Linear Array Pattern Synthesis Research Articles

Application of Dandelion Optimization Algorithm in Pattern Synthesis of Linear Antenna Arrays

This paper introduces an application of the dandelion optimization (DO) algorithm in antenna arrays. This is the first time that the DO algorithm has been used for optimizing antenna arrays. For antenna array optimization, sidelobe level (SLL) and deep nulls are key technical indicators. A lower SLL can improve the signal-to-noise ratio and reduce the impact of clutter signals outside the main beam. Deep nulls need to be aligned with the direction of interference to eliminate the influence of interference sources. The combination of the two can effectively improve the anti-interference ability of the entire system. Therefore, antenna arrays with ultra-low sidelobes and ultra-deep nulls are currently hot in the field of antenna array design and are also some of the key technologies needed to achieve modern high-performance radar systems. As a new type of evolutionary algorithm inspired by nature, the DO algorithm is inspired by the wind propagation behavior of dandelions in nature. This algorithm iteratively updates the population from three stages of ascent, descent, and landing, ultimately finding the optimal position. It has good optimization ability in solving complex problems such as those involving nonlinearity, discreteness, and non-convexity, and the antenna array pattern synthesis optimization problem belongs to multivariate nonlinear problems. Therefore, the DO algorithm can be effectively applied in the field of antenna array optimization. In this work, we use the following method to obtain an optimized pattern of a linear array with the lowest sidelobe level (SLL), null placement in particular directions, and a lower notch in particular directions: by controlling the antenna array’s element spacing and leaving the phase unchanged to optimize the current amplitudes and by controlling the excitation current and phase fixation of the antenna array and changing the element spacing. In the first and second examples, different algorithms are used to reduce the SLL of the antenna. In the first example, the DO algorithm reduces the SLL to −33.37 dB, which is 2.67 dB, 2.67 dB, 3.77 dB, 2.74 dB, and 2.52 dB lower than five other algorithms. In the second example, the SLL optimized by the DO algorithm is −42.56 dB, which is 5.04 dB and 1.48 dB lower than two other algorithms. In both examples, the DO algorithm reduces the SLL lower than other algorithms when the main lobe of the antenna is not significantly widened. Examples 3, 4, and 5 use the DO algorithm to optimize the amplitude of the current, generating deep nulls and deep notches in specific directions. In Example 3, the DO algorithm obtains a depth of nulls equal to −187.6 dB, which is 66.7 dB and 44.3 dB lower than that of the flower pollination algorithm (FPA) and the chaotic colony predation algorithm (CCPA), respectively. In Example 4, the deep null obtained by the DO algorithm is as low as −98.69 dB, which is 6.67 dB lower than the deep null obtained by the grey wolf optimization (GWO) algorithm. In Example 5, the deep notch obtained by the DO algorithm is as low as −63.1 dB, which is 6.4 dB and 1.9 dB lower than the spider monkey optimization (SMO) algorithm and the grasshopper optimization algorithm (GOA), respectively. The data prove that the DO algorithm produces deeper nulls and notches than other algorithms. The last two examples involve reducing sidelobe levels and generating deep nulls by optimizing the spacing between elements. In Example 5, the SLL obtained using the DO algorithm is −22.8766 dB, which is 0.1998 dB lower than the lowest SLL of −22.6768 dB among other algorithms. In Example 6, the SLL obtained using the DO algorithm is −20.1012 dB, and the null depth is −125.1 dB, which is 1.592 dB lower than the SLL obtained by the cat swarm optimization (CSO) algorithm and 19.1 dB lower than the deep null obtained by the GWO algorithm, respectively. In summary, the results of six simulation experiments indicate that the DO algorithm has better optimization ability in linear array optimization than other evolutionary algorithms.

Efficient Phase-Only Symmetric Pattern Synthesis for Linear and Circular Planar Arrays via Phase Perturbation in Low-Dimensional Space

Efficient Phase-Only Symmetric Pattern Synthesis for Linear and Circular Planar Arrays via Phase Perturbation in Low-Dimensional Space

Simple Matrix Equation (SME) Method for Pattern Synthesis of Conformal Antenna Array with Arbitrary Architecture

A novel noniterative method for pattern synthesis of conformal antenna array is put forward. First, a new pattern function formula for general conformal antenna array is derived. Then, according to the new pattern function formula, a new block matrix equation (BME) and a simple matrix equation (SME) are obtained. SME has the same form as the equation of linear array pattern synthesis. The new method can be applied to pattern synthesis of any conformal array. Moreover, due to SME having the same form as the matrix equation of linear array pattern synthesis, the new simple matrix equation can be dealt with by the approaches for linear array pattern synthesis, which significantly expands the existing approaches for conformal antenna array pattern synthesis. Two different conformal array configurations are taken as the examples to demonstrate the advantages of the new method. Results of the simulations show that the new method can flexibly and effectively be applied to synthesize patterns for various conformal array architectures.

