Array Pattern Synthesis Research Articles

Synthesis of linear thinned array based on improved binary brain storm optimization

In this paper, an improved binary brain storm optimization (ImBBSO) method is presented for pattern synthesis of linear thinned array. To avoid local convergence and obtain the global optimum, on the basic of original binary brain storm optimization (BBSO) algorithm, the designed method mainly modifies three aspects, containing the clustering centers selection, the forced bit transposition mechanism and the survival of population. The interactions of these three operations drive optimization variables to move toward a better direction. During optimization process, the formulated cost function balances the relationship among the number of active elements, the peak sidelobe level and the half power beam width, which are eventually in the best balance state after completing iterations. Besides, the subarray partition strategy is also integrated into the proposed optimization framework with slight amendments, which can be applied to many engineering fields with space restrictions. Finally, several numerical examples demonstrate the effectiveness and applicability of the proposed method compared with other existing results of state-of-the-art methods, whether in benchmarking functions or linear array application.

Grating Lobe Suppression for Distributed Phased Array via Accumulated Array Pattern Synthesis

Long-sparse distributed phased array (DPA) is a promising technique for increasing resolution and reducing expense. However, inherent grating lobes (GLs) caused by large internode distance are hard to suppress, especially for the limited available nodes case. To solve this problem, a novel accumulated array pattern synthesis (AAPS) scheme to suppress the GLs is proposed, utilizing the time-varying node motion to fill the spatial domain sampling. Furthermore, the high sidelobe level problems caused by mismatching between the actual and nominal position of moving nodes due to imperfect motion control are also considered. Hence, under the AAPS scheme, a measurement-based matching (MBM) algorithm is supplementally proposed based on measuring the relative position and angle between nodes. Simulations are provided to validate the effectiveness of the proposed algorithm.

Multiband Pattern Synthesis of Time-Modulated Conformal Array with Quadratic Convex Optimization Algorithm

Aiming at the multiband pattern synthesis problem of time-modulated conformal array antenna, a quadratic convex optimization algorithm is proposed for sum and difference beamforming with low sidelobe levels. This articles method synthesizes a difference beam with a low sidelobe level by generating nulls at the center frequency band and optimizing the switch-on duration time of array elements. And the sum beamforming and sidelobe suppression of the first-order sideband are realized by optimizing the switch-on instant time of the array elements. The proposed algorithm has excellent properties of sidelobe suppression and angular sweep. The simulation results of circular and satellite array antenna verify the effectiveness of the algorithm.

Beam Stabilization of Deformed Conformal Array Antenna Based on Physical- Method -Driven Deep Learning

The array antenna will be inevitably deformed affected by the motion of the communication system or other special requirements, which will reduce the original good radiation performance, such as the gain dropping, the side lobes increasing, and even the beam splitting. In order to cope with the beam deterioration caused by the array antenna’s deformation, it is necessary to quickly manipulate the amplitude and phase distribution according to the current conformal array shape to stabilize the beam. This paper proposes a physical-method-driven deep-learning-based (PMDL-based) fast beam stabilization algorithm for the antenna array deformation. Firstly, we theoretically analyze the radiation pattern synthesis of the conformal array with the arbitrary surface to design the corresponding physical method, and we verify the accuracy of the method by the calculated and simulated results. Then, the deep neural network driven by the physical method is designed integrated with the aforementioned radiation pattern synthesis, whose training process is given. Finally, a 1×16 array antenna is taken as an example to verify the validity of the beam stabilization algorithm when the designed array is deformed. The simulated and measured results both indicate that the gain dropping and the sidelobe level rising are respectively less than 1.5 dB and 2 dB by applying the proposed PMDL-based fast beam stabilization when the array antenna is deformed within the range of 100° of the normal vector of each array element, while the beam stabilization time is less than 1.0 ms (testing time).

Efficient and Accurate Pattern Synthesis for Radome‐Enclosed Planar Arrays Using Iterative FFT via Two‐Dimensional Least‐Square Active Element Pattern Expansion

