Antenna Aperture Research Articles

3D Radio Imaging Under Low-Rank Constraint

Radio frequency (RF) imaging has been of interest for years due to its ability to create images of targets without being affected by weather and light conditions. The existing heuristic solutions such as back projection (BP), suffer from the sidelobe interference due to limited antenna aperture. In this paper, we propose a super-resolution 3-D imaging algorithm to enhance imaging performance. Mathematically, the reconstruction problem is an inverse problem that can be formulated as an optimization problem. The low-rank property of the object is exploited to regularize the imaging problem by nuclear norm minimization. We also develop a coarse-to-fine scan structure to reduce the computational complexity of the proposed algorithm. We evaluate the proposed algorithm with both simulations and measurements. With a frequency band range from 2.7-4.1 GHz and a 16×6 multiple-input-multiple-output (MIMO) antenna array, simulation results show high imaging quality with a median boundary keypoint precision of 2 cm, and experimental results validate the feasibility of the proposed algorithm in a real-world environment.

Pattern-Division Multiplexing for Multi-User Continuous-Aperture MIMO

In recent years, thanks to the advances in meta-materials, the concept of continuous-aperture MIMO (CAP-MIMO) is reinvestigated to achieve improved communication performance with limited antenna apertures. Unlike the classical MIMO composed of discrete antennas, CAP-MIMO has a quasi-continuous antenna surface, which is expected to generate any current distribution (i.e., pattern) and induce controllable spatial electromagnetic (EM) waves. In this way, the information is directly modulated on the EM waves, which makes it promising to approach the ultimate capacity of finite apertures. The pattern design is the key factor to determine the communication performance of CAP-MIMO, but it has not been well studied in the literature. In this paper, we develop pattern-division multiplexing (PDM) to design the patterns for CAP-MIMO. Specifically, we first study and model a typical multi-user CAP-MIMO system, which allows us to formulate the sum-rate maximization problem. Then, we develop a general PDM technique to transform the design of the continuous pattern functions to the design of their projection lengths on finite orthogonal bases, which can overcome the challenge of functional programming. Utilizing PDM, we further propose a block coordinate descent (BCD) based pattern design scheme to solve the formulated sum-rate maximization problem. Simulation results show that, the sum-rate achieved by the proposed scheme is higher than that achieved by benchmark schemes, which demonstrates the effectiveness of the developed PDM for CAP-MIMO.

SAR Imaging Based on OAM‐ωK Algorithm

AbstractTraditional radar imaging was restricted by the antenna aperture and imaging scene. It was difficult to improve azimuth resolution greatly. The vortex electromagnetic (EM) waves carrying orbital angular momentum have a special helical phase wavefront structure. The vortex EM waves could bring more degrees of freedom when applied to synthetic aperture radar imaging, make it possible for ultra‐high resolution imaging, provide a new possibility for the bottleneck problem of azimuth resolution in traditional radar imaging. In this paper, an OAM‐ωK algorithm was used to compensate the Bessel term and residual azimuth angle term which in the echo signal. Because the azimuth term and azimuth angle term were fused into a new azimuth term, the Doppler bandwidth was broadened and high resolution imaging was achieved. The theory verified the advantages of the algorithm in azimuth resolution. By comparing simulation experiments of single target point and multi‐target points with the traditional ωK algorithm, the proposed OAM‐ωK algorithm had higher azimuth resolution, proving the algorithm’s effectiveness.

Formulas for Beam Shift and Beam Narrowing in 1-D Leaky-Wave Antennas Due to Element Pattern

The radiation pattern of one-dimensional (1-D) unidirectional leaky-wave antennas (LWAs) is typically derived from the analysis of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">space factor</i> (SF) only. However, when the antenna aperture is characterized by a longitudinal radiating current, a cosine-type <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">element pattern</i> term has to be included: this factor may considerably affect the beam properties. Specifically, the beam peak is shifted and the beamwidth is narrowed when the element pattern is included. These effects are more prominent as the antenna size decreases and the beam angle increases. Approximate but accurate analytical formulas are here provided and numerically validated to predict the beam angle and the half-power beamwidth for these kinds of 1-D unidirectional LWAs when the element pattern is included.

