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Phased array antenna handbook / Robert J. Mailloux.

Phased array analysis using a modified Chebyshev approach [electronic resource] / Aris Alexopoulos.

Chases and escapes : the mathematics of pursuit and evasion / Paul J. Nahin.

Cyclostationarity in communications and signal processing / edited by William A. Gardner.

The functional organization of the compound eye : proceedings ... ... ... / Edited by C. G. Bernhard.

We design a logical qubit consisting of a linear array of quantum dots, we analyze error correction for this linear architecture, and we propose a sequence of experiments to demonstrate components of the logical qubit on near-term devices. To avoid the difficulty of fully controlling a two-dimensional array of dots, we adapt spin control and error correction to a one-dimensional line of silicon quantum dots. Control speed and efficiency are maintained via a scheme in which electron spin states are controlled globally using broadband microwave pulses for magnetic resonance, while two-qubit gates are provided by local electrical control of the exchange interaction between neighboring dots. Error correction with two-, three-, and four-qubit codes is adapted to a linear chain of qubits with nearest-neighbor gates. We estimate an error correction threshold of10−4. Furthermore, we describe a sequence of experiments to validate the methods on near-term devices starting from four coupled dots.

Physical review. X, 2018-06, Vol.8 (2), p.021058, Article 021058

Logical Qubit in a Linear Array of Semiconductor Quantum Dots

Semiconducting nanowires in proximity to superconductors are promising experimental systems for realizing the elusive Majorana fermions, which, because of their non-Abelian anyonic braiding statistics, may ultimately be used as building blocks for topological quantum computers. A serious challenge in the experimental realization of the Majorana fermions is the suppression of topological superconductivity by disorder together with the tunability of carrier density for semiconductors in close proximity to superconductors. Here we show that Majorana fermions that are protected by a disorder robust topological gap can occur at the ends of a chain of gate-tunable quantum dots connected by
s
-wave superconductors. Such an array of quantum dots provides the simplest realization of Majorana fermions in systems as simple as a few quantum dot array. The proposed system provides a very practical and easily realizable experimental platform for the observation of non-Abelian Majorana modes.
Majorana fermions—the particles renowned for being their own antiparticles—have been proposed as candidates for storing qubits for quantum computers. Sau and Das Sarma propose a method for creating stable Majorana fermions in an array of quantum dots.

Nature communications, 2012-07, Vol.3 (1), p.964-964, Article 964

Realizing a robust practical Majorana chain in a quantum-dot-superconductor linear array

A novel approach to linear array antennas with adaptive inter-element spacing is presented for the first time. The main idea is based upon electronically displacing the phase center location of the antenna elements, which determine their relative coordinates in the array configuration. This is realized by employing dual-mode microstrip patch antennas as a constitutive element, whose phase center location can be displaced from its physical center by simultaneously exciting two modes. The direction and the amount of displacement is controlled by the amplitude and phase of the modes at the element level. This in turn facilitates reconfiguring the inter-element spacing at the array level. For instance, a uniformly-spaced array could be electronically transformed into a non-uniform one without any mechanical means. The proposed idea is demonstrated in two- and three-element linear antenna arrays. The technique has the potential to control the radiation characteristics such as sidelobe levels, position of the nulls, and the beamwidths in small arrays, which are useful for adaptively controlling the array performance in emerging wireless communication systems and radars.

Scientific reports, 2021-03, Vol.11 (1), p.5584-5584, Article 5584

Principles of adaptive element spacing in linear array antennas

This work introduces a new holographic subsurface radar (HSR) system designed with a cross-arranged linear array antenna. In non-destructive applications, holographic subsurface radar utilizes continuous wave, high-density spatial sampling, and a wide synthetic aperture to achieve high azimuth resolution. However, this results in a low data acquisition speed, which limits the detection efficiency. In this work, we designed a cross-arranged linear array antenna, where the transmitting- and receiving-antennas are layered on two parallel baselines. In this way, the space between the neighboring sampling points can still meet the spatial sampling criterion. The use of the electric-switching antenna array reduces 2-dimensional mechanical scanning to a 1-dimensional scan, significantly improving data acquisition speed while maintaining sufficient spatial sampling density. The prototype of the system was also detailed in the paper. The experiments show that the newly designed HSR system can improve detection efficiency by more than 10 times while maintaining imaging resolution.

