Study On Fast Algorithm Of Pattern And Grating Lobe Suppression For Large Non-uniform Phased Array Antennas

The large non-uniform phased array antenna uses the variability of its element position to form different spatial phases in the specified radiation direction,and then realizes the low grating lobe characteristics of far-field pattern based on the principle of inverse phase cancellation.It has very important applications in military,astronomical exploration,long-distance communication and other fields.Unlike the phase-only synthesis method,the non-uniform array layout has almost no effect on the main lobe gain without considering the coupling factors,while the phase synthesis method needs to sacrifice a certain main lobe gain in order to effectively reduce the grating lobe level(GLL).Compared with the amplitude-only synthesis method,the non-uniform array can realize full-power feeding of all elements.Howeer,the amplitude-only synthesis method has to feed different amplitudes of excitation to different elements according to the results of the synthesis,which results in a fact that the radiation capacity of most elements is not fully utilized.Non-uniform arrays can still achieve low grating lobe characteristics of pattern under full-fed conditions,so they have great potential for applications.However,when the size of array antenna is large enough,it is difficult to study non-uniform array directly based on full-wave method.The clustering optimization algorithms commonly used in small or medium-sized arrays may not work properly because of the large size of array.Therefore,this paper mainly studies the fast calculation method of far-field pattern and pattern lobe suppression for large-scale non-uniform phased array.The aim is to establish a feasible method of grating lobe suppression(GLS)for phased array with the characteristics of "non-uniformity" and "large-scale",which can not only calculate the far-field pattern quickly,but also have the ability to deal with large-scale variables effectively.Firstly,Taguchi optimization algorithm is further studied in this thesis.Taguchi algorithm is an optimization algorithm with strong global searching ability,which is different from some clustering algorithms whose results depend heavily on the selection of initial population.Based on the study of the conventional Taguchi algorithm,the interpolation fitting of the average signal-to-noise ratio(SNR)factors of each variable is proposed,and then the possible optimal solution in each iteration step is predicted according to the fitting results.The optimal solution was determined by comparing the experimental results of the predicted solution with that of the screening solution obtained by steps of conventional Taguchi algorithm.Several test functions are applied to verify the optimization efficiency of Taguchi algorithm based on fitting prediction method.The results show that the convergence effect of this proposed method is better than that of conventional Taguchi algorithm.In addition,the improved Taguchi algorithm is applied to two linear array pattern synthesis with target direction null and flat main beam respectively.The comparison of the final results further proved the effectiveness of using the fittingprediction method to improve the convergence rate of conventional Taguchi optimization algorithm.By making full use of the constructional characteristics of orthogonal matrices,Taguchi algorithm can implement as uniform a seeking-optimal operation as possible in the whole solution space.In theory,Taguchi algorithm can be used in the global optimization of large-scale arrays,but the disadvantages are that largescale orthogonal matrices need to be constructed,and the number of experiments will be greatly increased.Therefore,for the GLS of large non-uniform phased arrays,it is still necessary to solve the chanllege of how to realize fast calculation of their far-field patterns.A fast method for calculating the far-field pattern of large non-uniform arrays is studied in the third part.Considering that it is impossible to directly use the Fast Fourier Transform(FFT)algorithm to deal with large non-uniform phased arrays in the calculation of their far-field patterns,a convolutional non-uniform Fast Fourier Transform(Nu FFT)algorithm is employed.The convolutional Nu FFT algorithm makes full use of the Fourier transform relationship between the data of the spatial domain and the angular spectrum domain.The problem of superposition of nonuniform array pattern is turned into dealing with a simple convolution problem in spatial domain by using the Richter transform relation.Accordingly,a division operation is adopted in angular spectrum domain to eliminate the effect caused by the convolution in spatial domain,then the fast calculation of far-field pattern of large-scale non-uniform phased array is realized.Referring to the electric field results of common superposition method,the calculation accuracy and efficiency of the two methods are compared and verified.The far-field patterns of three nonuniform arrays,like non-uniform array based on rectangular grid,large-scale annular grid array and multi-layer nested large-scale array,can be quickly calculated by using Nu FFT.As a supplement,the active subarray pattern method is used to consider the coupling factors of a class of arrays with specific layout.Then,an optimization algorithm of GLS based on gradient-Sigmoid function is proposed,which is suitable for large non-uniform phased array antennas and can avoid the problem that Taguchi algorithm needs too many experiments.On the basis of calculating the position gradient of far-field pattern,the proposed gradientSigmoid algorithm establishes the relationship between the position of each element and the far-field pattern.After employing the Sigmoid function,an adjustment scheme based on dynamic amplitude coefficient of Sigmoid function is proposed to optimize the convergence process in a GLS problem.In this way,the gradient-Sigmoid function-based GLS algorithm can not only keep fast convergence in the early stage of optimization,but also obtain relatively better convergence results in the end of optimization.The effectiveness of gradientSigmoid algorithm for GLS is verified by three optimization examples of 16×16small-scale non-uniform subarray,100×100 large-scale non-uniform array and100×100 non-uniform nested array.Finally,the gradient-Sigmoid algorithm is applied to the layout design of nonuniform wide-angle scanning array.As well known,wide-angle scanning array elements generally have wide beam characteristics.Therefore,the artificial dielectric layer with high refractive index is realized which is consisted of doublelayer small rectangular patch and a medium layer.The half-power beam width of the element antenna is successfully broadened,and its the potential in the applications of wide-angle scanning array is improved.In another aspect,a 16×16non-uniform array with low garting lobe and wide scanning angle is optimized by using the gradient-Sigmoid algorithm.After the simulation by using full-wave method,the results show that the array can achieve a wide beam scanning of about60 degrees on the xoz plane with the highest grating lobe(side lobe)level down below-20 d B.On the yoz plane,it achieves a scanning angle of about 50 degrees.This result also proves that the gradient-Sigmoid algorithm can be successfully applied to the layout optimization of wide-angle scanning array.