Synthesis Of Sparse Arrays Research Articles

Synthesis of sparse rectangular planar arrays with weight function and improved grey wolf optimization algorithm

AbstractThe 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.

Sparse linear array synthesis using artificial neural network and nonconvex optimization

AbstractThe concept of sparse array synthesis has attracted considerable attention due to its potential to reduce hardware costs in array design and enhance the efficiency of array aperture utilization. In contrast to conventional artificial neural networks (ANNs), a more efficient encoder–decoding ANN framework is proposed in this letter for designing sparse linear arrays. The decoder is pretrained with a randomly generated training set, enabling its ability to rapidly predictiction of far‐field patterns. This process considers the actual coupling effect among the antenna elements. The output of the encoder is used as the input of the decoder to synthesize the sparse arrays by providing the desired pattern to the encoder. During the training process, a novel ‐norm minimization nonconvex optimization method is integrated into the proposed framework to reduce the number of activated elements. The effectiveness and efficiency of the method are demonstrated through numerical and full‐wave simulations for synthesizing various linear sparse arrays, including large‐scale arrays. In comparison to existing algorithms, our proposed method exhibits superior computational efficiency and predicted accuracy with fewer elements.

Synthesis of Sparse Arrays With Discrete Phase Constraints via Mixed-Integer Programming

Synthesis of Sparse Arrays With Discrete Phase Constraints via Mixed-Integer Programming

Sparse Array Synthesis with Two-Stage Progressive BCS and Undirected Graph-Based Spacing Constraint

Sparse Array Synthesis with Two-Stage Progressive BCS and Undirected Graph-Based Spacing Constraint

Synthesis of Large Ultra-wideband Sparse Circular Planar Arrays Based on Rotationally Symmetric Structure

This article aims to improve the synthesis efficiency and radiation performance of large ultra-wideband (UWB) rotationally symmetric sparse circular planar arrays by using a modified differential evolution algorithm (MDEA). In the proposed MDEA, we adopt a new encoding mechanism in which an individual represents an element position expressed in polar coordinates. Importantly, such an encoding mechanism can facilitate the multiplication calculation for the array factor in the individual being updated while making it easier to meet the given minimum element spacing constraint. Moreover, to cater to the new encoding mechanism, some low-dimensional evolution operators are introduced to avoid the prematurity. In particular, the UWB rotationally symmetric sparse planar array synthesis problem is transformed into the sidelobe suppression problem of the array pattern at the highest frequency under the given array aperture, and the minimum spacing constraints is used to guarantee enough space to place physical UWB antenna elements. Two synthesis examples of UWB sparse planar arrays based on rotationally symmetric structures are presented. The results show that the peak sidelobe level (PSL) obtained by the proposed MDEA is significantly lower than the results obtained by some existing algorithms in an acceptable CPU time, which proves the effectiveness and superiority of the proposed MDEA.

Synthesis of Linear Sparse Array Using DNN-Based Machine-Learning Method

In this paper, a deep neural network (DNN)-based machine learning (ML) approach is presented to synthesize linear sparse arrays (LSAs). Due to the powerful fitting capability of neural networks, a DNN framework is established to map the relation between the desired array pattern and LSA geometry. In this manner, the array synthesis is accomplished by training a proper DNN that can generate the desired LSA geometry. To obtain better training, the density tapering (DT) technique is introduced to the training process as the prior domain knowledge to specify the varying boundaries of each element in the LSA. Consequently, an efficient DT-assisted DNN (D-DNN) synthesis method is developed. The proposed D-DNN method has the ability to simultaneously optimize the element positions and excitations, and directly constrain the inter-element spacings. Furthermore, by introducing the active element pattern (AEP) technique, the presented method can synthesize both ideal arrays and arrays with mutual coupling. Numerical results of a wide variety of synthesis scenarios are presented to demonstrate the validity, efficiency, and flexibility of the proposed method.

