Virtual Array Research Articles

Increasing the resolution of phased antenna arrays of the optical wave band by forming a virtual antenna array

Formulation of the problem. When solving the direction-finding problem of determining the direction to radiation sources located at an angular distance less than the width of the main lobe of the direction-finding antenna, the problem of insufficiency of resolution arises. This leads to the fact that two closely located sources will be perceived by the direction finding complex as one. Purpose. The purpose of this work is to study the possibility of solving the problem of resolution of two sources using an optical antenna array with a width of the main lobe smaller than the angular distance between the radiation sources. Results. As a solution to the problem of insufficient resolution, it is proposed to use the method of virtual antenna arrays, which consists in the formation of additional ("virtual") antenna elements using the mathematical apparatus of the Kirchhoff integral and the method of point sources. The article presents the results obtained with the help of mathematical modeling, which confirm the high efficiency of the proposed method. Practical significance. The obtained results can be used to improve the resolution of the direction finders of the optical range only due to an additional signal processing procedure, without making changes to the design of the direction-finding antenna.

Multi-Objective Optimization Approaches for Physical Layer Secure Communications Based on Collaborative Beamforming in UAV Networks

Unmanned aerial vehicle (UAV) communications and networks are promising technologies in the forthcoming 5G/6G wireless communications. However, they have challenges for realizing secure communications. In this paper, we consider to construct a virtual antenna array consists UAV elements and use collaborative beamforming (CB) to achieve the UAV secure communications with different base stations (BSs), subject to the known and unknown eavesdroppers on the ground. To achieve a better secure performance, the UAV elements can fly to optimal positions with optimal excitation current weights for performing CB transmissions. However, this leads to extra motion energy consumption. We formulate a physical layer secure communication multi-objective optimization problem (MOP) of UAV networks to simultaneously improve the total secrecy rates, total maximum sidelobe level (SLL) and total motion energy consumption of UAVs by jointly optimizing the positions and excitation current weights of UAVs, and the order of communicating with different BSs. Due to the complexity and NP-hardness of the formulated MOP, we propose an improved multi-objective dragonfly algorithm with chaotic solution initialization and hybrid solution update operators (IMODACH) and a parallel-IMODACH (P-IMODACH) to solve the problem. Simulation results verify that the proposed approaches can effectively solve the formulated MOP and it has better performance than some other benchmark algorithms and approaches. Moreover, some unexpected circumstances are considered and discussed.

Efficient binary sequence set designs for MIMO PMCW radar

Multiple-input multiple-output (MIMO) phase-modulated continuous wave (PMCW) radar systems have major advantages for mutual-interference mitigation over their linear frequency-modulated continuous wave (LFMCW) counterparts. To attain a virtual array length of M×M̃ with M transmit and M̃ receive antennas, a probing sequence set with both low auto-correlation sidelobes and low cross-correlations is needed for MIMO PMCW radar. To reduce the hardware cost of sequence generation, binary probing sequence (BPS) sets are desirable. We present herein four efficient computational algorithms to generate BPS sets with desirable properties, and arbitrary sequence lengths and arbitrary number of sequences in the set are allowed. When initialized by random BPS sets, they can be used to obtain many different BPS sets with similar properties, i.e., with large diversity. Moreover, fast Fourier transform (FFT) are exploited, making the algorithms computationally efficient. They can be used to design long BPS sets that are hardly possible using existing methods in the literature. The convergence properties and the relationships among the proposed algorithms are also analyzed under a unified framework. Numerical examples are included to illustrate the effectiveness of our designs.

Arbitrary Virtual Array Source Aperture (AVASA) Ultrasound Imaging Technique Using Phased Array Excitation

Arbitrary Virtual Array Source Aperture (AVASA) Ultrasound Imaging Technique Using Phased Array Excitation

A new synthesis method for complex electric field patterning using a multichannel dense array system with applications in low-intensity noninvasive neuromodulation.

