A Method of Sparse Plane Arrays Synthesis Based on Archimedean Spiral and Quantum Search Algorithm

For the element position synthesis of 2-dimension sparse rectangular arrays with the design constraints of the number of elements, the aperture and the minimum element spacing, an improved genetic algorithm (IGA) based on chromosome element resetting is presented in this paper. Compared with the synthesis method of thinned arrays, this new approach could exploit more degree of freedom of elements to control the characters of the sparse arrays. When the aperture, the number of elements and the minimum element spacing are fixed identical, the new approach can make the sparse plane array produce lower peak sidelobe level (PSLL). The simulated results show that the fitness function value of thinned plane arrays with 108 elements mentioned by Haupt can reduce 5.626 dB when the minimum element spacing of half wavelength was introduced into the optimization. And as well, the great efficiency and the robustness of IGA are shown in this paper

Designing sparse arrays with fewer antenna elements and lower peak sidelobe level (PSLL) is critical and challenging for antenna arrays in terminal devices in Internet of Things (IoT) systems. This article presents a deep learning method based on denoising diffusion probabilistic models (DDPM) for synthesizing sparse arrays. With predefined constraints such as aperture size, number of elements, and minimum element spacing, a training dataset that enables the proposed DDPM is generated to directly learn the distribution characteristics of these sparse arrays. To simplify the network architecture, the backbone network U-Net is replaced by a multilayer perceptron (MLP). In addition, an innovative conditional generation strategy is introduced to enhance the training accuracy, categorizing the training data into diverse cross-conditional labels based on PSLL and sparse ratio. During the training process, two separate regression networks are employed to predict the sparse ratio and the PSLL, and a Pareto-optimal weighting scheme (PWS) is designed to address the trade-off between them. Examples of two planar sparse arrays and a conformal sparse array demonstrate the effectiveness of the proposed DDPM-based method, highlighting its superiority in reducing PSLL and increasing sparse ratio, reducing inference time compared with the existing methods.

This paper presents a kind of particle swarm optimization (PSO) algorithm which is based on simulated annealing (SA) for the synthesis of sparse linear arrays. This algorithm is used to optimize the element positions to suppress the peak side lobe level (PSLL) of the array with many constraints. With this method the freedom increase amounts are used as optimization variables, which plus the minimum element spacing constraint is deemed as element spacing of the array. And the method has downsized the searching region by indirect expression of element spacing. The simulated optimization results demonstrate the better suppression effect of PSLL of the proposed algorithm.

This letter is concentrated on the peak sidelobe level (PSLL) suppression problem of equal amplitude concentric ring array (CRA), which is constrained by the array aperture, the minimum element spacing, and the number of elements. Taking the minimum PSLL as the optimization objective, the joint optimization strategy of CRA aperture and ring array spacing is adopted to reduce the computational complexity. A quantum genetic algorithm based on hybrid coding is used to optimize the CRA. The proposed method has the advantages of fast searching speed and powerful searching ability. The simulation results demonstrate the superiority of the algorithm.

A fully deterministic procedure for the synthesis of sparse antenna arrays radiating shaped beams is presented. The developed algorithm is based on a compressive sensing technique which, starting from an array with a very dense grid of elements, iteratively solves a minimization problem aimed at producing a sparse array with a strongly reduced number of elements. However, such technique solves a field synthesis problem. So, the constraints of the optimization problem are suitably modified during the iterations, in order to solve a power pattern synthesis problem. Numerical examples are provided, that show the improvements that can be achieved in terms of reduction of the number of radiating elements.

A novel method based on off-grid Compressed Sensing (CS) is proposed for the synthesis of sparse concentric ring arrays with the desired patterns. The synthesis is formulated as a sparse signal recovery problem with an unknown parametric dictionary by treating the concentric ring radii and weights as optimization variables. The proposed method allows the sparse rings to randomly distribute in the array aperture so as to find the true positions and overcome the grid mismatch compared to the traditional CS-based method. Numerical simulations are presented to validate the effectiveness of the proposed method.

To lower the peak sidelobe level (PSLL) of sparse concentric ring arrays, a method with multiple design constraints that embed a function model into modified real genetic algorithm (MGA) and select the grid ring radii as optimization individual to synthesize sparse concentric ring arrays is proposed. The multiple constraints include the array aperture, the minimum element spacing, and the number of elements. The proposed method dynamically calculates the ratio of element on each ring, and it has a faster convergence rate than other algorithms. The MGA uses real number to code the optimization variable, and it reduces the complexity of coding and improves the search efficiency. Finally, the results demonstrate the accuracy and effectiveness of the algorithm.

The present article proposes a novel hybrid approach for addressing the synthesis problem of rectangular planar arrays under multiple constraints, through joint optimization of the weight function and the improved grey wolf optimization (IGWO) algorithm. Firstly, the grey wolf optimization (GWO) algorithm is improved by using tent chaotic mapping, nonlinear convergence factor, dominant wolf dynamic belief strategy, and opposition‐based learning strategy to increase the population diversity and the ability to jump out of the local optimum. Secondly, the array elements are weighted using the weight function to generate the position distribution matrix, which reduces the thinned matrix optimization time and improves the optimization efficiency. Finally, the position distribution matrix is used to generate the thinned array, and the IGWO algorithm is applied to perform the sparse optimization with multiple constraints. The effectiveness of the method is verified through numerical simulation and full‐wave simulation experiments, demonstrating its capability to enhance array antenna performance and reduce peak sidelobe level (PSLL). These experimental results hold significant engineering implications and provide valuable references for addressing the array distribution problem under multiple constraints.