Synthesis of Large Ultrawideband Sparse Planar Arrays by Utilizing a Cooperative Coevolutionary Iterative Fourier Transform

This letter introduces a cooperative coevolutionary iterative Fourier transform (CCIFT) technique to extend the conventional IFT to large ultra-wideband (UWB) sparse planar array synthesis. In the proposed CCIFT, a dense initial element position grid such as a spacing of half a wavelength at the highest frequency is adopted to avoid the presence of grating lobes at high frequency band, and a probability-assisted element selection mechanism is presented to guarantee the obtained array layout to meet a preset minimum spacing constraint, enabling the placement of physical UWB antenna elements. In addition, a cooperative coevolutionary strategy is presented to avoid prematurity by establishing the information interaction between different excitation distributions from multiple parallel IFT procedures. Two examples are conducted and results show that the CCIFT can achieve a considerably lower peak sidelobe level (PSL) than some state-of-art algorithms within an acceptable CPU time, which demonstrates its effectiveness and superiority.

Teaching quality evaluation-based differential evolution and its application on synthesis of linear sparse arrays

Teaching quality evaluation-based differential evolution and its application on synthesis of linear sparse arrays

Sparse hydrophone array synthesis for frequency‐invariant and multi‐angle beampatterns using block‐structured Bayesian compressive sensing

AbstractTo solve the synthesised accuracy degradation of traditional Bayesian compressive sensing (BCS) in wideband multi‐beam hydrophone array synthesis, a novel sparse array synthesis method based on block‐structure Bayesian compressive sensing (BS‐BCS) is proposed for frequency‐invariant and multi‐angle beampatterns. The multi‐angle beampatterns at different frequencies are synthesised in block structure using the shared position strategy which effectively reduces the number of array elements. In order to meet the minimum spacing requirement of adjacent array elements in practical engineering, the constraint converted off‐grid method is proposed to improve the array synthesis accuracy. The grid scaling is introduced to obtain the possible array element positions. The array positions and weights can be solved by the BCS solver and corrected by Taylor perturbation. To validate the effectiveness and feasibility of the proposed method, simulations and actual experiments are carried out. The synthesised errors and peak sidelobe levels (PSLLs) of multi‐angle beampatterns obtained by the constraint converted off‐grid method outperforms those of other methods. The beamforming results of actual experiments in marine environment show that the PSLLs of the beampatterns obtained by BS‐BCS is lower at least 6.3 dB than that of uniform array, which demonstrates the effectiveness of the proposed method.

Convex Optimization-Based Design of Sparse Arrays for 3-D Near-Field Imaging

A convex optimization-based method of sparse array synthesis (SAS) for wideband near-field millimeter-wave imaging is proposed by extending our previous work. We construct a monostatic sparse array synthesis optimization model from the electromagnetic propagation formula. The reweighted l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm decoding algorithm is utilized to enhance the sparsity. A modified iterative element weighting merging method is also proposed to put constraints on the minimum element spacing to synthesize a practicable sparse layout. Through the proposed SAS method, the customized sparse monostatic array for near-field imaging can be generated with different schemes, such as 1-D linear arrays, 2-D planar arrays, etc. The imaging performance of the synthesized planar sparse array, is studied by examining the properties of focusing, sidelobe-suppression, and grating lobe suppression both theoretically and by simulation. It is shown that the optimized array is superior to the arrays with equally spaced antennas or randomly spaced antennas, using approximately the same number of antenna elements. Experimental results further indicate the advantages of the optimized wideband sparse array through the three-dimensional imaging reconstruction.

An Improved Synthesis of Sparse Planar Arrays Using Density-Weighted Method and Chaos Sparrow Search Algorithm

This paper presents an improved approach for the synthesis of sparse planar arrays using density-weighted method and chaos sparrow search algorithm (CSSA) with multiple constraints. The approach consists of two stages and has an efficient way in dealing with multiple constraints, including the array aperture, number of elements, and minimum spacing between adjacent elements. In the first step, a density-weighted method is implemented to generate a thinned array structure by introducing the weighted coefficient based on the distribution function of a uniform full array to the elements, which can reduce the time and improve the efficiency of the optimization of sparse matrices. On the basis of a density-weighted array, tent chaotic mapping is introduced to initialize the population, then sparrow search algorithm (SSA) is used to further optimize the location of each element of the array antenna to search for the global optimal solution. As a consequence, the proposed method exhibits improved flexibility with respect to other analytical techniques, and reduces the computational cost of the optimization algorithm. Numerical validation results demonstrate the effectiveness and reliability of the proposed method, showing that it can achieve better results than existing methods in the design of sparse planar array arrangements.

