Research On Optimization Algorithms For Non-uniform Antenna Array Pattern Synthesis

In practical engineering applications,non-uniform array pattern synthesis plays an important role for reducing the number of antenna elements,simplifying the feed network,and efficiently suppressing grating lobes,etc.In recent decades,many methods mainly including numerical analysis method,stochastic optimization algorithms,and convex optimization have been developed to address the non-uniform array pattern synthesis.However,for some specific cases,such as calculating array pattern including coupling effects,optimizing elements' positions with minimum element spacing control,arranging the array on an arbitrarily curved surface,etc.,current synthesis methods still show drawbacks and face challenges.In this paper,firstly,the stochastic optimization algorithms widely used for synthesizing the non-uniform array pattern are introduced.Then,a fast calculation method for equally spaced and unequally spaced array patterns considering the mutual coupling is proposed.By integrating the calculation method into stochastic optimization algorithms,improved particle swarm optimization(PSO)and improved genetic algorithm(GA)have been achieved,which can effectively increase the calculation efficiency for the non-uniform array pattern synthesis.Secondly,convex optimization method employed for simultaneously optimizing positions and excitations of non-uniform array pattern synthesis is considered.In terms of an issue that minimum element spacing cannot be controlled using convex optimization in the non-uniform array pattern synthesis,an alternating convex optimization is proposed.In the proposed alternating convex optimization,exciting vector and weighting vector are alternately used as the optimization variables.Minimum spacing constraints for linear arrays and planar arrays are analyzed and are interpreted as convex constraints in the alternating convex optimization,thus controlling the minimum element spacing in the non-uniform array pattern synthesis can be realized.Finally,non-uniform array pattern synthesis using the iterated perturbation method is introduced,and various strategies have been proposed to advance the iterated perturbation based convex optimization method.(1)One method called escape strategy can avoid an issue of easily getting stuck in local extremum values in the perturbation method,enhance local search ability of iterated perturbation method,and achieve better performance when applied to wideband array or scanning array.(2)Iterated normalizing beam pointing electrical field at beam point and compensating beam offset strategies can make the iterated perturbation method well suitable for phase-only synthesis with a focused beam.(3)Reference pattern perturbation method can arbitrarily set the initial reference pattern and almost achieve the same performance,thus reducing the dependence of beamforming pattern on the reference pattern.(4)Continuous tangential plane perturbation method can make the optimized element positions confined on an arbitrary curved line or surface.With regards to sparse array pattern synthesis,we propose an iterated perturbation based convex optimization sparse array synthesis method.Good results have been achieved,and computational efficiency is highly improved.Meanwhile,pre-setting number and positions of array elements in our proposed sparse array synthesis method are also explored,and a strategy that can maximize the number of array elements under the constraint of minimum element spacing in a prescribed array margin(full array arrangement strategy)is presented.Moreover,by combining the above research on the minimum element spacing,the full array arrangement strategy with 0-1 programming is realized.The common sterelithography file in the 3D model is employed to describe an arbitrary curved surface,and sparse array synthesis method applied in an arbitrary curved surface is put forward by integrating the continuous tangential plane perturbation method.