Sparse conformal array design for multiple patterns generation through Multi-Task Bayesian Compressive Sensing

This paper presents an improved snake optimization (ISO) algorithm for the beamforming design of sparse conformal arrays. To reduce the array element number and achieve the best sparse array configuration, the ISO algorithm employs the Sobol sequences for population initialization, resulting in enhanced uniformity and comprehensive coverage of the solution space as compared with the conventional random initialization method. Besides, the ISO algorithm employs the Cauchy mutation operator to escape local optimization and suppress the sidelobe levels of the conformal array. To increase array sparseness and optimize the radiation patterns, the ISO algorithm is further equipped with a nonlinear time-varying factor inspired by the whale algorithm and a modified flag control function, which improve its capacity for global exploration and local development. Simulation verification of a sparse cylindrically conformal array has demonstrated the superior performance of the proposed ISO algorithm over conventional optimization algorithms. It achieves a 50% array sparsity, and lower sidelobe levels as compared with the genetic algorithm (GA), particle swarm optimizer and traditional snake optimizer (SO). Moreover, it features notably faster convergence rates, outpacing the SO by 10% and GA by 46%, respectively. In addition, the sparse conformal array exhibits good radiation characteristics over a relatively wide beam scanning range of 54° in the azimuthal plane and 90° in the elevation plane, respectively.

In this paper we present the recent advances on the design of sparse arrays using log-periodic antennas for the SKA AA-Mid instrument. The SKA AA-Mid instrument will explore the southern hemisphere sky from ∼400 MHz up to 1.4 GHz with unprecedented sensitivity and survey speed. Large collecting area, low system noise and great survey speed are key to achieve the demanding requirements of the SKA. The University of Cambridge proposes designing this instrument as a collection of stations, each of them being a random sparse array of ultra wideband log-periodic antennas. The advantage of this approach, amongst others, is the increasing collecting area with wavelength (as a square of the wavelength) that sparse arrays offer over dense arrays, and which facilitates the realization of the SKA science goals. We have now advanced our developments to study the system implications of this decision and have started the design of a 16-element prototype array that will be located at the MRAO Observatory at Lords Bridge, Cambridge, UK. This array will help us progress our developments.

This paper addresses a novel rotationally symmetric technique with multiple constraints for sparse conformal array synthesis. The purpose is to synthesis a sparse optimal common element positions on the conformal surface varying multiple patterns of wide angle scanning with the behavior of low sidelobe levels (SLL). The conformal surface aperture is partitioned into several rotationally symmetric sections. The element positions and element numbers of only one section need to be optimized, which contribute to the reduction of optimizing variables and computation resources. We formulate the synthesis problem as a constrained optimization problem, which takes the peak sidelobe level (PSLL) as the fitness function, and sets the total number of array elements, the minimum spacing between two adjacent elements to form multiple constraints. The Brain Storm Optimization (BSO) is further exploited into the synthesis problem with multiple constraints. A set of representative numerical examples are presented to assess the advantages and effectiveness of the proposed method.

The work presents a design of a cylindrical conformal phased microstrip antenna array. Based on the HFM and the parallel feed network, a conformal microstrip 2 times 8 array on a cylinder surface is designed by the isotropic transformation theory (IT). Simulation results show that the conformal array works at 35GHz and the gain is 19.6dB at the center frequency. The phase-scanned patterns of the conformal 2 times 8 array are analyzed by the CST using phase control method. From the comparison of the scanning results at different phase division, it can be found that the scan angle, the angular width and the side lobe level varies following the trends of the phase division, at the same time, the gain of the conformal array changes markedly opposite the trends of the phase division. Therefore, this is a shortcoming of the conformal phased array. This kind of conformal phased sub-array can be easily expanded into a large-scale conformal array and be suitable for active integration with other microwave circuits and communication systems if this disadvantage was eliminated after further discussion in future.

The three-dimensional multiple-input-multiple-output radar (MIMO) system has been applied in various situations such as security inspection and ground exploration. The conventional dense MIMO radar array has excellent imaging performance but large spacing redundancy between antenna elements. In this paper, two-dimensional (2-D) MIMO sparse array design is discussed. The difference basis and the cyclic difference set are combined to construct a one-dimensional (1-D) sparse array with less spacing redundancy, which would be placed reasonably to construct the 2-D MIMO sparse array. Finally, the pattern and target imaging results of the array are given through simulation experiments, demonstrating that the square array proposed has good imaging performance especially in terms of side lobe level and grating lobe. The proposition of 2-D square sparse MIMO array would facilitate the development of sparse MIMO array design and improve the application capabilities of MIMO radar.