Journal of physics. Conference series, 2024-11, Vol.2887 (1), p.12040

Design of A Linear Array Holographic Subsurface Radar System

The functional linear array model (FLAM) is a unified model class for functional regression models including function-on-scalar, scalar-on-function and function-on-function regression. Mean, median, quantile as well as generalized additive regression models for functional or scalar responses are contained as special cases in this general framework. Our implementation features a broad variety of covariate effects, such as, linear, smooth and interaction effects of grouping variables, scalar and functional covariates. Computational efficiency is achieved by representing the model as a generalized linear array model. While the array structure requires a common grid for functional responses, missing values are allowed. Estimation is conducted using a boosting algorithm, which allows for numerous covariates and automatic, data-driven model selection. To illustrate the flexibility of the model class we use three applications on curing of resin for car production, heat values of fossil fuels and Canadian climate data (the last one in the electronic supplement). These require function-on-scalar, scalar-on-function and function-on-function regression models, respectively, as well as additional capabilities such as robust regression, spatial functional regression, model selection and accommodation of missings. An implementation of our methods is provided in the R add-on package FDboost.

Statistical modelling, 2015-06, Vol.15 (3), p.279-300

The functional linear array model

The frequency–azimuth (FRAZ) spectrum is a critical characteristic in passive target detection and tracking, as it encapsulates information regarding the signal’s frequency and azimuth. However, due to the inherent limitations in the sonar array’s physical aperture and the analysis time of the system, the signal often suffers from undersampling in both spatial and temporal dimensions. This undersampling leads to energy leakage across the azimuth and frequency domains, adversely affecting the resolution of the FRAZ spectrum. Such a reduction in resolution hampers multitarget resolution and feature extraction. To address these challenges, this study introduces a deconvolution-based FRAZ spectrum estimation method tailored for uniform linear arrays. The proposed method initiates by decoupling the azimuth and frequency in the FRAZ spectrum, forming a two-dimensional point scattering function that possesses shift-invariance. Subsequent to this, the power spectrum and the two-dimensional point scattering function undergo deconvolution using the Richardson–Lucy (R–L) iterative algorithm. The final stage involves calculating the signal azimuths and frequencies based on the deconvolution results from the preceding step. Comparative analyses involving simulations and sea test results reveal that the proposed method achieves a narrower main lobe width and diminished background noise in contrast to traditional FRAZ spectrum estimation techniques. This improvement is instrumental in minimizing the target’s energy leakage in both the azimuth and frequency domains.

Remote sensing (Basel, Switzerland), 2024-01, Vol.16 (3), p.518

A Frequency–Azimuth Spectrum Estimation Method for Uniform Linear Array Based on Deconvolution

Most ultrasonic flowmeters utilize several wedge sensors for transmission and reception. Thus, the location and alignment of the sensors are critical factors that determine the performance of the ultrasonic flowmeter. In this study, we proposed an ultrasound liquid flowmeter utilizing a 128-element linear array transducer with a transmit delay control for varying the incidence angles of ultrasound wave transmission. The performance of the flowmeter was evaluated at flow rates of 0–50 L/min in a specially designed pipe system. Flow estimation was performed with the transit-time method using cross-correlation with phase zero-crossing for sub-sample estimation. While a single plane wave approach performed invasive electromagnetic measurements with only 74% accuracy as a reference, a multiple angular compensation method with 24 angles was proposed to increase the accuracy of measurements up to 93%. This study demonstrated the capability of the non-invasive single-sided ultrasonic flowmeter with a linear array transducer for liquid flow measurements in the metal pipe system.

Sensors (Basel, Switzerland), 2020-01, Vol.20 (2), p.388

Multi-Angle Liquid Flow Measurement Using Ultrasonic Linear Array Transducer

In this paper, the direction of arrival (DOA) estimation problem for the unfolded coprime linear array (UCLA) is researched. Existing common stacking subarray-based methods for the coprime array are invalid in the case of its subarrays, which have the same steering vectors of source angles. To solve the phase ambiguity problem, we reconstruct an improved unfolded coprime linear array (IUCLA) by rearranging the reference element of the prototype UCLA. Specifically, we design the multiple coprime inter pairs by introducing the third coprime integer, which can be pairwise with the other two integers. Then, the phase ambiguity problem can be solved via the multiple coprime property. Furthermore, we employ a spectral peak searching method that can exploit the whole aperture and full DOFs of the IUCLA to detect targets and achieve angle estimation. Meanwhile, the proposed method avoids extra processing in eliminating ambiguous angles, and reduces the computational complexity. Finally, the Cramer–Rao bound (CRB) and numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed method.

