Minimum Element Spacing Research Articles

Improved Sparrow Search Algorithm for Rectangular Planar Array Synthesis

To optimize sparse rectangular planar array antennas under multiple constraints, including array aperture, number of elements, and minimum element spacing, an improved sparrow search algorithm (ISSA) is proposed. Initially, a position distribution matrix is generated using the Blackman window weighting method. The sparrow search algorithm (SSA) is then enhanced by incorporating Kent mapping for population initialization, which improves the initial population’s diversity. Additionally, the strategy for updating the discoverer’s position integrates elements from the sine cosine algorithm (SCA), along with a nonlinear sine learning factor, thereby enhancing global search capability. Finally, a crossover strategy is embedded into the SSA to refine the optimization accuracy by improving the search methodology used by the vigilantes. To verify the efficacy of our approach, we carried out simulation experiments. The results demonstrate that this method significantly enhances the performance of the array antenna by reducing the peak sidelobe level and minimizing the zero-trap depth. These findings validate the reliability and effectiveness of the suggested method.

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.

Pattern-Reconfigurable Sparse Linear Array Synthesis Under Minimum Element Spacing Control by Alternating Sequential Quadratic Programming

A new method called alternating sequential quadratic programming (ASQP) is proposed to synthesize pattern-reconfigurable sparse linear arrays with minimum element spacing control. The method can find the common element positions and multiple sets of excitations for generating multiple reconfigurable patterns which accurately meet their given upper and lower pattern bounds. In addition, by introducing auxiliary weighting coefficients and collective excitation coefficient vectors and choosing them as optimization variables alternately, the proposed method can appropriately incorporate the minimum element spacing constraint into the pattern synthesis. Synthesized results show that the proposed method can give satisfactory reconfigurable pattern performance but save much more elements compared with some existing methods.

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.

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.

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.

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.

Synthesis of Sparse Array With Sum and Difference Patterns Under Minimum Element Spacing Control by Alternating Linear Programming Optimization

A novel method based on alternating linear programming optimization is presented to synthesize sparse linear arrays with sum and difference patterns. This method can find the optimized element positions and excitations shared for both sum and difference patterns with accurate control of multiregion sidelobe distribution and difference pattern null slope. In addition, the constraints on the minimum element spacing and dynamic range ratio of the obtained excitations can be also appropriately incorporated into this alternating optimization process. Two synthesis examples with different pattern shape requirements are conducted to validate the effectiveness and advantages of the proposed method.

Improved Beam-Scannable Ultra-Wideband Sparse Antenna Arrays by Iterative Convex Optimization Based on Raised Power Series Representation

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.

Synthesis of Multibeam Sparse Circular-Arc Antenna Arrays Employing Refined Extended Alternating Convex Optimization

A refined extended alternating convex optimization (REACO) method is presented to synthesize multibeam sparse circular-arc antenna arrays with minimum element spacing control by considering real antenna array structure characteristics. This method consists of the initial step and a few refining steps. At the initial step, an initial array with dense elements distributed on a circular-arc is considered, and its array manifold vector is described by rotating a simulated isolated element pattern (IEP) without considering element mutual coupling. The collective excitation coefficient vector (CECV) and its energy bound are introduced for each element, and consequently, the common element positions for generating desired multibeam patterns can be found by minimizing the number of active CECVs under multiple constraints. This minimization problem is further formulated as performing a sequence of alternating convex optimization (ACO) in which the CECV and an auxiliary weighting vector are alternately chosen as the optimization variables so that the minimum element spacing constraint can be easily dealt with. Once the initial optimization step is finished, a few refining steps are performed in which the element positions and excitations are successively updated in each step by renewing the array manifold vector through rotating the simulated nearby active element patterns (AEPs) of the antenna array obtained at the previous step. In such a way, the mutual coupling can be incorporated into the multibeam sparse array synthesis. An example of synthesizing a sparse circular-arc conformal array with 23 beams covering the space from −63.25° to 63.25° is conducted to validate the effectiveness and advantage of the proposed method.

Synthesis of Large Unequally Spaced Planar Arrays Utilizing Differential Evolution With New Encoding Mechanism and Cauchy Mutation

This article presents a differential evolution algorithm with a new encoding mechanism and Cauchy mutation (DE-NEM-CM) for optimizing large unequally spaced planar array layouts with the minimum element spacing constraint. In the new encoding mechanism, each individual represents a certain element position rather than an entire array layout used in traditional stochastic optimization algorithms. Such an encoding mechanism has the following advantages: 1) in each individual updating, the array pattern can be efficiently evaluated by only considering the radiation contribution variation from one element movement, which can greatly reduce the computational time; 2) it naturally facilitates the generated new array layout in population updating to meet the minimum element spacing constraint, and 3) each individual is searched always in 2-D space as the array size increases. These advantages enable it to be very suitable for synthesizing large arrays. Besides, DE serves as a search engine, and Cauchy mutation with chaotic mapping is proposed to enhance the local search while preserving the diversity of the population. A set of experiments for synthesizing different types of unequally spaced planar arrays in both narrow-and broadband applications are conducted. Synthesis results show that the proposed method achieves much lower sidelobe level than some state-of-the-art stochastic optimization methods for all the test cases. Importantly, the proposed method is much more efficient than conventional stochastic optimization algorithm especially for the case of synthesizing large unequally spaced planar array layouts. A array layout optimization with more than 1000 elements can be achieved within acceptable CPU time cost, which has not yet been reported for the existing stochastic optimization methods without resorting to supercomputing facilities.