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.

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.

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.

Pattern synthesis of linear and ring arrays with minimum number of elements using FFT and Bessel transformation

In antenna engineering, to reduce the final cost of array design, it is often necessary to design an array with the minimum number of elements. So, proper selection of the number of array elements and the location of the elements are two important factors in array design. In this work, a novel analytical approach for designing an array with optimal parameters is described. The Nyquist–Shannon sampling theorem is used to determine the number of array elements and the distance between them. The array's excitation coefficients are then determined using the recursive least square approach and the Bessel transform of the array factor. It is also demonstrated that the introduced procedure can be extended to include the concentric ring arrays. Several practical arrays are evaluated to verify the performance of the suggested approach. The results show that the introduced approach is a good candidate for designing practical arrays with acceptable accuracy.

Null-Steering Beamformers for Suppressing Unknown Direction Interferences in Sidelobes

This paper proposes an efficient null-steering beamformer for adaptive pattern synthesis of uniform linear arrays based on binary bat algorithm (BBA) and the amplitude-only control of array excitation weights. The proposed beamformer is able to suppress unknown direction interferences in the sidelobes while simultaneously maintaining the main lobe and suppressing the sidelobes. The performance of the proposal has been investigated via a couple of scenarios including operation speed and adaptive null-steering ability with or without the effect of mutual coupling in half-wave dipole uniform linear arrays (DULA). The simulation results have proved that the proposed beamformer is a promising approach for adaptive pattern synthesis in the case of interference suppression. In addition, this proposal outperforms those using binary particle swarm optimization (BPSO) on the operation speed and null-steering efficiency.

Synthesis for sidelobe suppression of linear array based on improved grasshopper optimization algorithm with adaptive chaotic strategy

In view of the shortcomings of grasshopper optimization algorithm(GOA), such as insufficient exploration ability in the early stage and insufficient development ability in the later stage, this paper proposes a new adaptive chaotic GOA (ACGOA) by using curve adaptive adjustment strategy to replace the existing linear adaptive strategy, and using uniform chaos optimization to update the grasshopper position, so as to further improve the comprehensive ability of grasshopper swarms in the early exploration and later development, and better realize the balance between global search and local optimization ability. The effectiveness and stability of ACGOA in optimization calculation are tested by using a variety of single/multi peak benchmark function to get the extremum, and then applied to pattern synthesis of linear array for the first time, the target optimization performance of ACGOA is verified by suppressing the maximum SLL of linear array. The results show that compared with other existing algorithms, the algorithm has lower maximum sidelobe level and narrower first null beam width. The ACGOA results and convergence test show that the algorithm has superior applicability in antenna optimization.

Pattern Synthesis for Sparse Linear Arrays via Atomic Norm Minimization

In this letter, a novel pattern synthesis algorithm that jointly optimizes the number, positions, and excitation of elements in a sparse linear array (SLA) is designed based on continuous compressed sensing. The pattern synthesis problem is first formulated as a sparse recovery problem, which can be solved using semidefinite programming involving atomic norm minimization (ANM). The parameters of the designed SLA, including the corresponding element positions and excitations, are determined via Vandermonde decomposition and least squares in the continuous domain. As ANM works directly in the continuous domain, the proposed algorithm is able to synthesize the desired patterns with a small mismatch and a small number of elements. A number of representative numerical experiments show the effectiveness of our algorithm.

Synthesis of sparse linear arrays using reweighted gridless compressed sensing

Pattern synthesis of the sparse linear array (SLA) has played an important role when the antenna size is extremely limited. Although grid-based compressed sensing (CS) algorithms have been widely utilised to synthesise the SLA, the performance is greatly affected by the grid mismatch problem. To solve the problem, a reweighted gridless CS (RGCS) algorithm based on the reweighted atomic norm minimisation and the rotational invariance propagator method is introduced. In the RGCS algorithm, the number of antenna elements can be efficiently reduced through the reweighted gridless convex optimisation, which utilises a reweighted strategy to break the limit of the atomic norm and improves the performance of the SLA. More importantly, in addition to the focussed-beam pattern, the proposed algorithm can also synthesise the SLA with the asymmetric beam pattern. Numerical experiments show that the RGCS algorithm can save about 18.75%–46% array elements for the uniform linear array.