Sensors (Basel, Switzerland), 2024-09, Vol.24 (19), p.6205

An Improved Unfolded Coprime Linear Array Design for DOA Estimation with No Phase Ambiguity

A method for the synthesis of equally spaced antenna arrays based on the extension of the Orchard–Elliott–Stern technique to radiation patterns with three roots on the negative real axis of the Shelkunoff unit circle is presented. One of these roots is placed on the unit circle and the other two are off the unit circle with coordinates r and 1/r. For a desired side lobe level (SLL), the synthesis of patterns with these roots allows for a multiplicity of solutions with different amplitude ratios, obtained by varying the value of r, each of which presents radiation patterns with different beamwidths and directivity, but with two fewer side lobes than the patterns obtained without these restrictions in the roots. The technique has been thoroughly applied to Dolph–Chebyshev patterns of 10, 18 and 40 elements, with a λ/2 spacing and an SLL that guarantees maximum directivity in both cases. This approach ensures the study of examples of all sizes, from small to large. The findings derived from this technique would be applicable in the domain of wireless communications, where the necessity arises for radiation patterns that exhibit low SLL and adaptive beamwidth.

Sensors (Basel, Switzerland), 2025-03, Vol.25 (6), p.1685

Synthesising a Fixed-Length Equispaced Linear Array to Produce Dolph–Chebyshev Patterns with Deep Nulls, a Desired Side Lobe Level and Different Beamwidths

In wireless communication systems, array antennas with high gain and low sidelobe performance can enhance the system’s signal processing and anti-interference capabilities, using intelligent optimization algorithm to optimize the performance of array antenna can achieve this goal. This article proposes an optimization algorithm called Chaos Triangular Pelican Optimization Algorithm (CTPOA), which combines Logistic chaotic mapping initialization and triangle walk strategy with original Pelican Optimization Algorithm (POA). The results of eight test functions show that CTPOA is quite excellent in both convergence and optimization ability. In addition, we also applied CTPOA for the first time to design the pattern synthesis of linear array antennas (LAA). According to the simulation results of four designed LAA, CTPOA also has excellent performance in antenna optimization. From this, it can be seen that the CTPOA proposed in this article has a certain position in the field of optimization.

Scientific reports, 2025-04, Vol.15 (1), p.11972-17, Article 11972

Pattern synthesis of linear array antennas based on Chaos Triangular Pelican Optimization Algorithm

With the rapid development of radio technology and its widespread application in the military field, the electromagnetic environment in which radar communication operates is becoming increasingly complex. Among them, human radio interference makes radar countermeasures increasingly fierce. This requires radar systems to have strong capabilities in resisting electronic interference, anti-radiation missiles, and radar detection. However, array antennas are one of the effective means to solve these problems. In recent years, array antennas have been extensively utilized in various fields, including radar, sonar, and wireless communication. Many evolutionary algorithms have been employed to optimize the size and phase of array elements, as well as adjust the spacing between them, to achieve the desired antenna pattern. The main objective is to enhance useful signals while suppressing interference signals. In this paper, we introduce the dandelion optimization (DO) algorithm, a newly developed swarm intelligence optimization algorithm that simulates the growth and reproduction of natural dandelions. To address the issues of low precision and slow convergence of the DO algorithm, we propose an improved version called the chaos exchange nonlinear dandelion optimization (CENDO) algorithm. The CENDO algorithm aims to optimize the spacing of antenna array elements in order to achieve a low sidelobe level (SLL) and deep nulls antenna pattern. In order to test the performance of the CENDO algorithm in solving the problem of comprehensive optimization of non-equidistant antenna array patterns, five experimental simulation examples are conducted. In Experiment Simulation Example 1, Experiment Simulation Example 2, and Experiment Simulation Example 3, the optimization objective is to reduce the SLL of non-equidistant arrays. The CENDO algorithm is compared with DO, particle swarm optimization (PSO), the quadratic penalty function method (QPM), based on hybrid particle swarm optimization and the gravity search algorithm (PSOGSA), the whale optimization algorithm (WOA), the grasshopper optimization algorithm (GOA), the sparrow search algorithm (SSA), the multi-objective sparrow search optimization algorithm (MSSA), the runner-root algorithm (RRA), and the cat swarm optimization (CSO) algorithms. In the three examples above, the SLLs obtained using the CENDO algorithm optimization are all the lowest. The above three examples all demonstrate that the improved CENDO algorithm performs better in reducing the SLL of non-equidistant antenna arrays. In Experiment Simulation Example 4 and In Experiment Simulation Example 5, the optimization objective is to reduce the SLL of a non-uniform array and generate some deep nulls in a specified direction. The CENDO algorithm is compared with the DO algorithm, PSO algorithm, CSO algorithm, pelican optimization algorithm (POA), and grey wolf optimizer (GWO) algorithm. In the two examples above, optimizing the antenna array using the CENDO algorithm not only results in the lowest SLL but also in the deepest zeros. The above examples both demonstrate that the improved CENDO algorithm has better optimization performance in simultaneously reducing the SLL of non-equidistant antenna arrays and reducing the null depth problem. In summary, the simulation results of five experiments show that the CENDO algorithm has better optimization ability in the comprehensive optimization problem of non-equidistant antenna array patterns than all the algorithms compared above. Therefore, it can be regarded as a strong candidate to solve problems in the field of electromagnetism.

