Direction Finding Array Research Articles

Electrodynamic modeling of a four-channel antenna with an operating frequency band of octave

The actual problem of electrodynamic modeling of a four-channel antenna with an octave operating frequency range has been considered. The results of numerical electrodynamic modeling of a four-channel antenna have been presented. The considered antenna with an octave operating frequency range is a rectangular curtain comprising four independent non-equidistant channels. Numerical electrodynamic modeling of a four-channel antenna has been carried out in the ANSYS HFSS software package, with the convergence parameter DeltaS = 0.01. As a result of the simulation, the frequency characteristics of each channel have been obtained: VSWR, gain, reflection coefficient, directional pattern. The antenna provides a scanning angle as part of an ultra-wideband digital antenna array of at least ±30° in azimuth and from 0° to 60° in elevation. The gain of the antenna channels in the operating frequency range is not lower than 6 dB. According to the simulation results, the VSWR of each channel of the antenna in the operating frequency range does not exceed 2.55. To minimize the influence of mutual coupling of channels on the antenna characteristics, the distance from the phase centers of the curtain emitters to other elements of the ultra-wideband digital antenna array should be at least a wavelength in free space at the lower frequency of the operating frequency range. It has been shown that the considered four-channel antenna provides an octave operating frequency band and can be used as part of an ultra-wideband digital antenna array for direction finding of radiation sources.

Angle Rigidity for Multiagent Formations in 3-D

This paper establishes the notion and properties of angle rigidity for 3D multi-point frameworks with angle constraints, and then designs direction-only control laws to stabilize angle rigid formations of mobile agents in 3D. Angles are defined using the interior angles of triangles within the given framework, which are independent of the choice of coordinate frames and can be conveniently measured using monocular cameras and direction-finding arrays. We show that 3D angle rigidity is a local property, which is in contrast to the 3D bearing rigidity as has been proved to be a global property in the literature. We demonstrate that such angle rigid and globally angle rigid frameworks can be constructed through adding repeatedly new points to the original small angle rigid framework with carefully chosen angle constraints. We also investigate how to merge two 3D angle rigid frameworks by connecting three points of one angle rigid framework simultaneously to the other. When angle constraints are given only in the surface of a framework, angle rigidity of convex polyhedra is studied, in which the cases of triangular face and triangulated face are considered, respectively. The proposed 3D angle rigidity theory is then utilized to design decentralized formation control strategies using local direction measurements for teams of mobile agents. Simulation examples are provided to validate the convergence of the formations.

전후방비 개선 설계 기법을 이용한 ISM 대역 방향 탐지 안테나

In this study, a direction-finding array antenna with an improved front-to-back ratio was developed by inserting meander slots into the ground plane of an electrically small antenna. The proposed ground slot structure improves direction-finding capabilities while maintaining the electrically compact structure of the antenna. The overall size of the antenna is 58 mm×58 mm×40 mm, with each array element measuring 40 mm×22 mm×1.6 mm. The antenna consists of eight elements attached to a vertical column, forming an octagonal structure that affords omnidirectional detection. The measured S11 bandwidth (≤−10 dB) is between 2.37 and 2.48 GHz. At 2.44 GHz, the maximum gain is −2.71 dBi, the 3-dB beamwidth occurs at an elevation angle of 74.2° and azimuth angle of 84.4°, and the front-to-back ratio is 8.89 dB.