Synthesis of Linear Antenna Arrays using the Differential Evolution Algorithm with Current-Only Adaptive Nulling Technique

This paper presents an efficient method for the pattern synthesis of linear antenna array based on the differential evolution algorithm. A number of examples are presented to demonstrate the various capabilities of the this method for different number of elements. The main objective of this paper is to achieve a set of current weights in order to steer the nulls in undesired directions (nulling the undesired signals) and steering the main beam towards the desired direction(direction of desired signal) by changing the phase excitation currents. The fitness function is obtained from maximization of error between actual pattern and desired pattern.

Fast Synthesis Method for Large Aperture Array Pattern in the Presence of Array Errors

In this paper, an improved array synthesis method with array errors is proposed for large aperture arrays. Because of the array errors such as amplitude-phase errors and positions errors, the performance of the array synthesis is reduced seriously. Firstly, the ideal fast low sidelobe synthesis method is obtained based on the discrete Fourier transform (DFT) method. Then, by using Taylor expansion to remove the coupling relationship between the position of the element and the scanning angle, the compensation matrix for the pattern function and the array weighted vector with amplitude phase and position errors are derived. At last, the conversion relationship between the array with errors and the array weight vector is corrected in the iterative process. The theoretical simulation experiments verify the effectiveness and robustness of the proposed method for the linear array and rectangular array pattern synthesis. Then, the influence of Taylor expansion order on the pattern synthesis results is analysed.

Optimization of linear arrays using modified social group optimization algorithm

In this paper, optimization of the linear array (LA) antenna is performed using modified social group optimization algorithm (SGOA). First step of the work involves in transforming the electromagnetic engineering problem to an optimization problem which is completely described in terms of objectives. Linear array synthesis is inherently considered as a multi-attribute problem. The pattern synthesis of LA is carried out with several objectives involving sidelobe level (SLL), beam-width (BW) and desired nulls. The SLL suppression with BW constraint is considered as first objective of this work and the results are compared with several evolutionary computing algorithms like ant lion (ALO), grey wolf (GWO) and root-runner (RRA). Following this, the MSGOA is further used to synthesise null patterns in which the pattern is completely described in terms of nulls with SLL and BW as constraints. The entire simulation-based experimentation is performed using Matlab® on i5 computing system.

Linear Arbitrary Array Pattern Synthesis With Shape Constraints and Excitation Range Control

This letter proposes a method based on primary-dual iteration to address the array pattern synthesis problem of minimizing the peak sidelobe level (PSL) under the constraints of controlled mainlobe ripples and dynamic range ratio (DRR) of current excitations. Especially, when DRR = 1, the phase-only beampattern synthesis problem is solved. Simulation examples are presented to verify the effectiveness of the proposed method in terms of PSL and DRR.

Pattern Synthesis of Uniform and Sparse Linear Antenna Array Using Mayfly Algorithm

Pattern synthesis is a significant research focus in smart antennas due to its extensive use in several radar and communication systems. To improve the optimization performance of pattern synthesis of uniform and sparse linear antenna array, this paper presents an optimization method for solving the antenna array synthesis problem using the Mayfly Algorithm (MA). MA is a new heuristic algorithm inspired by the flight behavior as well as the mating process of mayflies, it has a unique velocity update system with great convergence. In this work, the MA was applied to linear antenna arrays (LAA) for optimal pattern synthesis in the following ways: by optimizing the antenna current amplitudes while maintaining uniform spacing and by optimizing the antenna positions while assuming a uniform excitation. Constraints of inter-element spacing and aperture length are imposed in the synthesis of sparse LAA. Sidelobe level (SLL) suppression with the placement of nulls in the specified directions is also implemented. The results gotten from this novel algorithm are validated by benchmarking with results obtained using other intelligent algorithms. In the synthesis of uniform 20-element LAA with nulls, MA achieved an SLL of -31.27 dB and the deepest null of -101.60 dB. Also, for sparse 20-element LAA, an SLL of -18.85 dB was attained alongside the deepest null of -87.37 dB. MA obtained an SLL of -35.73 dB and -23.68 dB for the synthesis of uniform and sparse 32-element LAA respectively. Finally, electromagnetism simulations are conducted using ANSYS Electromagnetics (HFSS) software, to evaluate the performance of MA for the beam pattern optimizations, taking into consideration the mutual coupling effects. The results prove that optimization of LAA using MA provides considerable enhancements in peak SLL suppression, null control, and convergence rate with respect to the uniform array and the synthesis obtained from other existing optimization techniques.