ДВУХПОЗИЦИОННЫЙ ГЕОРАДИОЛОКАТОР НА БПЛА ДЛЯ ОПЕРАТИВНОГО МОНИТОРИНГА ПОДПОВЕРХНОСТНЫХ ВОДНЫХ РЕСУРСОВ

This paper considers the implementation of a two-position ground penetrating radar (GPR) located on board unmanned aerial vehicles (UAVs) and designed for the operational search for groundwater in arid and desert regions of Mongolia, which is an extremely urgent task. With the help of synthesizing the GPR antenna aperture on the UAV, a significant increase in information content is achieved compared to existing GPRs, since it becomes possible to obtain a panoramic radar image of the subsurface layers of the probed medium with the required resolution with a sufficiently wide swath. On the other hand, the necessary efficiency (required, for example, when monitoring vast desert areas) can only be achieved with a sufficiently wide field of view created on the basis of the two-position sounding principle, where the emitting and receiving signals are formed and processed on UAVs of different or equal heights flying with the same speed and spaced orthogonally to the direction of their movement, which makes it possible to use quasi-mirror reflection. In this case, the swath will be noticeably larger than in the case of nadir sounding. In a condensed form, the article considers the following issues: the model of a subsurface aquifer, the geometry of a two-position GPR in the quasi-mirror sounding mode, up to the features of synthesizing the aperture (Doppler narrowing of the radiation pattern) of the receiving antenna, resolution, the required potential of a two-position GPR for reliable detection of an aquifer subsurface horizon, accuracy measurements of its depth, as well as the need for experimental work to test the theoretical provisions.

Ultra-Wideband and High-Gain Vivaldi Antenna with Artificial Electromagnetic Materials.

An ultra-wideband and high-gain Vivaldi antenna with artificial electromagnetic material, suitable for ground-penetrating radar (GPR) systems, is proposed. Directors loaded inside the antenna gradient slot direct electromagnetic waves by inducing current to improve gain. The artificial electromagnetic material, also called metamaterial, is composed of multiple "H"-shaped units arranged in a certain regular pattern, loaded at the antenna aperture. The artificial electromagnetic units affect the antenna radiation waves by changing the refractive index to improve radiation directivity. The four Vivaldi units are arranged into a horn-shaped array, and each two units are orthogonally fed to realize dual polarization. Experimental results demonstrate that the antenna has good impedance matching of S11≤-10 dB in 0.9-4 GHz, and the maximum realized gain can reach 15.2 dBi.

DETECTION OF THE SIGNALS OF THE TERRESTRIAL RADAR STATIONS BY SPACECRAFT WITH A PASSIVE SYNTHESIS OF THE ANTENNA APERTURE

Context is due to the need to analyze the electromagnetic accessibility of terrestrial radio radiation sources at long distances, which is typical for the operation of a spacecraft of radio technical intelligence with a passive synthesis of the antenna aperture.&#x0D; Objective is to calculate the probability indicators of detecting the fact of signal emission of ground-based radar stations using radio-technical intelligence installed on a space carrier.&#x0D; Method. Analytical calculation of the correct detection probability of the signal of the radio radiation sources by the spacecraft of radio technical intelligence based on the determination of the signal-to-noise ratio at the input of the detection device. The analysis of the technical characteristics of the group of ground radars made it possible to calculate the probability of correct detection only for the virtual radar, which generates the minimum number of pulses with the minimum energy during reconnaissance among all the analyzed radars.&#x0D; Results. The fulfillment of the conditions of electromagnetic accessibility is checked and the correct detection probability of the signals of modern radar stations by the space radio-technical intelligence system with a passive synthesis of the antenna aperture was calculated.&#x0D; Conclusion. Proposed use of the correct detection probability of the signal as the resulting indicator of electromagnetic accessibility of the radio radiation source. In the example radar stations of the air defense proved, that the proposed parameters of the space radio technical intelligence system with a passive synthesis of the antenna aperture provide the values of the correct detection probability of the signal, which are quite acceptable for modern monitoring systems.

