proposed antennas were integrated into a commercial smartphone for an active performance test, as depicted in Fig. 10. The smartphone used for this test has dimensions of 165 mm × 75 mm. The layout for the antenna placement was designed as shown in Fig. 1. The C_F, C_R1, and C_R2 of the proposed antenna were optimized as 0.9, 0.75, and 0.75 pF, respectively. As presented in Table 2, the radiation performance metrics closely mirror those observed in the bare-board experiments detailed in Table 1. Moreover, Fig. 11 illustrates the tested SNR data using this smartphone platform. It is important to note that the measurements were carried out in an open field, utilizing the AndroiTS GPS Test application, to ensure consistency in the testing environment. Note that in the realm of mobile handsets, industry standards for acceptable receiver performance dictate that the device must establish connections with at least three satellites at an SNR above 4 dB and with six satellites at an SNR above 35 dB. Evaluation of the reference antenna reveals connectivity to three satellites with SNRs exceeding 40 dB and to five satellites with SNRs surpassing 35 dB. Conversely, the proposed antenna demonstrates enhanced performance, connecting to five satellites with SNRs above 40 dB and seven satellites with SNRs exceeding 35 dB. Furthermore, the proposed antenna boasts a peak SNR that is 2 dB higher than that of the reference antenna. This enhancement is crucial for ensuring high-precision services from GPS antennas in practical scenarios, particularly in challenging conditions.

To underscore the innovation of the proposed technique, Table 3 contrasts it with current state-of-the-art approaches in the literature. This comparison reveals that the proposed method offers distinct advantages in terms of simplicity, integration, and ease of fabrication. Crucially, according to the authors’ comprehensive review, there has not yet been a report in the literature of a receiving antenna for mobile devices that achieves high efficiency in the upper hemisphere. This pioneering antenna design approach presents a compelling solution for high-precision GNSS applications, marking a significant advancement in the field.

This study proposed a novel receiving antenna with improved upper hemisphere efficiency by using dual capacitive ends so that higher upper hemisphere efficiency can be produced by exciting the horizontal mode of the ground plane. The proposed antenna has two capacitive ends loaded by lumped capacitors to achieve antenna miniaturization and simple resonance control simultaneously. In terms of performance metrics, the proposed antenna delivers a 2 dB higher increase in radiation gain when oriented in the +z direction, alongside a 1.5 dB improvement in efficiency across the upper hemisphere, than the reference antenna. Additionally, an active test conducted on a commercial smartphone demonstrated the proposed antenna’s ability to connect to five satellites with SNRs above 40 dB and to seven satellites with SNRs exceeding 35 dB. These results, obtained from both passive and active testing scenarios, underscore the proposed antenna’s superior reception capabilities. The antenna showcases a more robust signal connection with a greater number of satellites, enhancing its appeal for real-world applications.