Optimal Pattern Synthesis of Linear Antenna Arrays Using Modified Grey Wolf Optimization Algorithm

The aim of this work is to show the effectiveness of a new algorithm named as modified grey wolf optimization (MGWO) algorithm to determine the optimum combination parameters values of a linear antenna array which is widely used in the communication systems. The selection part of the classical GWO has been modified by adopting the competitive exclusion selection inspired from genetic algorithm. The objective to be attained is a directional array factor with a very low level of lateral lobs. To this effect, a Gaussian function centered at 90° with the total absence of secondary lobs is considered as a desired diagram in our simulation. To matches the desired pattern as closely as possible, we considered the optimization of interspacing elements, weights amplitude and phase excitation of the linear antenna array factor. It has been demonstrated that the performance of a printed linear antenna array depends on all parameters, in which simultaneous optimization is imperative to maximize its characteristics. The obtained results show the effectiveness and the flexibility of the proposed algorithm in terms of minimized lateral lobe level compared to PSO algorithm and the convergence speed towards the desired solution.

Pattern Synthesis of Linear Antenna Array Using Improved Differential Evolution Algorithm with SPS Framework

In this paper, an improved differential evolution (DE) algorithm with the successful-parent-selecting (SPS) framework, named SPS-JADE, is applied to the pattern synthesis of linear antenna arrays. Here, the pattern synthesis of the linear antenna arrays is viewed as an optimization problem with excitation amplitudes being the optimization variables and attaining sidelobe suppression and null depth being the optimization objectives. For this optimization problem, an improved DE algorithm named JADE is introduced, and the SPS framework is used to solve the stagnation problem of the DE algorithm, which further improves the DE algorithm’s performance. Finally, the combined SPS-JADE algorithm is verified in simulation experiments of the pattern synthesis of an antenna array, and the results are compared with those obtained by other state-of-the-art random optimization algorithms. The results demonstrate that the proposed SPS-JADE algorithm is superior to other algorithms in the pattern synthesis performance with a lower sidelobe level and a more satisfactory null depth under the constraint of beamwidth requirement.

Optimal Pattern Synthesis of Linear Array and Broadband Design of Whip Antenna Using Grasshopper Optimization Algorithm

Antenna arrays with high directivity, low side-lobe level, and null control in desired direction and whip antenna with wider bandwidth both need to be optimized to meet different needs of communication systems. A new natural heuristic algorithm simulating social behavior of grasshoppers, grasshopper optimization algorithm (GOA), is applied to electromagnetic field as a new effective technology to solve the antenna optimization problem for the first time. Its algorithm is simple and has no gradient mechanism, can effectively avoid falling into local optimum, and is suitable for single-objective and multiobjective optimization problems. GOA is used to optimize the side lobe suppression, null depth, and notch control of arbitrary linear array and then used to optimize the loading and matching network of 10-meter HF broadband whip antenna compared with other algorithms. The results show that GOA has more advantages in side-lobe suppression, null depth, and notch control of linear array than other algorithms and has better broadband optimization performance for HF whip antenna. The pattern synthesis and antenna broadband optimization based on GOA provide a new and effective method for antenna performance optimization.

Side lobe pattern synthesis using hybrid SSWOA algorithm for conformal antenna array

In this paper, the pattern synthesis of conformal antenna array using Salp Swarm Whale Optimization Algorithm (SSWOA) algorithm is proposed. The proposed hybrid algorithm is the combination of Salp Swarm Optimization (SSA) and Whale Optimization Algorithm (WOA). In the proposed algorithm, the SSA algorithm plays the role of guiding the evolution and the WOA algorithm works as an assistant. Moreover, after updating the salps position, with WOA the best known position are evolved to enhance the optimum search ability. When applied to antenna array pattern synthesis by taking advantages of SSA and WOA, the proposed optimization has high convergence accuracy and faster convergence speed. Several typical test functions and optimization examples of a linear array pattern synthesis are illustrated to show the performance of the hybrid algorithm. Experimental results show that the proposed hybrid algorithm is superior to SSA and WOA when applied to Sphere, Griewank, Rosenbrock, and Rastrigin test functions.