Optimization features of an aperture antenna with field variable-phase distribution

The solution of a number of tasks at maximum ranges in a wide sector of angles requires the use by radio engineering systems of an antenna with a quasi-sector directional pattern, the formation of which is provided by an variable-phase distribution of excitation sources (currents or fields). Taking into account the ambiguous influence of many parameters of such a distribution on the shape of the realized radiation pattern, the traditional optimization criteria for such an antenna are unacceptable. The possibilities and criteria of parametric optimization can be determined using numerical methods of mathematical modeling. In order to solve the problem of parametric optimization of an aperture microwave antenna with a quasi-sector radiation pattern and to select a criterion that allows achieving the best design solution of the projected antenna in this sense, its mathematical model has been developed. It is proposed to use a complex quality criterion for optimization in a uniform approximation of antennas with variable-phase field distribution in the aperture. The constructed mathematical model of a microwave antenna describing the quasi-sector radiation pattern and the corresponding field distribution in its aperture is presented, which makes it possible to determine the controlled parameters that ensure the achievement of a given optimization criterion. The determining influence of the fraction and amplitude of the antiphase section in the field distribution on the main parameters of the radiation pattern is shown. The results of mathematical modeling indicate the possibility of controlling the parameters of the quasi-vector radiation pattern of the aperture antenna and achieving a given criterion for its optimization. The results obtained can be recommended for practical use in the design of aperture antennas with variable-phase distribution of field.

A Ka-Band 64-Element Deployable Active Phased-Array TX on a Flexible Hetero Segmented Liquid Crystal Polymer for Small Satellites

A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Ka$</tex-math> </inline-formula> -band 64-element deployable active phased-array transmitter (TX) on a hetero segment liquid crystal polymer (LCP) substrate for small satellites is proposed. The proposed phased-array TX achieved a large array size implementation and a small form factor with integrated six-layer and two-layer LCP substrates. Antenna and transmission line designs considering hetero layer structure are presented in detail. Achieving 46.7 dBm electronically isotropically radiated power (EIRP), the proposed phased-array TX can support 256-APSK DVB-S2X. As a result, the proposed deployable active phased-array TX successfully realizes low-launch cost with a 9.65 g lightweight and large antenna aperture size with superior EVM performance.

A High Gain Vivaldi Antenna with Multiple Near-Field Dielectric Lenses and Grooved Edges

In order to expand the applications of the traditional Vivaldi antenna by addressing the low gain of the traditional Vivaldi antenna, this paper combines the phase distribution of the Vivaldi antenna aperture based on the analysis of the transmission characteristics of a dielectric unit by utilizing the advantages of artificial electromagnetic material. A more reasonable method of loading a dielectric lens is proposed and utilized in combination with edge grooving. A comparison of the results shows that the antenna operates in the frequency range of 4 to 16 GHz. The low-frequency boost is approximately 3 dB, and the high-frequency boost is approximately 9.6 dB.

Maximizing Antenna Array Aperture Efficiency for Footprint Patterns

Despite playing a central role in antenna design, aperture efficiency is often disregarded. Consequently, the present study shows that maximizing the aperture efficiency reduces the required number of radiating elements, which leads to cheaper antennas with more directivity. For this, it is considered that the boundary of the antenna aperture has to be inversely proportional to the half-power beamwidth of the desired footprint for each ϕ-cut. As an example of application, it has been considered the rectangular footprint, for which a mathematical expression was deduced to calculate the aperture efficiency in terms of the beamwidth, synthesizing a rectangular footprint of a 2:1 aspect ratio by starting from a pure real flat-topped beam pattern. In addition, a more realistic pattern was studied, the asymmetric coverage defined by the European Telecommunications Satellite Organization, including the numerical computation of the contour of the resulting antenna and its aperture efficiency.

An Online Measurement and Calibration Method for a Radio Telescope Sub-Reflector Support Structure Using Fiber Bragg Grating.