Multichannel coil array systems offer precise spatiotemporal electronic steering and patterning of electric and magnetic fields without the physical movement of coils or magnets. This capability could potentially benefit a wide range of biomagnetic applications such as low-intensity noninvasive neuromodulation or magnetic drug delivery. In this regard, the objective of this work is to develop a unique synthesis method, that enabled by a multichannel dense array system, generates complex current pattern distributions not previously reported in the literature. Simulations and experimental results verify that highly curved or irregular (e.g., zig-zag) patterns at singular and multiple sites can be efficiently formed using this method. The synthesis method is composed of three primary components; a pixel cell (basic unit of pattern formation), a template array ("virtual array": code that disseminates the coil current weights to the "physical" dense array), and a hexagonal coordinate system. Low-intensity or low-field magnetic stimulation is identified as a potential application that could benefit from this work in the future and as such is used as an example to frame the research.

Linear and 2D arrays for Focused Laser Differential Interferometry using a high-speed camera

Since the introduction of linear array focused laser differential interferometry (LA-FLDI), its use has rapidly proliferated as it extends the capabilities of FLDI to multiple measurement positions, greatly increasing the amount of data that can be simultaneously collected. To collect and store the signal data from LA-FLDI, arrays of photodiodes have primarily been utilized in recent literature, and, while photodiodes have the distinct advantage of reaching sampling rates on the order of 100＋ MHz, custom setups for photodiode arrays can be cumbersome to build and align as the number of points in the FLDI beam array increases and nonlinear array designs begin to be considered. As an alternative to photodiode arrays, high-speed cameras are promising, but their usage for LA-FLDI has been quite limited thus far. Compared to photodiodes, modern high-speed cameras are both expensive and possess lower sampling rates, but they are easy to align and provide expanded ability to measure larger arrays of FLDI points. The camera sensor needs only to be placed perpendicular to the array path, and, if appropriately sized, the entire array can be captured without individually aligning the beams. In this work, a high-speed camera is used to record measurements of spectral content, in a Mach 1 free jet flow obtained via imaging FLDI with 5 × 5, 3 × 3, 1 × 5, 1 × 10, and 1 × 12 arrays created using a combination of a 5 × 5 diffractive optical element and post-process sampling of individual pixels to form what we have named “virtual arrays”. For the sake of comparison and proof of similar applicability, the signal from the center point of the 5 × 5 grid is also measured using a high frequency bandwidth photodiode. The experiments show similar capability between the photodiode and camera results when measuring dominant frequencies in the spectral content, even when sampling individual pixels within FLDI points. Possibly due to the significantly smaller size of the pixels, the magnitudes of the individual pixel spectra are often less than that of the photodiode. However, the camera results imply the potential for arrays of arbitrary sizes and shapes, which are only limited by camera sensor size, to be imaged and yield informative estimates of spectral content. Furthermore, sampling individual camera pixels appears to provide significantly enhanced spatial resolution. For FLDI applications involving lower frequency ranges, say 0–2 MHz, current high-speed cameras may provide a suitable if not advantageous alternative to photodiode arrays.

DOA Estimation With Co-Prime Array by a Combined BNC-PFLOM Method in Presence of Impulsive Noise

Direction of arrival (DOA) estimation with co-prime array is well studied in the field of array signal processing, but most research assumes noise to be Gaussian white noise. In practical scenarios, there might be impulsive noise, which has neither second-order statistics nor high-order cumulant, therefore cannot be processed directly in co-prime array configurations. In addition, the signals received by the co-prime virtual array are of single snapshot, which can be considered as coherent virtual signals coming from the same source and therefore performance degradation in DOA estimation. To solve the above mentioned problems, a combined bounded non-linear covariance (BNC) and phase fractional low-order moments (PFLOM), called BNCPFLOM, is proposed in this paper. The proposed BNC-PFLOM combines the merits of both BNC and PFLOM by constructing equivalent data covariance matrices of the received signal to lower the impact of impulsive noise. Moreover, the proposed BNC-PFLOM can build multiple pseudo snapshots of virtual signals from the co-prime array by using different orders of the proposed method. With the increase of pseudo snapshots, the proposed method is more robust in DOA estimation. Besides, the pseudo snapshots are developed from different methods, which implies different virtual signals coming from different sources. Therefore, the correlation between the virtual co-array signals can be reduced; and the proposed method direct estimates the DOAs of signals without spatial smoothing when the number of incoming signals is small. The proposed method generates multiple pseudo snapshots, which improves the resolution and accuracy in DOA estimation with co-prime array, and can be used for radar, sonar, communication systems, etc. Simulation results demonstrate the effectiveness of the proposed method, which outperforms the conventional BNC, FLOM, and PFLOM with smaller root means square error (RMSE) in terms of the generalized signal to noise ratio (GSNR) and factor of impulsive noise.

