Analytical Method Of Array Transmitting Beampattern Synthesis And Its Applications

In recent decades,array transmitting beampattern synthesis has attracted widespread attention since it was an important research topic in the field of modern Radar and communication.The conventional ‘Phased-only' array beampattern synthesis represented by the Phased Array only considers the phase of the transmitting signal as a designed DoF(Degree of Freedom).In order to adapt the increasingly complex electromagnetic environment,it is necessary to adopt more designable variables for array beampattern synthesis problem to obtain additional Do F gain.Although much progress toward the multivariable array beampattern synthesis and its applications has been made recently,most of them are based on numerical methods and optimization algorithms.The computation complexity of these methods are relatively high,limiting their application in the scenarios such as large-scale array that requires beampattern agility.By establishing a closed-form mathematical relationship between the designed variables and the synthetical beampattern,the analytical method can directly design the parameters of array to meet the desired beampattern.However,the synthetical beampattern is usually a complex mathematical expreesion and the variables to be designed are usually implicit.Therefore,by introducing a series of approximations,this thesis extracts the designable variables from the beampattern expression and then establishs a closed-form mathematical relationship between the designed variables and the synthetical beampattern.Subsequtly,based on these analytic beampattern expressions,this thesis mainly studies the transmitting beampattern synthesis of the array with multiple designable variables and its specific applications in engineering.Then some corresponding analytical methods are proposed.These analytical methods not only cost small computational burden,but theoretical analysis and simulation experiments prove that they achieve better performance than the existing optimizing methods in the aspects of array energy delivery accuracy and beampattern matching flexibility.The specific content and innovations of this thesis are summarized as follows:1.The analytical method for FDA(Frequency Diverse Array)transmiiting beampattern synthesisWhen the carrier frequency of each array element is regarded as the designable variable of beampattern synthesis,the problem becomes FDA beampattern synthesis problem.However,the FDA beampattern is angle-range coupled.By deducing the closedform expression of FDA transmitting beampattern,this thesis directly illustrates the mechanism of how the FDA frequency increment influences its beampattern in mathematics.As a result,this thesis decouples the FDA beampattern and provides mathematical tool for the subsequent applications of FDA.In addition,based on the closed-form model of FDA beampattern and inspired by the Rayleigh-Ritz theorem,this thesis proposes a general focusing beamformer that can generate minimized-area beampattern.This beamformer can focus the transmitting energy of FDA on the desired area in the angle-range plane.Because it is an analytical method,the computational complexity is very small.2.The analytical method for MIMO(Multiple-Input Multiple-Output)array beampattern synthesisWhen the transmitting waveform of each array element is regarded as the designable variable of beampattern synthesis,the array becomes MIMO array or directional modulation array.Due to the gain of waveform diversity,MIMO array can design its transmitting beampattern more flexibly.Therefore,by designing the transmitting waveform of MIMO array,the synthesized beampattern can match the preset desired beampattern shape.That is the problem of transmit beampattern matching design for MIMO radar.Aiming at this problem,based on integral superposition,this thesis proposes a transmitting waveform design method.By analyzing the physical meaning of MIMO beampattern from scratch,we find that the MIMO transmitting beampattern can be seen as the superposition of the integral of multiple instantaneous beampatterns.Designing each instantaneous waveform is to design the integral of their corresponding instantaneous transmit beampattern.Therefore,by deducing the closed-form expression of this instantaneous integral,this thesis mathematically illustrates how the waveform influences the MIMO beampattern.Subsequently,the closed-form integral is used as a superposition module to superimpose the desired beamppatern shape.Compared with the existing waveform design method,this analytical method not only can match the flat-top shape beampattern,but also can match the arbitrary shape beampattern.It indicates the flexible beampattern matching capability of the proposed waveform design method.In addition,the computational complexity of the proposed method is very small.3.The analytical method for DM(Directional Modulation)array beampattern synthesisWhen the transmitting waveform of each array element is regarded as the designable variable of beampattern synthesis,another application scenario is the DM array.The difference between the DM and the MIMO array is that the desired beamppattern of DM problem is a modulation constellation point in spatial domain,i.e.,a complex number.This also means that the array beampattern synthesis with multiple variables not only can be used in Radar system,but also applicable for communication system.The DM technique can be used for physical layer secure commination.By designing the transmitting waveform of array,the beampattern of DM array in desired direction is expected to be the correct modulation constellation,while the beampattern in other direction is distorted.This thesis proposes an analytical waveform design method for DM.It can quickly calculate the transmit waveform that can form the correct modulation constellation point in the desired direction with small computational cost.