The position and altitude of a sub-reflector have an important influence on the pointing accuracy of a radio telescope. With the increase of the antenna aperture, the stiffness of the support structure for the sub-reflector decreases. This causes deformation of the support structure when environmental loads, such as gravity, temperature, and wind load, are applied to the sub-reflector, which will seriously influence antenna pointing accuracy. This paper proposes an online measurement and calibration method for assessing the deformation of the sub-reflector support structure based on the Fiber Bragg Grating (FBG) sensors. Firstly, a reconstruction model between the strain measurements and the deformation displacements of a sub-reflector support structure is established based on the inverse finite element method (iFEM). In addition, a temperature-compensating device with an FBG sensor is designed to eliminate the effects of temperature variations on strain measurements. Considering the lack of the trained original correction, a non-uniform rational B spline (NURBS) curve is built to extend the sample data set. Next, a self-structuring fuzzy network (SSFN) is designed for calibrating the reconstruction model, which can further improve the displacement reconstruction accuracy of the support structure. Finally, a full-day experiment was carried out using a sub-reflector support model to verify the effectiveness of the proposed method.

Mathematical model of phased array antenna aperture in the presence of errors in the position of antenna elements

The analysis of the directional characteristics of a phased array antenna is one of the main problems in the development of an antenna. The key issue in carrying out this analysis is an adequate representation of the directional characteristics of the phased array antenna with known directional patterns and the set-up as part of the aperture of antenna elements. There are many works considering the directional characteristics of the antenna, taking into account the mutual connection between the antenna elements. A number of works are devoted to the study of the directional characteristics of a phased array antenna in the presence of random errors of the amplitude-phase distribution in the radiating aperture. However, the issues related to the influence of the antenna elements installation error in the radiating aperture on the directional characteristics of the phased array antenna practically did not receive their consideration. With this in mind, this article discusses a mathematical model of the radiating aperture of a phased array antenna in the presence of errors in the antenna elements installation. At the same time, the installation error means not only the displacement of the antenna elements, but also its rotation relative to three axes, due to a violation of the shape of the radiating aperture. The objective of the article is to investigate the influence of the antenna element installation errors, including the displacement and reversal of the antenna elements in the radiating aperture, on the directional characteristics of the phased array antenna, based on strict consideration of the relationship between the directional characteristics of the phased array antenna and the parameters of the antenna elements installation in the radiating aperture. The main results obtained in the article are as follows. 1. A mathematical model of the radiating aperture of the phased array antenna, taking into account the errors of installation of the antenna elements in the aperture, including displacement of the phase center of the antenna elements and rotation of the antenna elements relative to the plane of the radiating aperture at three angles. 2. Investigation of the main patterns of changes in the directional characteristics of the phased array antenna due to the presence of errors in the antenna elements installation in the radiating aperture of the phased array antenna. In particular, errors in the installation of antenna elements practically do not lead to a change in the main beam either in width or in level. The most significant changes in the directional characteristics are manifested as follows: the structure and level of the side lobes of the directional patterns of the phased array antenna change; there is a cross-polarized component in the directional pattern, which, unlike the main component, is weakly directional. The developed mathematical model and the obtained simulation results allow us to determine the relationship between the parameters of the antenna elements installation errors as part of the phased array antenna aperture with a change in the amplitude, phase and polarization directional pattern, on the basis of which requirements for the accuracy of the parameters of the radiating aperture and the accuracy of the antenna elements installation can be formulated. These results are most significant for communication and radar systems that use orthogonal polarization signals when receiving and radiating.

Influence of a saltwater film on a radio-transparent dome on the amplitude-phase distribution of a millimeter-range antenna