Optimization of Sparse Concentric Ring Arrays Based on Multiple Constraints

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.

Position-only synthesis of uniformly excited elliptical antenna arrays with minimum element spacing constraint

Pattern synthesis of non-uniform elliptical antenna arrays is presented in this paper. Only the element positions of the antenna arrays are optimized by the combination of differential evolution (DE) and invasive weed optimization (IWO) to reduce the peak side lobe level (PSLL) of the radiation pattern. In order to avoid the overlap of the array elements, the minimum spacing of the adjacent elements is constrained. Also, the beam width of the radiation pattern can be constrained effectively. Three elliptical antenna arrays that have 8, 12, and 20 elements are investigated. The synthesis results show that the introduced method can present a good side lobe reduction for the radiation pattern. Compared with other optimization methods, the method proposed in this paper can obtain better performance.

Synthesizing Uniform Amplitude Sparse Dipole Arrays With Shaped Patterns by Joint Optimization of Element Positions, Rotations and Phases

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.

Optimization of Sparse Concentric Ring Arrays for Low Sidelobe

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.

Near-Field Pattern Synthesis for Sparse Focusing Antenna Arrays Based on Bayesian Compressive Sensing and Convex Optimization

An effective method based on Bayesian compressive sensing (BCS) and convex optimization for near-field sparse array synthesis is presented in this paper. An algorithm to generate reference-shaped beams in the near-field region with controllable sidelobe levels is first proposed. Then, the multitask BC is modified and generalized to synthesize a near-field sparse array radiating a desired near-field pattern with the co-polarization component. After that, a postprocessing of the final array excitation is employed to put constraints on the minimum element spacing to make the sparse layout practicable. The degradation of the near-field pattern is mitigated through reestimating the array excitation by a convex optimization. Three numerical examples show the effectiveness of the proposed method with more than 50% of elements saved compared to the uniformly distributed layout. The comparison to the result obtained by a full-wave simulator FEKO is also presented to demonstrate the validity of this method considering strong antenna mutual couplings.

An Effective Approach for the Synthesis of Uniform Amplitude Concentric Ring Arrays

In this letter, an effective approach that aims at minimizing the peak-sidelobe level of uniform amplitude concentric ring arrays (UACRAs) is presented. The element number in each ring is specified by a new deterministic formulation derived from the continuous weighting-density approximation. Meanwhile, the ring radii are adjusted by a fine-adjustment synthesis procedure. This newly developed method is flexible to synthesize UACRAs with multiple constraints, such as total number of array elements, aperture size, and minimum element spacing. Some examples are provided to demonstrate the outperformance of this approach.

Planar Array Synthesis for Optimal Microwave Power Transmission With Multiple Constraints

This letter describes a synthesis method of uniformly excited, unequally spaced planar array with maximum beam collection efficiency based on the chaotic particle swarm optimization algorithm. Here, the multiple optimization constrains include the number of array elements, the aperture, the minimum element spacing, and the maximum sidelobe level outside the receiving region. Through this method, feeding network of the array becomes simple and compact. Effectiveness of the proposed method is validated by comparing the simulation results obtained in this letter to those reported in the state-of-the-art literature.

An Effective Two-Step Approach to the Synthesis of Uniform Amplitude Linear Arrays

In this letter, with a minimum element spacing constraint, an effective two-step approach to the synthesis of uniform amplitude linear arrays, which aims at minimizing the peak-sidelobe level (PSLL), is developed. An analytical method is adopted to achieve a local optimum array at first, then an iterative local-adjust procedure is developed to adjust the element positions in expectation of reaching a lower PSLL. Several numerical results compared to global optimum approaches confirm the effectiveness and outperformance of the new proposed method.

A Hybrid Strategy Based on Weighting Density and Genetic Algorithm for the Synthesis of Uniformly Weighted Concentric Ring Arrays

A hybrid strategy based on weighting density and genetic algorithm for the synthesis of uniformly weighted concentric ring arrays (UWCRAs) aimed at minimizing the peak sidelobe level is proposed. In the strategy, an integer genetic algorithm is used to search the ring radii. Meanwhile, the element number of each ring is directly calculated from the quantized weighting density distribution constraint of a reference array. UWCRAs with a minimum element spacing constraint of half-wavelength and wide range array apertures from small diameters to the large ones are synthesized with this strategy. Numerical experiments validate the effectiveness of the proposed strategy, showing improvements with respect to the previous results.