Research On Pattern Synthesis Algorithms Of Nonuniform Antenna Arrays

The proliferation of wireless services drives the innovation of antenna array(array for short)technology and promotes the birth and development of many new array design schemes,among which the nonuniform array is one of the representatives.Compared with the traditional uniform array,the nonuniform array can usually achieve some similar performance indexes by fewer elements.This feature is conducive to reducing the construction cost,simplifying the feed network,reducing the weight,improving the heat dissipation performance,decreasing the failure rate,and upgrading the real-time performance of the array system.In addition,compared with uniform arrays,nonuniform arrays have greater design freedom,which makes them easier to satisfy certain specific performance indexes.The distances between adjacent elements of traditional ultrawideband,wide-angle scanning arrays may be relatively large,which makes them prone to grating lobes when scanning in high-frequency bands.Nonuniform arrays can break the periodicity of phase center position distribution of array elements,therefore,they can easily avoid the occurrence of grating lobes.In addition to suppressing grating lobes,the greater design freedom of nonuniform arrays also makes them possible to have higher directivity,lower sidelobe level,and more accurate main beam shape.However,the greater design freedom also means that the synthesis of nonuniform arrays is generally more difficult than that of uniform arrays,which limits the wide use of nonuniform arrays to a certain extent.To expand the application range of them,many excellent algorithms,such as the matrix pencil method(MPM),convex optimization method,genetic algorithm,and multi-task Bayesian compressive sensing(MT-BCS),have been developed to synthesize nonuniform arrays.However,most of the existing algorithms are only suitable for synthesizing single-pattern,single-frequency,and smallscale nonuniform arrays,which is no longer in line with the general trend that the array is gradually developing towards multiple-pattern,broadband,and large-scale.In addition,many existing algorithms assume that the array elements are isotropic ideal point sources in the synthesis process,which may make the actual pattern greatly different from the expected pattern when the synthesis results obtained by them are applied to the actual array.Facing the above problems in existing nonuniform array synthesis algorithms,this dissertation has done the following five parts of work:(1)Broadening the application range of MPM so that it can be used to synthesize multiple-pattern nonuniform planar arrays.In the process of expansion,firstly,a composite block Hankel enhanced matrix is constructed according to data samples of target patterns;secondly,MPM is used to process the constructed matrix to obtain two sets of position coordinates and the randomized singular value decomposition method,as well as block solution method of singular value decomposition,are used to speed up the process;then,the improved matching algorithm is used to pair the two sets of coordinates to obtain the position distribution of array elements;finally,the least-square method is used to obtain the excitations of array elements.Many numerical examples are given to show that the proposed algorithm can effectively reduce the number of array elements while guaranteeing the accuracy of all reconstructed patterns.(2)Broadening the application range of MT-BCS so that it can be used to synthesize multiple-pattern nonuniform planar arrays.In the process of expansion,firstly,the multiple-pattern nonuniform planar array synthesis problem is rewritten into a form that can be solved by MT-BCS,and the transformed problem is solved by MT-BCS;then,the array element merging method is used to adjust the array element position distribution obtained by MT-BCS to ensure that the minimum element spacing of the obtained array is greater than a preset value;finally,the convex optimization method is used to calculate the excitations of merging array elements.The numerical examples given in this dissertation show that the proposed algorithm can efficiently solve multiple-pattern largescale nonuniform planar array synthesis problems.(3)Broadening the application range of sequential convex optimization method so that it can be used to solve frequency-invariant shaped-beam pattern(SBP)nonuniform array synthesis problems.In the process of expansion,firstly,the sequential convex optimization method is used to obtain the array element excitations at sampling frequency points in the working band,and in the process of solving,the proposed algorithm assumes that the position distribution of elements is symmetrical about the origin and the excitations of symmetric elements are mutually conjugate complex numbers so that the nonconvex lower bound constraints on the SBP are transformed into convex constraints;then,the relationship between the coefficients of the finite impulse response filter required to realize the frequency-invariant SBP in time domain and element excitations is deduced;finally,the filter coefficients are solved by the derived relationship.Several numerical examples are given to illustrate the effectiveness of the proposed algorithm.(4)Proposing a nonuniform planar array synthesis algorithm that is based on the fast iterative shrinkage-thresholding algorithm(FISTA)and can strictly consider mutual coupling effects in the synthesis process.The algorithm has low computational complexity,fast convergence speed,and few preset control parameters,therefore,it is very suitable for solving large-scale nonuniform planar array synthesis problems.In the proposed method,firstly,the nonuniform planar array synthesis problem is expressed as an iterative weighted least absolute shrinkage and selection operator(LASSO)problem;then,the problem is solved by FISTA to acquire the position distribution of the array elements;finally,the least-square method or convex optimization method is used to calculate the excitations of array elements.Several numerical examples are given to illustrate the efficiency of the proposed algorithm.(5)Proposing a nonuniform array synthesis algorithm based on the artificial neural network(ANN)and differential evolution algorithm(DEA).The algorithm can simultaneously optimize the position distribution and excitations of array elements in the continuous domain while considering the mutual coupling effects so that the pattern and active S parameters of the synthesized array meet the preset requirements.The algorithm has two steps: firstly,ANN is used to construct the mapping relationship between the active element patterns,passive S parameters,and the position distribution of elements,respectively,and in this process,the subarray modeling method is introduced to relieve the curse of dimensionality when modeling large-scale arrays;secondly,based on the ANN model established in the first step,the DEA is used to optimize the position distribution and excitations of elements simultaneously to meet relevant requirements of the array on the pattern and active S parameters.Several numerical examples are given to assess the effectiveness of the proposed algorithm.