Transition of communication systems installed on naval ships to the millimeter range requires an analysis of the effect of the saltwater film formed on the radio-transparent dome (RTD) on the radiotechnical characteristics of the mirror antenna. The latter are determined by the amplitude-phase distribution in the antenna aperture, so the topic of research is relevant. The objective of the article is to analyze the effect of the salt-water film on the surface of a marine mounted RTD, as well as the effect of millimeter wavelength antenna placement inside the RTD on the distortion of the field generated in the outer region. It has been shown that when installing millimeter-wave range antennas on a naval ship under a radio-transparent dome it is necessary to consider the distortions introduced by the water film on the dome surface into the generated amplitude-phase distribution when calculating the radio technical characteristics. We do so because most of the known methods for calculating the directivity characteristics of mirror antennas are based on the known amplitude-phase distribution in the antenna aperture. In the paper, the influence of the spherical dome wall and the saltwater film on the amplitude-phase distribution is taken into account as follows. Distortions in the amplitude distribution are caused by energy losses of the electromagnetic wave due to the passage of the curved dielectric wall at different angles. Phase distribution losses are due to the phase shift from the original phase as the dome wall is passed through at different angles. The angles of radio wave entry into the dome wall depend on the location of the antenna inside the radio-transparent dome. The electrical parameters of the saltwater film are determined using the well-known ITU methodology, while its thickness is found using the Gibbs formula, assuming that sea spray is similar to the intensity of drizzle rain. The studies have been conducted for the highest stiffness mode. Studies for a single-mirror antenna with a parabolic reflector 5.4 m in diameter and a radio-transparent dome 18 m in diameter showed that the water film influence is manifested in the phase front distortion, as well as a symmetry violation of the generated amplitude distribution. The degree of water salinity is manifested mainly in the distortion of the phase distribution. This is due to the fact that the electrical parameters of salt and fresh water do not differ much. The detected distortions are stronger for the horizontally polarized waves and in the case when the antenna swing center is offset with respect to the dome symmetry line. The detected patterns allow to give a scientific justification for the choice of the amplitude-phase distribution of the mirror antenna when installing it inside the RTD on the naval ship.

3D printed variable aperture horn with modular ridges

3D printing technology has significant potential to modernize the student laboratory experience in the area of electromagnetic wave propagation and scattering. In this contribution, a fast and low-cost method to 3D print and metallize a variable aperture horn and waveguide launcher are presented. The launcher converts a SubMiniature version A (SMA) coaxial connector to WR 187 waveguide (standard size of waveguide for 3.95 GHz to 5.85 GHz) and is printed from plastic while being metallized with aluminum tape. The launcher provided similar performance to an off the shelf launcher at one 40th the cost. As a teachable extension to this launcher a variable aperture horn is 3D printed and metallized with aluminum tape. The aperture area of the horn is changed by rotating the walls of the horn away from each other by use of pivot in the transition between the launcher and the horn. This horn showed the expected decrease in beamwidth and increase in peak gain as the aperture area was increased while maintaining a usable impedance match. Modular center ridges were also printed to demonstrate the utility of center ridges in a horn antenna without walls. Overall, a modular, inexpensive, and easy to construct waveguide system is presented that is useful for teaching electromagnetics specifically the relationship between aperture area and antenna gain, as well as providing a platform for waveguide experiments.

Multi-panel extra-large scale MIMO based joint activity detection and channel estimation for near-field massive IoT access

The extra-large scale multiple-input multiple-output (XL-MIMO) for the beyond fifth/sixth generation mobile communications is a promising technology to provide Tbps data transmission and stable access service. However, the extremely large antenna array aperture arouses the channel near-field effect, resulting in the deteriorated data rate and other challenges in the practice communication systems. Meanwhile, multi-panel MIMO technology has attracted extensive attention due to its flexible configuration, low hardware cost, and wider coverage. By combining the XL-MIMO and multi-panel array structure, we construct multi-panel XL-MIMO and apply it to massive Internet of Things (IoT) access. First, we model the multi-panel XL-MIMO-based near-field channels for massive IoT access scenarios, where the electromagnetic waves corresponding to different panels have different angles of arrival/departure (AoAs/AoDs). Then, by exploiting the sparsity of the near-field massive IoT access channels, we formulate a compressed sensing based joint active user detection (AUD) and channel estimation (CE) problem which is solved by AMP-EM-MMV algorithm. The simulation results exhibit the superiority of the AMP-EM-MMV based joint AUD and CE scheme over the baseline algorithms.

A Monolithically Printed Filtering Waveguide Aperture Antenna

This letter presents the design of a 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> order filtering waveguide aperture antenna based on coupled cavity resonators. Three offset-coupled rectangular waveguide cavities are employed in the design realizing two nested loaded-stubs without costing extra structure and size. The loaded-stubs introduce two controllable transmission zeroes and enhance the out-of-band realized gain selectivity. To validate the predicted results, a prototype operating at the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X-</i> band frequencies has been fabricated monolithically using the 3-D selective laser melting printing technique. The measured results are in very good agreement with the simulated results, showing a flat gain response of 7.0 ± 0.2 dBi from 9.5–10.5 GHz with very good out-of-band selectivity. The fractional bandwidth is about 10% at 10 GHz when <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> = -20 dB. Compared to the previously designed filtering antennas, the proposed design has the advantages of stronger out-of-band gain selectivity and low profile.