AbstractThis work generalizes the iterative fast Fourier transform (FFT) via least‐square active element pattern expansion method to efficiently synthesize two‐dimensional (2D) patterns with accurate sidelobe and mainlobe shape control for planar arrays with radomes. The 2D active element patterns (2D‐AEPs) of a planar array‐radome structure are utilized to include the mutual coupling and radome effect. The 2D‐LSAEPE method is presented to approximate each 2D‐AEP as the pattern by exciting a virtual rectangular subarray with identical element patterns, and the weighting coefficients of the virtual subarray are found by minimizing the least‐square error of the 2D‐AEP approximation. With the help of the 2D‐LSAEPE, the pattern of a planar array with a radome can be efficiently calculated by FFT. To apply the FFT via 2D‐LSAEPE for planar array pattern computation, a blocked accumulating matrix is introduced which relates the virtual and physical excitation vectors. In addition, an interpolation‐based pre‐processing technique is implemented to obtain the virtual element pattern data in uniform grid of the (u, v)‐space so as to meet the requirement of employing the 2D‐FFT. By integrating the FFT with the 2D‐LSAEPE and the interpolation technique, an efficient iterative method is developed to implement accurate pattern synthesis for planar arrays with radomes. Three examples of synthesizing different planar array‐radome systems are conducted. Synthesis results show that the proposed method achieves much more accurate synthesis result than the traditional FFT‐based technique, while taking much less computation time than some other methods. This verifies the effectiveness of the proposed method.

Pattern synthesis of nonuniform linear antenna array based on FFDM

To optimize the number, spacing and excitation of nonuniform linear array at the same time, a Fourier basis filter diagonalization method (FFDM) is proposed in this paper. By constructing a set of Hamiltonian operator functions that can be decomposed by orthogonal eigenvectors, the synthesis of nonuniform linear arrays is transformed into a generalized eigenvalue decomposition under Fourier basis. The introduction of Fourier basis can improve the computational rate. The least square method (LSM) is used to solve the array element excitation, which improves the matching accuracy. A number of numerical simulations shown that the proposed algorithm can improve the accuracy of the array factor (AF) pattern of many types of practical arrays reconstruction.

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.

Robust Low Sidelobe Synthesis for Arbitrary Arrays Based on Gradient Ascent With Min-Oracle

This article studies the robust pattern synthesis of a narrow main beam and low sidelobes of arbitrary arrays, which represents a classical but challenging problem for array antennas. In addition, pattern synthesis for a given sidelobe envelope is discussed. The synthesis problem is formulated as a nonconvex–nonconcave minimax problem with nonconvex constraints, which avoids the design of the optimal desired pattern and ensures the robustness of pattern synthesis for arbitrary arrays by nonconvex constraints. An algorithm named gradient ascent with min-oracle (GAmin) is proposed to address the considered minimax problem. Furthermore, the majorization–minimization algorithmic framework is used to reduce computational complexity. It is shown that for arbitrary linear and planar arrays, the proposed GAmin-based pattern synthesis method can perform well for pattern synthesis both without and with a given sidelobe envelope. A variety of numerical examples are provided to demonstrate the superior performance of the proposed method.

Formulation of optimization problems with radiation field phases as design variables for pattern synthesis of linear antenna arrays

Pattern synthesise of antenna arrays is usually complicated optimization problems, while evolutionary algorithms (EAs) are promising in solving these problems. This paper does not propose a new EA, but does construct a new form of optimization problems. The new optimization formulation has two differences from the common ones. One is the objective function is the field error between the desired and the designed, not the usual amplitude error between the desired and the designed. This difference is beneficial to decrease complexity in some sense. The second difference is that the design variables are changed as phases of desired radiation field within shaped-region, instead of excitation parameters. This difference leads to the reduction of the number of design variables. A series of synthesis experiments including equally and unequally spaced linear arrays with different pattern shape requirements are applied, and the effectiveness and advantages of the proposed new optimization problems are validated. The results show that the proposing a new optimization formulation with less complexity is as significant as proposing a new algorithm.

Data of the paper "Efficient and Accurate Pattern Synthesis for Radome-Enclosed Planar Arrays Using Iterative FFT via Two-dimensional Least-Square Active Element Pattern Expansion" submitted to Radio Science

Data of the paper "Efficient and Accurate Pattern Synthesis for Radome-Enclosed Planar Arrays Using Iterative FFT via Two-dimensional Least-Square Active Element Pattern Expansion" submitted to Radio Science

Synthesizing Shaped-Beam Cylindrical Conformal Array Considering Mutual Coupling Using Refined Rotation/Phase Optimization

A novel method of synthesizing shaped-beam cylindrical conformal array by rotating the antenna elements and optimizing their excitation phases is presented. Rotation of antennas on curved surface is mathematically described by rotating its vectorial active element pattern (VAEP) in its local coordinate system (LCS). Then the scalar patterns and polarization unit vectors of all the rotated VAEPs are properly transformed and then interpolated at a unified angle sampling grid in a common coordinate system, where they are summed to obtain an approximated array expression. With this expression, element rotations and phases can be optimized using the constriction factor particle swarm optimization (CF-PSO) to synthesize desired shaped-beam pattern with controlled sidelobe level (SLL) and cross-polarization level (XPL). However, since rotations on curved surface introduce considerable variations to the element curvature and mutual coupling (MC), the synthesized array pattern would have considerable errors. A refined strategy is adopted then to improve the synthesis accuracy. The proposed method uses uniform amplitude weighting, thus saving many unequal power dividers. Three typical shaped pattern synthesis examples are provided to show the effectiveness of the proposed method. A cylindrical array prototype with 24 rotated U-slot loaded patch antennas is fabricated and measured for practical validation.