A Spatially Confined, Platform-Based HF Direction Finding Array

A spatially-confined, platform-based HF antenna array with enhanced bandwidth and direction-finding (DF) accuracy is presented. As the HF band is widely used in many important civilian and military applications, HF DF systems are of great interest in electronic warfare support applications. However, due to the large wavelength, practical DF arrays mounted on moving platforms tend to be electrically small, resulting in fundamental limitations on antenna bandwidth and DF accuracy. Furthermore, many applications require mounting the array at a single location on the platform due to limited space and mobility considerations. To alleviate these issues, we employ the platform as the major radiator by exciting several of its significant characteristic modes (CMs) using a spatially-confined antenna array. Specifically, we examined four DF array designs mounted on a representative, mid-size passenger airplane operating at 10 MHz in simulation, each of which is confined within a virtual sphere with a 3-m diameter. A scaled model of one design was fabricated and characterized. Cramer-Rao bounds and Monte-Carlo test results are also reported. Our results demonstrate that the proposed DF array can provide a 15% lower DoA estimation error than the theoretical limit of a standalone array possessing the same volume and having the same bandwidth.

Performance-Enhancement of Platform-Based, HF Direction-Finding Systems Using Dynamic Mode Selection

We present a method to enhance the accuracy of platform-based, high-frequency (HF) direction-finding (DF) systems using dynamic mode selection. To improve bandwidth and efficiency, the metallic platform supporting the DF array is used as the primary radiator by employing electrically small antennas to excite linearly independent combinations of its characteristic modes (CMs). However, the radiation characteristics of these modes vary dramatically over the HF band, making it difficult to achieve consistently good DF accuracy with a fixed system. To alleviate this, we propose a dynamic mode selection strategy to achieve enhanced DF accuracy. This strategy is based on the assumption that the number of available CMs of the platform is greater than the number of available coherent receive channels. Thus, dynamic mode selection allows for choosing the optimal antenna combination to obtain the best DF accuracy at each frequency. This strategy is demonstrated for an airborne DF system employing five electrically small antennas and up to four coherent receive channels. We demonstrate the efficacy of the proposed approach using computer simulations and scaled-model experiments. Simulation and measurement results show that dynamic mode selection can significantly enhance the DF accuracy of platform-based HF DF systems using a limited number of coherent receive channels.

Optimal Three-Dimensional Antenna Array for Direction Finding With Geometric Constraint

This paper studies the optimal three-dimensional (3-D) antenna array for direction finding when the antenna array is subject to geometric constraint. Two-dimensional (2-D) planar array has been widely used in existing direction finding systems, and the optimal geometry for planar array has also been investigated in existing works. However, the optimal antenna array in the 3-D space, especially when the positions of the antennas are subject to geometric constraint, has not been studied yet. In this paper, a novel approach based on coordinate transformation is proposed for optimal antenna array design in the 3-D space with geometric constraint. Due to geometric constraint, the position of each antenna has only two degrees-of-freedom even thought it has three coordinate values, so that coordinate transformation can be used to convert 3-D coordinates of the array elements to 2-D ones. Then, existing optimization approach for 2-D planar array can be applied to address the issue of optimal 3-D antenna array. Simulation results show that the proposed antenna array in this paper can outperform the defacto uniform circular array (UCA) even in the presence of geometric constraint. As a potential application, the result in this paper can be applied to design the high-frequency (HF) direction finding antenna arrays that are placed in mountain area.

Methodology of improvement of directional properties of aperture reception elements of direction-finding array

In this paper the single biconical ultra-wideband reception device which is a part of directional-finding array is considered. Directional characteristics and matching of this device well-known and this characteristics can be improvement in several ways, for example, by means of the dielectric lens. However, use of classical lens essentially increments the terminating dimension of a device and all system. In this paper methods of transformation of the shape of a radiation pattern by means of the different dielectric insert in interior volume of receptions device are described. Directional characteristics and matching of a reception element will be defined by shape and dielectric properties of an insert.