BD-CVSA: A Broadband Direction Finding Method Based on Constructing Virtual Sparse Arrays

As the electromagnetic environment becomes more complex, radio direction finding systems need to cover a wide frequency range. However, the phase ambiguity of high frequency limits the development of broadband direction finding technology. The existing methods in solving the phase ambiguity problem heavily rely on designing the precise actual sparse array structure by theoretical derivation, which is expensive and time-consuming. To solve this problem, we propose a broadband direction finding method based on constructing virtual sparse arrays. First, we perform the convolutional operation on the direction feature matrix to achieve the weighted summation of the original baselines, which generates numerous virtual array elements and virtual baselines with different directions. The virtual array elements are combined to form virtual sparse arrays with different aperture sizes. Second, we optimize the parameters through the error backpropagation algorithm and obtain the optimal combination of virtual sparse arrays, which eliminates the phase ambiguity. Meanwhile, the virtual sparse arrays can maintain the advantages of sparse arrays, which can accomplish high-precision broadband direction finding. The experimental results demonstrate that the proposed method can solve the phase ambiguity problem effectively. It has high accuracy and strong robustness in simulation environment.

Automated defect recognition (ADR) for monitoring industrial components using neural networks with phased array ultrasonic images

In this paper, we propose a framework to automate the process of defect characterizing for industrial structural component health monitoring by implementing automatic defect recognition (ADR) system. The ADR system consists of a convolutional neural network (CNN) and an edge detection algorithm medial axis transform (MAT). The CNN learns the defect feature space from the training dataset to detect and classify the defect. The MAT algorithm is used upon post-validation of the ADR, and the predicted feature’s edges are extracted to size them. The ADR is trained using the simulation-assisted finite element (FE) simulation datasets consisting of side drilled holes (SDH) and crack defects images. The training datasets are generated by introducing virtual array source aperture (VASA), which is a full matrix capture (FMC) scanning strategy by activating the group of elements in an active aperture with predefined focal laws to form a focused beam at a virtual source in the material. The VASA technique uses multiple virtual sources and active aperture positions in a given transducer, which are determined using the Poisson point process. The ultrasound beam is excited in sequence on each virtual source, and the reflected wave is recoded using all the transducers in the array to create FMC A-scans signals. The total focusing method (TFM) technique is a postprocessing algorithm implemented on the FMC signal to generate an image. A large quantity of training datasets is created for each defect by modeling various FE models with varying defect morphology. To create nearly close to experimental images, the experimental noise is introduced in the simulated images. The three separate ADR systems are trained with individual defects class and combined defects. The effectiveness of the trained ADR system is validated by conducting experiments on the plates with laboratory-made SDH and crack defects, the casting components, and weldments with unknown defect types and sizes. The mAP of ADR training is 82%, and the F1-score on testing image classification is 89%. The ADR system could detect and size the smallest defect is 0.219 mm, which is λ L /5.

Cramer-Rao bound investigation of a novel virtually extended nested arc array for 2D DOA estimation

This paper exploits a sparse array representation, a novel nested arc array, to generate a virtual non-uniform circular arrays that have been presented and investigated. To increase the array aperture, the virtual array has been developed using higher-order statistics, namely, the Forth-Order Cumulants (FOC). The extended array contains a combination of physical as well as virtual sensors. The increased degrees of freedom (DOFs) in the resultant virtual array make it suitable for over-and under-determined direction of arrival (DOA) estimation. The Cramer-Rao bound (CRB) and the (DOA) estimation for such an array are developed and investigated for various arrays. The proposed array performance is superior to that of the uniform one. Further, the offered array is suitable for two-dimensional (2D) DOA estimation problems.