Sensors (Basel, Switzerland), 2025-01, Vol.25 (3), p.861

Pattern Synthesis Design of Linear Array Antenna with Unequal Spacing Based on Improved Dandelion Optimization Algorithm

This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.

Journal of fluid mechanics, 2023-03, Vol.959, Article A39

Oscillating viscous flow past a streamwise linear array of circular cylinders

This article proposes a direction-of-arrival (DOA) estimation algorithm for a random sparse linear array based on a novel graph neural network (GNN). Unlike convolutional layers and fully connected layers, which do not interact well with information between different antennas, the GNN model can adapt to the goniometry problem of non-uniform random sparse linear arrays without any prior information by applying neighbor nodes’ aggregation and update operations. This helps the model in learning signal features under complex environmental conditions. We train the model in an end-to-end way to reduce the complexity of the network. Experiments are conducted on the uniform and sparse linear arrays for various signal-to-noise ratio (SNR) and numbers of snapshots for comparison. We prove that the GNN model has superior angle estimation performance on arrays with large sparsity that cannot be used by traditional algorithms and surpasses existing deep learning models based on convolutional or fully connected structures. The proposed algorithm shows excellent DOA estimation performance under the complex conditions of limited snapshots, low signal-to-noise ratio, and large array sparsity as well. In addition, the algorithm has a low time calculation cost and is suitable for scenarios that require low latency.

Sensors (Basel, Switzerland), 2023-12, Vol.24 (1), p.91

Direction-of-Arrival Estimation for a Random Sparse Linear Array Based on a Graph Neural Network

In this paper, we investigate the problem of sparse array design for the direction of the arrival (DOA) of non-Gaussian signals and exploit the unfolded coprime linear array with three subarrays (UCLATS) to obtain physical sensors location. With the motivation from the large consecutive degree of freedom (DOF), we optimize the process of obtaining physical sensors location from two steps. Specifically, the first is to model the process of obtaining the longest consecutive virtual sum co-array from a given number of physical array elements into a global postage-stamp problem (GPSP), whose solution can be employed to determine the locations of the longest possible consecutive sum co-array (2-SC) and initial physical array. The second step is to multiply the location of the virtual sum co-array by appropriate coprime coefficients to generate UCLATS and then multiply the initial physical array position by the same corresponding coefficients to obtain physical sensors location. Besides, an algorithm is proposed to obtain DOA estimates, which employs the discrete Fourier transform (DFT) method and partial spectrum searching multiple signal classification (PSS-MUSIC) algorithm to obtain initial estimates and fine estimates, respectively, termed as the DFT-MUSIC method. Compared with the traditional total spectrum searching MUSIC (TSS-MUSIC) algorithm, the DFT-MUSIC method performs the same asymptotical performance of DOA estimation with less than 10% complex multiplication times, which can be verified by numerical simulations under the same condition.