Broadband, Small-Aperture Direction-Finding Array With Azimuth and Elevation Estimation Capability

A broadband (VHF-UHF), compact antenna array capable of estimating the elevation and azimuth angles of arrival of an electromagnetic wave is presented. Small-aperture direction-finding (DF) arrays are widely used at lower frequency bands (e.g., HF and VHF bands) where the electromagnetic wavelength is large and the physical size needed to accommodate the array is generally small. To design the proposed small-aperture DF array, we examined different array topologies that provide elevation and azimuth estimation capabilities and that are immune to errors caused by cross polarization. All of these potential candidates occupy the same volume of $14\times 14\times5.5$ cm3 corresponding to a maximum linear dimension of 19 cm. Subsequently, we adopted the topology that provides the lowest Cramer–Rao bound (CRB). The topology of this array was further optimized to efficiently utilize an available volume, and its DF performance was characterized over a wide frequency range from 30 to 2000 MHz using computer simulations. A prototype of the array was also fabricated and characterized using field tests at a number of discrete frequencies within this band. The measurement results show very good agreement with simulations and validate the DF capabilities and the expected accuracy levels predicted by the theoretical analyses.

Design of Platform-Based HF Direction-Finding Antennas Using the Characteristic Mode Theory

A systematic method for utilizing the characteristic modes (CMs) of a platform to design a direction finding (DF) system operating at the high-frequency (HF) band is presented. In this band, due to the large wavelengths, practical antennas used for DF are electrically small and have limited bandwidths. When such a DF array is mounted on a platform, however, the platform’s presence can be exploited to considerably improve the performance of the platform-based DF system compared to that of a stand-alone DF system. Our proposed approach relies upon selecting and exciting a group of the platform’s CMs that provides the lowest Cramer–Rao bound for the DF system’s accuracy. This approach allows for designing DF systems that can accurately detect the direction of arrival and the state of polarization of the wave over wide fields of views. This approach is used to design and simulate an HF DF system for an airborne platform. A scaled-model prototype of this platform-based DF array is fabricated and characterized. The measurement results of this array are used to perform DF experiments in an emulated environment. Measured results are found to be in good agreement with simulations, confirming the efficacy of the proposed design approach.

Rules-of-thumb to design a uniform spherical array for direction finding-Its Cramér-Rao bounds' nonlinear dependence on the number of sensors.

This paper discovers rules-of-thumb on how the estimation precision for an incident source's azimuth-polar direction-of-arrival (ϕ,θ) depends on the number (L) of identical isotropic sensors spaced uniformly on an open sphere of radius R. This estimation's corresponding Cramér-Rao bounds (CRB) are found to follow these elegantly simple approximations, useful for array design: (i) For the azimuth arrival angle: 2π(R/λ)(σs/σn)2LMCRB(ϕ) sin(θ)≈(Le1/14)-1+3→L→∞3, ∀(ϕ,θ); and (ii) for the polar arrival angle: 2π(R/λ)(σs/σn)2LMCRB(θ)≈3-(Le6/7)-1→L→∞3, ∀(ϕ,θ). Here, M denotes the number of snapshots, λ refers to the incident signal's wavelength, and (σs/σn)2 symbolizes the signal-to-noise power ratio.

Decoupled two-dimensional direction of arrival estimation of single distributed source by vectoring differential phases

In practical applications such as radar, sonar, and mobile communications, transmitted signals are often affected by the scattering and reflection phenomena, which causes the signal energy received by the antenna array to be distributed into a certain space. In this case, a distributed source model will be more applicable. In general, the distributed sources have been classified as coherently distributed (CD) source and incoherently distributed (ID) source, which prove to be suitable for the cases of slowly time-varying and rapidly time-varying channels, respectively.In this paper, we consider the two-dimensional direction of arrival (DOA) estimation of distributed sources (including CD source or ID source). Specifically, uniform circular array (UCA) is widely used because of its ability to measure full azimuth angle and high resolution. However, the existing estimation algorithms all require spectral peak searching and the eigenvalue decomposition, which can bring a large computational complexity. To solve this problem, a decoupled rapid two-dimensional DOA estimation algorithm is proposed based on vectoring differential phases considering the two cases of single CD source and ID source. Firstly, based on spatial frequency approximation model, it is proved that none of differential phases between the received signals of different sensors in the UCA is affected by angle spread parameters when there is only a single distributed source. Under the premise of such a property, the central DOAs can be decoupled through obtaining the differential phases. Next, we can obtain the phase angles of strictly upper triangular elements in the sample covariance matrix, which correspond to differential phases between different sensors. Finally, by vectoring these differential phases, the central azimuth and elevation DOAs are estimated in the closed form from a least-squared problem, where the spectral peak searching and eigenvalue decomposition can be avoided, hence the computational complexity is reduced greatly. Theoretical analysis and simulation results show that the proposed algorithm has higher estimation accuracy and does not require prior information about the distribution of angular signals. With both low computational complexity and low hardware complexity, the proposed algorithm is beneficial to the engineering practice of array direction finding in complex environment.