Robust adaptive beamforming algorithm for coherent signals based on virtual array

Robust adaptive beamforming algorithm for coherent signals based on virtual array

Fast Numerical Reconstruction of Integral Imaging Based on a Determined Interval Mapping

In this paper, a fast numerical reconstruction of the integral imaging based on a determined interval mapping is proposed. To reduce the computation time, the proposed method employs the determined interval mapping instead of the use of magnification. In the numerical reconstruction procedure, the acquired elemental image array (EIA) from the 3D object is displayed. The flipped elemental image (EI)s are numerically formed by the virtual pinhole array. Then, the determined interval depending on the reconstruction plane is calculated and applied to each flipped EI. These flipped EIs are shifted to match the determined interval at the reconstruction plane and superimposed together. After this superimposed image is divided by the number of the superposition, the position error between the location of the shifted EI and the pixel position of the reconstruction plane is corrected by interpolation. As a result, the refocused image depending on the reconstruction plane can be reconstructed rapidly. From the experimental result, we confirmed that the proposed method largely decreased the computation time compared with the conventional method. In addition, we verified that the quality of the reconstruction by the proposed method is higher than the conventional method by the use of the structural similarity index method.

DOA estimation for uniform circular array without the source number based on beamspace transform and higher-order cumulant

Fourth-order cumulant is one of most widely used high-order cumulant for direction of arrival (DOA) estimation due to its ability of expanding the virtual array aperture as well as suppressing Gaussian noise. To address the two-dimensional (2D) DOA estimation problem, we propose a modified MUSIC scheme for uniform circular array (UCA) in this paper. Firstly, the fourth-order cumulant of UCA is considered to construct a new propagator, resulting in the elimination of a priori knowledge of the number of signals. Secondly, the UCA is transformed by beamspace transformation, reducing the time computational complexity of the algorithm since the two-dimensional grid search and singular value decomposition are avoided. And finally a low-rank recovery algorithm is adopted to improve the accuracy regarding the limited snapshots scenario. The numerical simulations validate the superiority of the proposed method.

Joint estimation of DOA and coupling matrix based on linear prediction for small spacing antenna array

A method for joint estimation of DOA and coupling matrix based on linear prediction is proposed for low resolution of mutual coupling calibration method in the case of small spacing antenna array. This method augments array aperture virtually according to linear prediction principle and calculates the coupling matrix by this virtual array. Then, this coupling matrix is used as the initialization matrix of joint estimation algorithm for coupling calibration. Simulation results confirm the effectiveness of the proposed method and provide the theoretical foundation for engineering realization. This method could also be applied in the field of tactical anti-jamming communication.

Transformation of a circular array to a linear array with a Vandermonde structure

We address the transformation of a uniform circular array to a virtual uniform linear array. This phase mode transformation is widely used because many computationally efficient techniques that are not applicable to circular arrays can be implemented after the transformation. However, the transformed array is only approximately linear and its steering vector lacks a crucial property of a uniform linear array: a Vandermonde structure. The performances of the algorithms designed for uniform linear arrays can be substantially improved by removing the error in the transformation, thereby enforcing the Vandermonde structure in the steering vectors. We present an analytical technique to remove errors in the transformation and validate its efficacy by demonstrating an improvement in the root MUSIC algorithm.

Improved imaging technique for nondestructive evaluation using arbitrary virtual array source aperture (AVASA)

In this paper, we propose a new phased array imaging technique called Arbitrary Virtual Array Source Aperture (AVASA) to image deeper defects with an improved SNR with fewer transmissions. The approach is to transmit the ultrasound waves by electronic beamforming at several arbitrary virtual source positions to achieve higher focal depth to increase the SNR of the received A-scans. Backscattered signals are recorded with all the array elements. A high-resolution image is obtained on reception by virtually focusing on every point in the region of interest by signal coherence summation. In this paper, the proposed AVASA and TFM methods are employed for scanning the larger thickness structure with an unknown defect nature to contrast the defect SNR and the number of defect imaging. Compared with TFM imaging, the AVASA method shows a significantly increasing defect-detecting range with higher amplitude. To further improve the imaging quality and reduce the reconstruction time, the influence of the virtual source parameters on the AVASA imaging and a scanning strategy is demonstrated. A good agreement between the AVASA and TFM is observed, and the number of transmissions is required to inspect the test specimen using AVASA reduced by a factor of four to eight.