Three-dimensional (3D) ultrasonic imaging enables the viewing of internal features in a more accurate way than cross-sectional imaging. 3D imaging requires two-dimensional (2D) ultrasonic phased arrays to resolve all three spatial dimensions through beamforming along azimuthal and elevation angles. 2D phased arrays pose a manufacturing and control challenge due to the requirement of large number of elements to satisfy the Nyquist sampling limit. This problem can be alleviated through the use of sparse ultrasonic array designs. The optimization process is critical, as this dictates the efficiency of suppression of grating lobes. The aim of this work is to establish a framework for design of optimized sparse 2D phased arrays. This is enabled by exploiting the reconfigurability of Laser Induced Phased Arrays (LIPAs). LIPAs are synthetic arrays produced by scanning one laser for ultrasound generation and another for ultrasound detection, independently of each other. The reconfigurability and decoupled ultrasonic generation and detection of this systems enables easy and fast implementation of any arbitrary array layout. The framework consists of an analytical model for parametric evaluation of designs. The model performs a parametric sweep on the generation and detection element positions for each array design in order to identify the optimal parameters, based on mean and maximum side-lobe level. In the presented framework, four array designs are utilized for the optimization process: matrix, random, Vernier and a novel array design the Rotated Array (RA).

We present novel generalized non-redundant sparse array design strategies that achieve the highest possible number of degrees-of-freedom (DOFs) for direction-of-arrival (DOA) estimation. These array designs offer difference co-arrays that do not contain any lag redundancies except the unavoidable redundancies at lag zero. We first develop a co-array-based zero-redundancy design rule which serves as a baseline for constructing these non-redundant arrays, and a large-aperture naïve structured non-redundant sparse array is presented. We then develop a systematized design framework based on disjunctive programming to obtain non-redundant sparse array structures with a minimum array aperture, resulting in minimum hole arrays. The disjunctive programming framework is then extended to an equivalent mixed-integer linear programming problem. As a result, given the same number of physical sensors, the design framework provides a difference co-array with the maximum number of correlation lags and resolves more sources than existing sparse array structures. The non-redundant sparse array design is further generalized in two new directions, respectively achieving an arbitrary array aperture and reducing mutual coupling effects. Among the several new sparse array designs obtained from such generalizations, the hybrid non-redundant sparse array design simultaneously achieves the highest number of DOFs, meets a desired array aperture requirement, and reduces mutual coupling effects. Structured matrix completion methods are employed to interpolate the missing lags in the resulting difference co-arrays, thereby enabling high-resolution gridless DOA estimation with improved performance. Simulation results demonstrate the superiority of the generalized non-redundant sparse array design strategies over existing sparse array structures

Reducing the number of antenna elements within a fixed aperture while maintaining low sidelobe levels is a key challenge in sparse array design. Although various sidelobe suppression techniques exist, most are tailored for large-scale arrays and are not directly applicable to small-scale sparse arrays. This paper addresses a critical gap in array design for small sparse arrays with low sidelobes using mechanical rotation and time-averaging techniques. By continuously rotating the array and time-averaging radiation patterns, the mainlobe remains coherent and stable, while the rapidly varying sidelobes are effectively averaged out and suppressed. An analytical model is developed to determine the required integration time, optimize element placement, mitigate Doppler effects, and enhance time-selective radiation pattern strategies. Experimental validation using a four-element circularly polarized array with 0.74λ spacing demonstrates a PSLL reduction of 11.5 dB compared to a conventional non-rotated array, and can be further reduced by 4.7 dB through time-selected pattern optimization. The proposed method has many potential applications, such as passive remote sensing using rotating UAV swarm arrays, making it a flexible and low-cost solution for precision agriculture and environmental monitoring applications.

Sparse arrays are of great interest since they can identify O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) uncorrelated sources with N physical sensors. This stems from their large difference coarray, defined as the differences between sensor locations. In a recent study, desired array properties such as closed-form expression for sensor locations, symmetry and large hole-free difference coarray were considered and it was shown that most existing sparse arrays do not exhibit these characteristics simultaneously. Standard Cantor arrays were shown to satisfy all the criteria above, however, their difference coarrays are of size O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">log2 3</sup> ) which is smaller than that obtained with minimum redundancy arrays and nested arrays. In this paper, we introduce a fractal array design where a generator array is extended in a simple recursive fashion. In contrast to previous work, the generator is assumed to be a sparse array with a hole-free difference coarray. We study the resulting arrays and prove they inherit their properties from the generator. Thus, this approach can be used to extend any known sparse configuration to an arbitrarily large array. A small-scale array, which meets all design criteria, can be created and then expanded to generate a symmetric fractal array with a difference coarray of size O(N2), unlike Cantor arrays.