Design of an Optically Transparent Microwave Absorber Based on Coding Metasurface

In this paper, a metamaterial absorber with a checkerboard patterned ITO (indium tin oxide) film as the surface is obtained by using flexible and optically transparent wave-absorbing material ITO–PET (polyethylene terephthalate), and a coding arrangement of two basic coding units based on the APS-PSO (Array Pattern Synthesis -Particle Swarm Optimization) algorithm. The surface structure of the absorber consists of ITO rectangular patch structures and ITO circular patch structures (110 Ω/sq). The ITO rectangular patch structures and ITO circular patch structures are symmetrical. The middle layer is made up of two layers of PET and one layer of PMMA, and the bottom surface is covered with a layer of low square resistance ITO film (8 Ω/sq). The experimental results, which are consistent with the simulation results, show that the absorber has superior performance: over 90% absorptance in the 5.06–9.01 GHz band, high transmittance, and a −10 dBsm RCS (radar cross-section) reduction in the 5.3–8.7 GHz band. This design also has polarization insensitivity and angular stability.

Radiation pattern synthesis in conformal antenna arrays using modified convex optimization technique

In this paper, a modified convex optimization technique is used for radiation pattern correction in a cylindrical-shaped conformal microstrip array antenna. The technique uses numerical simulations to optimize the amplitude and phase excitations, with the goal to decrease the Euclidean distance between the desired field pattern and the obtained (simulated/measured) field pattern while maintaining the main beam direction, null's location, and side lobe levels under control. Two prototypes of 1 × 4 $$ 1\times 4 $$ and 2 × 4 $$ 2\times 4 $$ conformal microstrip antenna array deformed from linear/planar structure to the prescribed cylindrical shape, with different radii of curvature, are studied to demonstrate the performance of the proposed technique. The proposed convex optimization model when applied to conformal antenna array possesses fast computing speed and high convergence accuracy for radiation pattern synthesis, which can be a valuable tool for engineering applications.

The Robustness of Pencil Beam Synthesis Without Considering Sensor Uncertainties

Sensor uncertainties such as amplitude and phase errors may deteriorate the performance of array pattern synthesis. Therefore, several robust synthesis methods have been proposed. In this communication, we show that, for pencil beams, the direct synthesis method that does not take into account sensor errors also has robustness against sensor uncertainties. We first reformulate the robust synthesis method based on the worst-case performance criterion as a perturbation of the direct synthesis method. Then we prove that the direct and robust synthesis methods have the same solution up to a scaling factor. Thus, they produce the same array pattern (normalized). The condition for this result is that the error norms of steering vectors in different directions are equal to a small positive number, which is a reasonable assumption in practice. In addition, we derive a new optimization model for the robust synthesis method that can be solved much faster than the existing one.

Advanced Marine Predator Algorithm for Circular Antenna Array Pattern Synthesis.

The pattern synthesis of antenna arrays is a substantial factor that can enhance the effectiveness and validity of a wireless communication system. This work proposes an advanced marine predator algorithm (AMPA) to synthesize the beam patterns of a non-uniform circular antenna array (CAA). The AMPA utilizes an adaptive velocity update mechanism with a chaotic sequence parameter to improve the exploration and exploitation capability of the algorithm. The MPA structure is simplified and upgraded to overcome being stuck in the local optimum. The AMPA is employed for the joint optimization of amplitude current and inter-element spacing to suppress the peak sidelobe level (SLL) of 8-element, 10-element, 12-element, and 18-element CAAs, taking into consideration the mutual coupling effects. The results show that it attains better performances in relation to SLL suppression and convergence rate, in comparison with some other algorithms for the optimization case.