Interferometer angle‐of‐arrival determination using precalculated phases

AbstractA method has been developed to determine the angle of arrival (AoA) of incident radiation using precomputed lookup tables. The phase difference between two receiving antennas can be used to infer AoA as measured from the pair baseline, but there will be more than one possible solution for antenna spacings greater than or equal to half a wavelength. Larger spacings are preferable to minimize mutual coupling of elements in the receive array and to decrease the relative uncertainty in measured phase difference. We present a solution that uses all unique antenna pairs to determine probabilities for all possible azimuth and zenith values. Prior to analysis, the expected phase differences for all AoAs are calculated for each antenna pair. For a received signal, histograms of possible AoAs for each antenna pair phase difference are extracted and added to produce a two‐dimensional probability density array that will maximize at the true value of the AoA. A benefit of this method is that all possible antenna pairs are utilized rather than the restriction to specific pairs along baselines used by some interferometer algorithms. Numerical simulations indicate that performance of the suggested algorithm exceeds that of existing methods, with the benefit of additional flexibility in antenna placement. Meteor radar data have been used to test this method against existing methods, with excellent agreement between the two approaches. This method of AoA determination will allow the construction of low‐cost interferometric direction finding arrays with different layouts, including construction of difficult terrain and three‐dimensional antenna arrangements.

Direction-finding arrays of directional sensors for randomly located sources

The problem of directional sensor placement and orientation is considered when statistical information about the source direction of arrival is available. We focus on two-sensor arrays and form a cost function based on the Cramer–Rao bound that depends on the probability distribution of the coplanar source direction. Proper positioning and orientation of the sensors enable the two-sensor array to have an accuracy comparable to that of a three- or four-sensor uniform circular array.

Wideband direction finding using a photonic robust symmetrical number system technique

Dual electrode Mach–Zehnder modulators (DE-MZMs) are used to conduct phase detection for direct wideband direction finding (DF) of microwave signals. It is demonstrated theoretically and through simulation and experimentation that the normalized magnitude of the output signal phase detector circuit is equal to |sin(ψ/2)|, where ψ is the phase difference between the plane waves arriving at the reference and measurement antennas of a linear DF array. A four-element wideband photonic DF system with robust symmetrical number system preprocessing is presented. Simulation and experimental testing results are provided to demonstrate the theoretical concept. The results demonstrate a direct DF receiver using DE-MZMs that achieves fine angular resolution using a much smaller array size than is typically required for linear arrays employing super-resolution signal processing techniques.

An Array Design Method and Error Analysis for Terminal Trajectory Measurement

This paper introduces the implement method of system ,direction finding array design, time delay estimation of terminal trajectory measurement system. To measure the elevation angle in a vertical plane, discusses the azimuth angle, elevation angle measurement method and error analysis of planar cross array, five element conical array, symmetrical three-dimensional four elements array. After simulation the paper pointed out the last two arrays are better for terminal trajectory measurement based short baseline array.