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.

Three-dimensional (3-D) imaging sonar systems require large planar arrays, which incur hardware costs. In contrast, a cross array consisting of two perpendicular linear arrays can also support 3-D imaging while dramatically reducing the number of sensors. Moreover, the use of an aperiodic sparse array can further reduce the number of sensors efficiently. In this paper, an optimized method for sparse cross array synthesis is proposed. First, the beamforming of a cross array based on a multi-frequency algorithm is simplified for both near-field and far-field. Next, a perturbed convex optimization algorithm is proposed for sparse cross array synthesis. The method based on convex optimization utilizes a first-order Taylor expansion to create position perturbations that can optimize the beam pattern and minimize the number of active sensors. Finally, a cross array with 100 + 100 sensors is employed from which a sparse cross array with 45 + 45 sensors is obtained via the proposed method. The experimental results show that the proposed method is more effective than existing methods for obtaining optimum results for sparse cross array synthesis in both the near-field and far-field.

Synthesis of sparse planar arrays can effectively reduce hardware costs and computational complexity in phased array 3-D imaging sonar systems. Traditional stochastic methods, such as simulated annealing, require multiple experiments and parameter adjustments to obtain optimal results. Methods based on compressed sensing (CS) can overcome this defect. However, when applied to large arrays, CS methods require vast computational complexity and may not obtain optimal sparse results because of violating the restricted isometry property. To make CS methods more practical, a distributed convex optimization CS method is proposed here for the sparse planar array synthesis in 3-D imaging sonar systems. This method is based on the CS theory, solving the minimum number of active elements under certain beam pattern constraints using the iterative reweighted l 1-norm minimization algorithm. Then, a multistage distributed framework is proposed to decompose the array into multistage subarrays, and the array synthesis is performed sequentially for each stage subarray to reduce computational complexity and obtain higher sparsity rates. Some applications of sparse planar array synthesis are employed to evaluate the efficiency of the proposed method.

This paper presents a novel method for synthesizing sparse dipole arrays with shaped patterns by joint optimization of element positions, rotations and phases. Such joint optimization exploits maximum available degrees-of-freedom under the assumption of uniform amplitude excitations to improve the shaped power pattern synthesis performance, and it leads to a reduced number of elements and simpler feeding network without using unequal power dividers for the array. The copolarization (COP) and cross-polarization patterns for a rotated dipole array are derived in a 2-D case, and then the vectorial shaped pattern synthesis problem is formulated as finding the optimal solution by maximally approaching the desired COP pattern shape under multiple constraints on the sidelobe level (SLL) and cross-polarization level (XPL). In addition, an asymmetric mapping method is incorporated into the proposed joint optimization, so that the minimum element spacing constraint can be also used for the synthesis of planar sparse dipole arrays. The comprehensive learning particle swarm optimization (CLPSO) algorithm is adopted to optimize the element positions, rotation angles and phases. A set of synthesis experiments including linear and planar rotated dipole arrays with a different pattern shape requirements are conducted to validate the effectiveness and robustness of the proposed approach. Synthesis results show that the proposed approach can save about 17.24% – 55.86% elements as well as many unequal power dividers for test cases.

A hybrid algorithm based on the invasive weed optimization (IWO) and the convex optimization (CVX) is proposed for minimizing the peak sidelobe level (PSLL) of linear array with focused and/or shaped beam pattern. In this approach, IWO is adopted to produce the array (described by element positions), and CVX is used to determine the excitations for each produced array. Then the corresponding PSLL acts as the fitness function of IWO to find the optimal positions which lead to the minimum PSLL. Numerical experiments are conducted to validate the effectiveness and robustness of the proposed hybrid approach. Compared with other techniques, a lower PSLL can be achieved with a fixed main beam width or with a shaped main beam using this hybrid algorithm. Moreover, this method can easily cope with some constraints on the aperture, such as the minimum element spacing and the total number of elements.

A novel method is presented to design beam-scannable ultra-wideband (UWB) sparse arrays. A concept of design frequency is introduced which transforms the beam-scannable UWB array design to the problem of synthesizing a broadside-beam array at single frequency. The raised power series (RPS) representation with appropriate parameter selection is adopted to generate initial element positions, and then an iterative convex optimization is applied to successively optimize the element positions for further sidelobe level (SLL) reduction. Multiple constraints for controlling the first-order Taylor expansion accuracy, the minimum element spacing, and the array aperture are incorporated in the iterative convex optimization to obtain stable and practical synthesis results. Several examples for synthesizing UWB arrays with different frequency bands, beam scanning, ranges and element counts are conducted to validate the effectiveness and advantages of the proposed method. It is shown that the proposed method achieves much lower SLLs than those by the original RPS method for all test cases, and it also significantly outperforms some conventional stochastic optimization methods for large UWB array cases.

Planar sparse array synthesis plays a critical role in modern radar and wireless communication systems. However, it remains challenging to simultaneously minimize the number of antenna elements while maintaining a low peak sidelobe level. Inspired by typical electromagnetic compatibility (EMC) phenomena, we previously developed the Maxwell’s Equations Derived Optimization (MEDO) algorithm, which enables accurate and robust solutions for complex electromagnetic optimization problems. In this paper, we extend MEDO to a multi-objective version (MO-MEDO), by incorporating non-dominated sorting with elitism and an external archive mechanism for Pareto front preservation. The proposed MO-MEDO algorithm exhibits excellent performance in sparse planar array synthesis, effectively achieving a favorable trade-off between array sparsity and sidelobe suppression.