To address the issue of traditional Particle Swarm Optimization (PSO) being prone to local optima and insufficient global search capability in sparse phased array optimization, a hybrid optimization algorithm integrating PSO with a Genetic Algorithm (GA) is proposed. Within the PSO framework, the proposed algorithm incorporates the adaptive crossover and mutation operations of the GA to enhance population diversity. It combines an adaptive weighting factor and a constriction factor to balance global exploration and local exploitation capabilities. Furthermore, a density-weighted method is employed to generate a high-quality initial population, thereby accelerating convergence. The proposed algorithm is applied to an 8 × 8 planar sparse array. On the E-plane (φ = 0°) and H-plane (φ = 90°), simulation results indicate that the achieved normalized maximum sidelobe level is −23.14 dB, which is significantly superior to those obtained by standalone PSO and GA. Based on these simulation results, microstrip patch antennas are introduced for array constitution and analysis. Full-wave electromagnetic simulation proves that the proposed sparse array has the ability of wide-angle scanning and low sidelobe. Our work demonstrates that the PSO-GA hybrid algorithm effectively enhances search capability and convergence performance, providing a reliable solution for sparse array design.

This paper presents our study on a sparse antenna array for 0.22 THz imaging. Based on the effective aperture concept for the design of sparse antenna array, two schemes for high performance THz imaging of a target at distance of 1 m have been achieved in simulation. Then, different schemes of larger array element spacing and mechanical scanning spacing have been investigated to build the relationship between their configurations and imaging performance. Based on the study, it is predicted theoretically and from the reconstructed images that only 16 transmitting and 16 receiving antennas will be sufficient to scan a 2.0 m * 0.8 m target. And the spatial resolution of 4.44 mm at 5 m is potentially achieved. Therefore, this study will provide a valuable guideline for the following sparse array design in a high performance THz imaging system.

An innovative technique based on the enhanced unitary matrix pencil (MP) method is presented for the design of sparse multiple-pattern linear arrays. By virtue of the equivalent MP obtained with a unitary transformation, the relation between the element positions and the generalized eigenvalues is achieved in this method, which contributes to the real solutions of the common element positions for all multiple patterns. Owing to the utilization of a unitary transformation that can convert a complex matrix to a real one, the computational complexity can be significantly reduced since only the real computations are involved in the singular value decomposition and eigenvalue decomposition procedures. Consequently, by only varying the obtained excitation distributions, different patterns are generated with a higher matching accuracy. Representative experiments are provided to validate the effectiveness and advantages of the proposed method.

The design of sparse antenna arrays is realized by a novel and effective method based on convex programming in this paper. By the use of synthesis model in terms of thinned arrays, a novel binary quadratic optimization problem is established for design of sparse array, where the required antenna element number satisfying user-defined constraints (peak sidelobes and directivity) is fully minimized. To reduce computational cost, an effective optimization approach combining the reweighted <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{1}$</tex> -norm minimization with the element location expansion and contraction is proposed. By comparing to fully populated half-wavelength arrays, a numerical example is presented to assess the advantages of the described approach.

An effective sparse array synthesis approach based on recently introduced compressed sensing theory has been proposed and applied to the design of pencil beams with the minimum number of sensors.

The manuscript reports phase compensation technique for improving the directionality and gain of a conformal phased array antenna on a cylindrical surface while steering the beam. The investigation reports two different components of phase compensation required for enhancing the directionality: (i) compensation required to mitigate the effect due to the vertical displacements of antenna elements on the conformal surface and (ii) additional phase shift required to align the broadside of each element in the direction of scan angle. It is highly effective in the restoration of the beam of a phased array mounted on conformal surfaces of a smaller radius causing significant deformation in the radiation pattern. The proposed formulation is implemented through Matlab and verified using CST for a 1-D circumferential phased array with 7 elements of a rectangular patch antenna of dimensions L = 8.72 mm and W = 14.52 mm designed for 10 GHz on a cylindrical surface of 10 cm radius. The model is also applicable to a Concave conformal phased array and can be extended to 2-D arrays. To the best of our knowledge, this is the first report on such a study and will find direct applications in the design and development of conformal phased arrays with high directionality and gain.