Beam-forming Synthesis Technique For Array Antennas

The shaped-beam pattern synthesis technology that forms a specific shaped-beam in a specific airspace has a wide range of applications in the field of satellite communications and radar detection.In different shaped-beam pattern synthesis applications,apart from the demands for the shape of the main lobe be arbitrary complex,it requires that the side lobe levels should be as low as possible as well.In addition to the single beam synthesis,sometimes the shaping of multiple beams is also necessary.In order to meet the requirements for the shaped-beam pattern synthesis applied in real environment,many practical factors need to be considered during the process of the array antenna pattern synthesis,such as the differences between the array element pattern and the embedded array element pattern,the array element excitation amplitude quantization restrictions,the occurrence of the array elements excitations errors and so on.This paper focuses on the beamshaping requirements in satellite communications and radar detection,and conducts researches on the application of arbitrary shaped-beam pattern synthesis,with arbitrary shaped footprint and array.The main works of this paper are listed as follows:1.In view of the situation that all the embedded array elements patterns are different,a shaped-beam pattern synthesis algorithm using joint optimization of element excitations amplitudes and phases is proposed.The algorithm is based on Weighted Generalized Rayleigh Quotient Approximation(WGRQA)framework.By using the principle of pattern multiplication and the embedded array element patterns,a new pattern synthesis model is presented.Through this model,a new cost function composed of side lobe levels,main lobe ripples and main lobe gains is constructed.The generalized Rayleigh quotient approximation method is then used to get the final array excitation,thus achieving the goal of generating the pattern with arbitrary footprint using arbitrary shaped arrays involved with the embedded array elements patterns.In addition,since the accuracy of the synthesized pattern in every space point can't be precisely controlled during the synthesis process,a set of weight matrix is designed in order to improve the performance of the synthesized pattern.The effect of the proposed method is also illustrated by the simulations.2.In view of the array elements excitations amplitudes quantization restrictions,a new array element excitations amplitudes quantization algorithm is proposed.The algorithm is divided into three steps.Firstly the WGRQA method is used to acquire the joint optimization array element excitations,then the elements excitations amplitudes are quantized using probability density theory.Finally,a set of new elements excitations phases according to the quantized elements amplitudes is obtained..The simulation results illustrate that the proposed method is very fast,while the performance is not that much different from the pattern synthsized using both the element excitations ampltudes and phases,hence it can meet the practical engineer needs in most cases.3.In view of the array elements excitations amplitudes restrictions during multi-beam pattern synthesis,a novel multi-beam pattern synthesis algorithm based on kernel principal component analysis and semi-definite relaxation method is proposed.The algorithm is divided into three steps.Firstly,each beam is synthesized using WGRQA algorithm,and all the elements excitations amplitudes are formed into an element excitations amplitudes matrix(EEAM).Second,the kernel principal component analysis(KPCA)is used to acquire a group of common element excitation amplitudes(CEEA).Finally,the semi-definite relaxation(SDR)method is employed to obtain the element excitation phase of each beam.The use of KPCA can reserve the valid information of all the elements excitations with amplitude phase joint-optimization.Besides,KPCA is a quasi-analytical process,hence the overall algorithm is speeded up.Compared to the iterative multi-beam pattern synthesis algorithm,nearly half of the synthesis time is reduced.Seeing from the simulation results,the proposed method can betterly satisfy multi-beam pattern synthesis requirements.4.In view of the occurrence of the array elements excitations errors during the synthesis process,the interval analysis method is used to analyze the tolerance of the shaped beam pattern synthesis.Considering the elements excitations amplitudes errors,the interval model of the synthesized power pattern with the embedded element pattern is deduced,and the performance of three tolerance parameters which are maximum sidelobe levels errors,maximum mainlobe ripples errors and maximum mainlobe gains errors are also given,so as to estimate the performance of the synthesized pattern with the existence of the elements excitations amplitudes errors,and provide a theoretical standard for the shaped-beam pattern synthesis.In the simulation part,the upper and lower boundaries of the synthesized patterns and three tolerance parameters are given,and the influence of array and error parameters on the synthesized patterns are also analyzed.