Extreme Sparse-Array Synthesis via Iterative Convex Optimization and Simulated-Annealing Expanded Array

Sparse-array synthesis can considerably reduce the number of sensor elements while optimizing the beam-pattern response performance. The sparsity of an array is related to the degrees of freedom of the array elements. A sparse-array method based on iterative convex optimization and a simulated-annealing expanded array is proposed in this paper. This method transforms the sparse-array problem into a minimum l1 norm problem and obtains the sparse array by solving the convex optimization problem using the primal-dual algorithm. Meanwhile, to improve the degree of freedom, array elements are expanded using stochastic perturbation. According to the simulated-annealing algorithm, the closed array elements are reopened with a specific probability, which is iteratively thinned and expanded. The results show that the proposed method can obtain an extremely sparse array, which is better than that obtained using the existing methods.

Go-Caterpillar Mutation and Its Optimization Algorithm for Synthesis of Large-Scale Sparse Planar Arrays

Optimizing the layout of sparse planar arrays constrained by minimum element spacing to reduce the peak sidelobe level (PSLL) is a difficult and challenging task in engineering applications. Here, a new sparse array design method is proposed under the constraints of aperture size, the number of array elements, and minimum spacing between elements. The approach is based on a new element mutation method which is proposed for mutating the position of any element within the aperture without changing the position of other elements. Because a mutating element can be thought of as being placed inside the board like a black/white stone in go or crawling somewhere nearby like a caterpillar, we call it go-caterpillar-mutation (GCM). Based on GCM, a stochastic optimization algorithm (GCM-OA) is proposed to optimize the layout of sparse planar arrays. Several examples demonstrate the robustness and rapidity of GCM-OA in reducing PSLL by adjusting the array element positions under various constraints.

Pattern Synthesis for Different Sparse Planar Arrays by a Hybrid Unconstrained-Heuristic Approach

A hybrid approach that combines the strategy of partial density tapering (PDT) and the multiobjective particle swarm optimization (MOPSO), called PDT-MOPSO, is proposed to address the synthesis of sparse planar arrays (SPAs) of different shapes. By performing the PDT, not only the strong constraint of element placement in SPAs is eased to nonconstrained issue, but also the element locations are forced to follow the distribution of density tapering somewhat to facilitate the sidelobe suppression. Then, by taking the sidelobe level (SLL) and directivity as the optimization objectives, the traditional MOPSO is used to optimize the element locations so that the SPAs with reduced number of elements, minimized SLL and nondegraded directivity are achieved. Some numerical instances confirmed the effectiveness of the proposed method.

Low-Complexity Sparse Array Synthesis Based on Off-Grid Compressive Sensing

In this letter, a novel sparse array synthesis method for nonuniform planar arrays is proposed, which belongs to compressive sensing (CS) based synthesis. Particularly, we propose an off-grid refinement technique to simultaneously optimize the antenna element positions and excitations with a low complexity, in response to the antenna position optimization problem that is difficult for standard CS. More importantly, we take into account the minimum interelement spacing constraint for ensuring the physically realizable solution. Specifically, the off-grid orthogonal match pursuit algorithm is first proposed with low complexity and then off-grid look ahead orthogonal match pursuit is designed with better synthesis performance but higher complexity. In addition, simulation results have shown that the proposed schemes have more advantages in computational complexity and synthesis performances compared with the related method.

Synthesis of Low Sidelobe Pattern with Enhanced Axial Radiation for Sparse Conformal Arrays Based on MCDE Algorithm

A hybrid optimization method for the synthesis of a sparse conformal array with the verification of a truncated cone antenna array is proposed in this manuscript. This array synthesis is studied aiming at enhancing axial radiation and reducing the peak sidelobe level (PSLL) by figuring out the optimal antenna element arrangement and corresponding feeding scheme. A multi-agent composite differential evolution (MCDE) algorithm is established by integrating a multi-agent system (MAS) with a differential evolution (DE) algorithm. In addition, a hybrid strategy method and a time-varying weighting factor are added to the mutation operator to accelerate convergence. Two examples of 64-element and 900-element truncated cone antenna arrays were synthesized. After forming a sparse antenna array out of the original full array, the number of antennas was decreased to 80% and 56.8%, respectively. The results show that the main beam of the sparse conformal antenna array is accurately fixed to the axial direction with the PSLL less than −20 dB at both the φ = 0° and φ = 90° planes, which proves the effectiveness of this method in conformal sparse array synthesis.