Beampattern Synthesis and Optimization for Frequency Diverse Arc Array Based on the Virtual Element

With its special, arch-shaped array structure, a frequency diverse arc array (FDAA) can perform beam scanning in 360 degrees in azimuth and in arbitrary ranges by selectively activating array elements in different positions, utilizing array element phase compensation, and adopting a frequency offset design. In this paper, a beampattern synthesis and optimization method for FDDA using the virtual array element based on the geometric configuration of FDDA is proposed. First, the position of the virtual array element is determined by the direction of the target, and then activated array elements are selected. Afterwards, the frequency offset of each array element is set up on the equiphase surface to obtain the dot-shaped beampattern. Finally, amplitude weighting is introduced to suppress the increased sidelobe level of the dot-shaped beampattern, which is caused by inverse density weighting of the arch-shaped array structure. Simulation results validate the proposed method for beampattern synthesis and optimization in FDAA.

DOA estimation method for incoherently distributed sources based on spatial–temporal generalized ESPRIT

This paper proposes a spatial–temporal generalized ESPRIT parameter estimation method to solve the estimation problem of the central angles and spread angles of incoherently distributed sources. To begin with, a virtual array covariance matrix is built by conducting time-delay autocorrelation operation on the original received data. The central angles are then estimated with the generalized shift invariance property inside the virtual array manifold. Next, the spread angles are obtained with resorting to the estimated central angles and the central moments of the angular distribution function. Compared with the existing algorithm, the proposed algorithm does not require the signal to have non-circular characteristics, and has higher parameter estimation accuracy and can distinguish more sources. In addition, the proposed method is robust to types of spread angles, as verified by a series of simulation results.

Collaborative WSN-UAV Data Collection in Smart Agriculture: A Bi-objective Optimization Scheme

Smart agriculture which integrates the agriculture with Internet of Things (IoT) has attracted attention since it contributes to increase the productivity and quality of crops, reduce energy consumption and facilitate the farmers. Wireless sensor networks (WSNs) and unmanned aerial vehicles (UAVs) are two most commonly deployed devices that are used for enabling the smart agriculture. In this paper, we design a collaborative WSN-UAV system, wherein different clusters of sensor nodes form different sensor-based virtual antenna arrays (SVAAs) to transmit the collected data towards different receiver UAVs via adopting collaborative beamforming (CB), then the receiver UAVs will take the collected data back to the ground control station (GCS). We formulate a transmission rate and battery energy bi-objective optimization problem (TRBEBOP) to simultaneously maximize the total transmission rate of the sensor-based CB clusters and the total remaining battery energy of the selected sensor nodes, by selecting appropriate sensor nodes in each cluster that can form a predominant SVAA, determining suitable receiver UAVs and optimizing the excitation current weights of the selected sensor nodes. To handle the formulated TRBEBOP that is demonstrated to be non-convex and NP-hard, an enhanced non-dominated sorting genetic algorithm II (ENSGA-II) with several specific designs is presented. Simulation results validate the effectiveness of the proposed ENSGA-II for solving the formulated TRBEBOP. Moreover, compared with other benchmark algorithms, the superiority of the proposed ENSGA-II is demonstrated. In addition, the impacts of several fortuitous circumstances on the system are estimated, and the results illustrate the robustness of the proposed scheme. Finally, the discussion about several mechanisms to deal with the interference induced by the sidelobe levels and the impact of UAV movement on receiving rate are provided.

Investigation of methods for the formation of virtual antenna arrays under conditions of strong distortion of the electromagnetic field structure near the receiving antenna array

Investigation of methods for the formation of virtual antenna arrays under conditions of strong distortion of the electromagnetic field structure near the receiving antenna array