Several Optimization Synthesis Techniques For Unequally-Spaced Antenna Arrays

Compared with a single antenna,the antenna arrays generally have the radiation patterns with superior characteristics,such as high directivity,narrow beam,and low sidelobes.In recent years,many experts and researchers have carried out research on the synthesis of unequally-spaced antenna arrays,and many optimization methods are proposed.By optimizing the position and the excitation of element,patterns with low peak sidelobe level(PSLL),patterns with low PSLL and specified null depth(ND),and shaped patterns are obtained.Multiple constraints such as the number of antennas,the array length,and the minimum/maximum spacing are generally taking into account in the synthesis problems.In this circumstance,array synthesis problem is a complex nonlinear constrained optimization problem,which can be hardly solved by conventional methods.Therefore,several novel methods are proposed in this dissertation.And several kinds of unequally-spaced antenna arrays are synthesized,such as linear arrays with low PSLL and multi-NDs,linear arrays based on subarrays with low PSLL,circular planar arrays with low PSLLs over wide bandwidths.The main works and contributions are summarized as follows.1.Optimization techniques for synthesizing unequally-spaced linear arrays with low PSLL and multi-NDs are studied.First,the optimization model for the low sidelobe synthesis problem of unequally-spaced linear arrays is established and solved by the differential evolution(DE)algorithm.Then,unequally-spaced linear arrays are synthesized for the suppressed PSLL and the suppressed NDs in some specified directions.Under the fixed array length,the predefined beamwidth,the minimum element spacing constraint,and the null depth constraint,the multi-constrained optimization model is established.It is quite difficult to find feasible solutions by using the DE algorithm due to the complex constraints.By defining a constrained vector projection(CVP),a modified differential evolutionconstrained vector projection(MDE-CVP)algorithm is proposed.Finally,several kinds of arrays are synthesized by the MDE-CVP algorithm,such as uniform excited array with low PSLL and single ND,uniform excited array with low PSLL and multi-NDs,non-uniform excited array with low PSLL and multi-NDs.Numerical results are compared to those obtained by other methods.The MDE-CVP algorithm is demonstrated to possess an improved performance in terms of PSLL and ND levels under the same element number and the same array length.2.Optimization techniques for synthesizing unequally-spaced linear arrays based on a subarray structure with low PSLLs are studied.First,an unequally-spaced linear array is partition into several subarrays,while number,spacing and excitation in each subarray are optimized with the constraints of element number,array length,and minimum/maximum spacing.The complex multi-constrained optimization model is established with the PSLL minimized.Then,the auxiliary vectors are introduced,the vector mapping relations are defined,and the equivalent optimization model with upper and lower bounds is established.The cuckoo search-convex programming(CS-CP)algorithm is proposed with its optimization steps explained in detail.Finally,uniform excited subarrayed linear arrays are synthesized by the cuckoo search algorithm,while non-uniform excited subarrayed linear arrays are synthesized by the CS-CP method.Pattern with symmetrical low sidelobes,scannable pattern with asymmetrical low sidelobes,pattern with low sidelobes and wide angle nulls are obtained.Numerical results verify that the CS-CP algorithm can effectively design subarrayed linear arrays with symmetric/asymmetric low sidelobe patterns.Compared to some state-of-the-art results,the improved PSLL and reduced excitation control numbers are observed,which validate the superiority of the CS-CP algorithm to other methods.3.Optimization techniques for synthesizing novel circular planar arrays with low PSLLs over wide bandwidths are studied.For the unequally-spaced circular planar arrays,it is difficult to handle the constraints of element number,array length,and minimum/maximum spacing,due to the irregularly element distributions.First,the circular aperture is divided into several rotationally symmetric sections,and then each section is divided into several annular sectors.The subarray is composed of the elements distributed over one annular sector.Then,the synthesis of the array with predefined sub-numbers(element number in each subarray)and the synthesis of the array without predefined sub-numbers are carried out,respectively.When the sub-numbers are predefined,the position of element are optimized under the constraints of array aperture and minimum element spacing.The arrays with low PSLL are synthesized by the vector mapping-harmony search and differential evolution(VM-HSDE)algorithm.When the sub-numbers are not predefined,the position of element and sub-number are optimized under the constraints of total number,array aperture and minimum element spacing.The arrays with low PSLLs over a wide bandwidth are synthesized by the improved harmony search(Im HS)algorithm.Simulation results verify the effectiveness of the VM-HSDE algorithm and the Im HS algorithm in synthesizing the unequally-spaced circular planar arrays.Compared with the wide-band low sidelobe circular planar arrays in the existing literatures,the optimal arrays obtained in this dissertation have lower PSLLs and wider bandwidths.