Synthesis of sparse square arrays with high beam collection efficiency under minimum element spacing constraints

AbstractThis letter presents a large spacing nonuniform distribution, uniform excitation sparse square array model to maximize beam collection efficiency (BCE) and minimize sidelobe level outside the collection area (CSL) of the transmitting antenna in microwave wireless power transmission (MWPT) systems. We improve the position update parameters in the dynamic weight particle swarm optimization (DWPSO) algorithm by adding multiobjective learning features (MODWPSO). We use MODWPSO to optimize the elements' positions to maximize BCE and minimize CSL and discuss the effect of the minimum element spacing value on BCE and CSL. By comparing the array performance with a typical array model, it can be concluded that the proposed large spacing sparse nonuniform distribution, uniform excitation square array model has higher BCE, lower CSL, and fewer costs.

Sparse Array Synthesis Including Mutual Coupling for MU-MIMO Average Capacity Maximization

A hybrid optimization algorithm, including mutual coupling (MC), is proposed to synthesize an irregular sparse array (ISA) for average capacity maximization in a multiuser multiple-input–multiple-output (MU-MIMO) system. The hybrid approach is composed of two phases to suboptimally determine the location of a fixed number of omnidirectional thin dipole antennas in an arbitrary sparse aperture via a diagonal antenna selection matrix. In Phase I, the problem is relaxed to a convex optimization by ignoring the MC and weakening the constraints. The output of Phase I is accounted as a reliable initial guess for the genetic algorithm (GA) in Phase II, which incorporates the MC effects through the coupling matrix and avoids the convex relaxation technique. The proposed approach outperforms the conventional GA with a random initial population, while it avoids trying several starting positions. Meanwhile, the undesirable appearance of grating lobes, due to the undersampling, and the degrading MC effects are suppressed by aperiodicity. It is observed that doubling the conventional interelement spacing (half-wavelength) and finding the location of eight dipoles in a sparse aperture by the proposed method improve the average capacity by 3.27%–11.9% when the number of users varies from two to eight, and the signal-to-noise ratio (SNR) is 30 dB.

Synthesis of uniform amplitude sparse linear dipole arrays with multiple shaped‐beam patterns by sharing element rotations and positions

In this article, a novel method of synthesizing sparse linear dipole arrays with multiple shaped-beam patterns is proposed by finding a set of common element rotations and positions along with individual excitation phases. Compared with most shaped multiple-pattern synthesis methods using nonuniform amplitude excitations, the proposed method adopts the uniform amplitude excitation and exploits the element rotation as a supplementary degree of array freedom. Such a method enables each amplifier to work at its optimal level and avoids the usage of unequal power dividers for the array feeding network, thus reducing the cost, space, and weight of the radiation system. The shaped multiple-pattern synthesis problem with multiple constraints including the peak sidelobe level, cross-polarization level, minimum element spacing, and array length is formulated and optimized by particle swarm optimization. Two examples for synthesizing sparse linear dipole arrays with multiple shaped-beam patterns are conducted to validate the effectiveness and superiority of the proposed method. Synthesis results show that the proposed method can save antenna elements and avoid the usage of unequal power dividers for test cases. Moreover, the full-wave simulations are also conducted in these two examples.

An Effective Method for the Synthesis of Wideband and Wide-Scanning Sparse Planar Array

The matrix enhancement and matrix pencil (MEMP) has been used to reduce the number of array elements in the planar array with a shaped-beam pattern. This work extends the MEMP-based synthesis method to the synthesis of pattern reconfigurable sparse planar arrays in wide angle scanning and wide-band, which exploits a necessary restriction on finding the common element positions and individual element excitations for multiple patterns. Moreover, a unitary transformation is exploited into the multiple-composite equivalent Hankel matrix, which converts the complex computations of singular value decomposition (SVD) and eigenvalue decomposition (EVD) courses into real ones and effectively reduces the computation complexity. A new tactic is also restricted on avoiding too small element spacing with the consideration of the size of array antenna element. A set of numerical experiments is provided to validate the effectiveness and advantages of the proposed method.