A filtering waveguide aperture antenna based on all‐resonator structures

AbstractIn recent years, there has been a large amount of attention focused on the design of filtering antennas to reduce the front‐end size of modern wireless communication systems. Although numerous design approaches are presented in the literature, they are usually applicable to a certain microwave circuit structure. Additionally, their implementations demand extra matching circuits or a structure which leads to an increase in the filtering antenna size. In this paper, the design of a 3rd‐order filtering antenna operating at the X‐band frequencies is presented utilizing the coupling matrix approach. It is based on 3rd order coupled‐resonators filter without employing any extra structure. For the physical configuration, three inline coupled rectangular waveguide cavity resonators operating at TE101 mode are employed. The output of the last resonator is coupled to free space via a rectangular aperture. The dimensions of the aperture are manipulated to control the radiation quality factor (Qr). To validate the simulated results, the design has been fabricated using the Computer Numerical Control technique. Excellent agreement between the simulation and measurement results has been obtained. The fractional bandwidth (FBW) is more than 10% when the reflection coefficient S11 = −20 dB. The gain response is very flat (7.54 0.2 dBi) from 9.5 to 10.5 GHz. The proposed filtering antenna is compact and low profile which may be of interest in radar applications.

Development of a deployable Synthetic Aperture Radar antenna for a nanosatellite conceptual design

For a real-time maritime surveillance application in the extended territorial waters of New Zealand, this work aims to develop a viable concept design for a deployable Synthetic Aperture Radar (SAR) antenna to fit in a CubeSat design space. To trade off a large antenna aperture, which is essential to enhance SAR performance, and a high packaging efficiency, potentially ≤ 12U, a 4 m x 0.3 m reflectarray with a stiff-and-flexible and novel passive deployable system is selected as the most promising solution for this application. A High Strain Composite (HSC) structure with a shallow “tape-measure” inspired shape is presented to support the SAR reflectarray and compactly stow it through a rollable deployment system. The release of the elastic energy stored in the coiled structure will enable the deployment, and the structural stiffness will be provided by a boundary condition that maintains the naturally curved cross-section during stowage. With this design constraint, the transition zone (ploy region) that develops between the stowed and deployed state may significantly impact the stowage capabilities. The elastic behaviour of the structure will be analytically studied in terms of the change of curvatures and bending stiffness as they dominate the deformed shape in the coiling process. Existing analytical models that predict the ploy regions are considered to estimate the natural ploy length and the equivalent coil diameter. Finite Element (FE) models are developed to compare the analytical models and explore the stress field generated within the ploy region when the length of this region is forced to be shorter than the natural ploy length. FE model observations and data are also used to improve the analytical model that describes the deformed shape by imposing non-uniform boundary conditions on the curvatures’ field distribution within the ploy region.

Engineering Designs of Dual-Polarized Antennas With Reduced Profile and Mutual Coupling for 5G Microcell Application

In this letter, a miniaturized, low profile and low mutual coupling antenna array with stable radiation pattern for fifth-generation microcell is presented. The antenna element contains three parts, folded dipole radiator, vertical feeding baluns, and reflector. Four striplines with end connections and stepped slots etched on the main radiator are adopted to enhance the impedance bandwidth and miniaturized the antenna's aperture in the low-profile configuration. While folded stripline structure is applied to reduce the mutual coupling in dual-polarized antenna. The height of proposed antenna is only 0.1 λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> is the free-space wavelength referring to the center operation frequency) and the antenna's aperture is only 0.4 λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> × 0.4 λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> . Measured results show that the antenna array has good performances, exhibiting low voltage standing-wave ratio (VSWR < 1.5), high isolation (> 30 dB), and wide bandwidth (3.2–3.9 GHz, 20%). Stable radiation patterns are measured across the operating bandwidth.