Extended Closed-Form Expressions for the Robust Symmetrical Number System Dynamic Range and an Efficient Algorithm for Its Computation

The robust symmetrical number system (RSNS) is a number theoretic transform based on N ≥ 2 sequences that can extract the maximum amount of information from symmetrical folding waveforms. The sequences, based on coprime moduli, exhibit an integer gray code property making the RSNS well suited for many applications that benefit from an inherent error detection and correction capability, such as analog-to-digital converters, direction finding arrays, and radar waveform design. To use the RSNS, it is necessary to know the greatest length of combined sequences without ambiguities, called the dynamic range M, for which only a few closed-form expressions currently exist. In this paper, an efficient algorithm for computing M and its position within the combined set of sequences is presented and shown to be independent of the size of the moduli. The algorithm is used to generate the equations for several groups of additional moduli arrangements. Closed-form expressions for M are conjectured and proved using the obtained congruence equations that define the ambiguity locations.

Compact Wideband Direction-Finding Antenna

In this paper, we describe a compact, wideband (70-3000 MHz), and high-gain antenna technology that can replace multiple types of antennas currently in use to cover the wide frequency band. The design eliminates the frequency-band breaks associated with the use of multiple arrays. The wideband direction-finding array (with a height of 5.5 in and a diameter of 15.5 in) is the result of end-to-end integration of the antenna array with the receivers presently used, or to be used, on platforms of interest. Development of the wide-bandwidth direction-finding antenna array is described, and computer simulations of its performance are presented. The wideband direction-finding antenna system has been verified on the receiver manufacturer's outdoor test range.

Design and full-wave analysis of conformal ultra-wideband radio direction finders

The design and full-wave analysis of radio direction finders (RDFs) for ultra-wideband direction-of-arrival estimation is addressed. Conformal elliptically shaped dipoles are selected as antenna sensors by virtue of their good input impedance matching property, performance robustness and conformability. In order to achieve a full angular scanning coverage in the azimuthal direction, a uniform circular direction finding array topology is adopted. The parasitic coupling between the array elements is analysed rigorously, and a dedicated calibration method is used to compensate for non-idealities of the system. In particular, a computationally efficient design procedure for radio direction finding structures is proposed. This procedure, based on a suitable iterative approach, can be usefully adopted to determine the optimal array geometry in terms of number of antenna sensors and volume occupation, while providing a good insight into the physical limitations of the system. By using the developed optimisation technique, a novel RDF operating in the frequency range between 250 MHz and 3.3 GHz is designed, and the relevant performance is thoroughly investigated in realistic operative scenarios. It has been found that the proposed system is rank-1 ambiguity-free, and can be used for tracking both narrow and wideband radio signals.

A Multi-Channel Correlative Vector Direction Finding System Using Active Dipole Antenna Array for Mobile Direction Finding Applications

A fast correlative vector direction finding(CVDF) system using active dipole antenna array for mobile direction finding(DF) applications is presented. To develop the CVDF system, the main elements such as active dipole antenna, multi-channel direction finder, and search receiver are designed and analyzed. The active antenna is designed as composite structure to improve the filed strength sensitivity over the wide frequency range, and the multi-channel direction finder and search receiver are designed using DDS-based PLL with settling time of below 35 us to achieve short signal processing time. This system provides the capabilities of the high DF sensitivity over the wide frequency range and allows for high probability of intercept and accurate angle of arrival(AOA) estimation for agile signals. The design and performance analysis according to the external noise and modulation schemes of the CVDF system with five-element circular array are presented in detail.

Improved compensation for the mutual coupling effect in a dipole array for direction finding

A new and practical method is proposed to compensate for the mutual coupling effect in a dipole array deployed for direction finding. This method does not require either the current distributions on the antenna elements or the elevation angles of the incoming signals to be known. A new definition of mutual impedance is introduced to characterize the effect due to mutual coupling between dipole elements. The new mutual impedances are calculated based on an estimated current distribution. It is shown that the current method has a significantly better ability to compensate for the mutual coupling effect than previous methods. Computer simulations using the MUSIC algorithm are provided to demonstrate this method.