Pattern Synthesis With Closed-Form Array Response Control Algorithms

In this letter, the problem of array pattern synthesis is considered by developing two array response control algorithms. The devised two algorithms build on the basis of the accurate array response control approach, and both of them have closed-form solutions and low computational complexities. More specifically, the first proposed algorithm realizes multipoint array response control from an any given weight vector, and the second algorithm modifies the first one by avoiding the possible beam axis shift. The proposed two algorithms are able to control array responses accurately under the conditions of independence on steering vectors. By applying the first and the second array response control algorithm, two effective pattern synthesis methods for focused patterns and shaped patterns are devised, respectively. Representative examples are presented to demonstrate the performance of the proposed algorithms in array response control and pattern synthesis.

Effect of chaos factor in radiation pattern in planner antenna arrays with chaos adaptive invasive weed optimization

For mobile <span>communication and spatial detection of antennas should have high directive radiation pattern, in this context pattern synthesis of planar circular antenna arrays is highly significant such design has been done inverse weed optimization. The basic objective e is to study invasive weed optimization in compression with modified chaotic adaptive invasive weed optimization. The focus of the study is the effect of chaotic factors suitable for sinusoidal mapping for chaos as applicable to the context of the design of antennas. Taking various numbers of elements of the antenna and the distance between the antenna’s radiation patterns are studied by varying chaos factors through MATLAB programming. It is found that the critical point of 2.3 for chaos factor makes the map enter into phase of chaos prior to the critical point is a phase of periodicity starting with chaos factor of 2. Below this value there is no chaos but a phase of convergence. These phases are useful having a trade of convergence and chaos. By varying the factor of chaos the impact on the radiation factor of non-uniform planar antennas has been found to give phases of convergence of chaos which are essential for making trade of between exploitation and exploration required in optimization.</span>

Efficient and Accurate Synthesis for Array Pattern Shaping.

Array pattern synthesis (APS) aims to create the desired array pattern as closely as possible to the prescribed mask template by varying the element excitations of the array. Herein, an efficient approach for the APS to control the sidelobe level is proposed. After designing the mask template to meet the prescribed sidelobe requirements and the waveform pattern, a set of element excitations is calculated through the Fourier transform performed on the projection the waveform pattern onto the mask template. Then, a desired array pattern can be synthesized from this updated set of excitation coefficients. The proposed APS approach directly presents a mathematical formulation of the exact set of excitations without any iterative optimization process. The proposed method is particularly suited for many array elements in linear antenna array. Thus, the proposed APS achieves substantial improvements in terms of computation complexity, performance, and ease of implementation in the algorithm when compared with conventional methods. Several simulation results are provided to verify the efficacy and effectiveness of the proposed method.

Highly Directive Array Pattern Synthesis in Different phi Planes of a Large CCRAA Using Array Thinning Technique

This paper presents a pattern synthesis method of a sizeable concentric circular ring array (CCRAA) of isotropic antennas using Evolutionary Algorithms. In this method, the array is thinned using the optimum set of binary excitations to achieve the desired highly directive pencil beam patterns with lower peak side lobe level(SLL). The half-power beam width and first null beam width is kept constant to obtain such highly directive beam patterns with lower peak SLL. This pattern is not synthesized to a particular azimuth plane rather in four different ' planes from entire azimuth planes. The isotropic elements are uniformly spaced in the concentric ring. The achieved set of optimum amplitudes are constructed with either 1 or 0 using Differential Evolutionary Algorithm(DE), Genetic Algorithm (GA), and Particle Swarm Optimization Algorithm (PSO). These excitations show the state of the elements. The elements are in “ON” state or in “OFF” state depending upon the excitation ‘1’ or ‘0’. It is also helpful to reduce the complexity of the feed networks. The excitations are also verified in the whole range (0o <phi<360o) of ' planes by selecting four phi planes arbitrarily. The outcomes established the superiority of GA and DE over PSO and also the effectiveness of the proposed method.

Two-Dimensional Beam Pattern Synthesis for Phased Arrays With Arbitrary Element Geometry via Magnitude Least Squares Optimization

In this paper, an optimization procedure for synthesizing shaped beams with an arbitrary geometry phased array system with real-time capability is presented. The algorithm involves a combination of an arbitrary extension of the Woodward-Lawson synthesis procedure with the magnitude least-squares optimization method. This simple combination significantly reduces the optimization time, enabling real-time beam shaping in response to changing requirements on beam shape or evolving geometry in distributed arrays. The technique places no restrictions on element positioning in all three spatial dimensions and is demonstrated to accurately reproduce the desired beam shape in both angular dimensions. The algorithm is demonstrated for multiple beam cases with a large, randomly generated array in computational simulation. The applicability of the algorithm to practical phased array hardware is also demonstrated using full-wave electromagnetic simulations and measurements of a realized arbitrary phased array system using a near-field scanner in an anechoic chamber.