相控阵天线面阵方向图（三种表示方法）

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   均匀面阵方向图的三种不同的表达式
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clc; 
close all;
clear all;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%             参数设置
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% theta是俯仰角 fine是方位角
c=3e8;       % 光速
f=3e10;     % 载波频率
lamda=c/f;  % 波长
d=lamda/2;   % 阵元间距
M=8;
N=8;     % 8*8的矩阵
% 波束指向角度(theta0,fine0)
theta0=30;
fine0=200;
bujing=0.5;
theta=0:bujing:90;   % 俯仰角取值范围
fine=0:bujing:360;   % 方位角取值范围




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%           第1种表达式
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%-----------权值
W =[];
for m=1:M
    for n=1:N
        x = (m-1)*sind(theta0)*cosd(fine0)+(n-1)*sind(theta0)*sind(fine0);% 波程差
        W(m,n) = exp(1j*2*pi*f*d*x/c);    
    end
end
W1=reshape(W,[],1); % 将8*8的矩阵变成64*1的向量


%---------方向矢量计算
E=[];
for p = 1:length(theta)
    for q = 1:length(fine)     
        for m=1:M
             for n=1:N
                 %-------权值扫描
                 x = (m-1)*d*sind(theta(p))*cosd(fine(q))+(n-1)*d*sind(theta(p))*sind(fine(q));
                 V(m,n) = exp(1j*2*pi*f*x/c); %  方向矢量的求解
             end
        end
        V1=reshape(V,[],1); % 将8*8的矩阵变成64*1的向量
        
        E1(p,q)=W1'*V1;% 相控阵天线的方向图
        Beam_F1(p,q)=abs(E1(p,q));

    end
end
figure(4)
mesh(fine,theta,Beam_F1);
xlabel('方位角');ylabel('俯仰角');zlabel('方向图');



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%           第二种表达式
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for p=1:length(theta)      % 俯仰角取值范围
    for q=1:length(fine)   % 方位角取值范围
        % 64个阵元功率叠加
        for m=1:M  
            for n=1:N  
                 r(m,n)=exp(1i*2*pi/lamda*( (m-1)*d*(sind(theta(p))*cosd(fine(q))-sind(theta0)*cosd(fine0))...
                                           +(n-1)*d*(sind(theta(p))*sind(fine(q))-sind(theta0)*sind(fine0)) )  );
            end
        end
        E(p,q)=sum(sum(r)); % 将64个阵元的合成场强放到对应的扫描角度上
    end
end
Beam_F2=abs(E);      % 取实部
figure(2)
mesh(fine,theta,Beam_F2); hold on;
xlabel('方位角');ylabel('俯仰角');zlabel('方向图'); 



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%           第三种表达式
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for p=1:length(theta)      % 俯仰角取值范围
    for n=1:length(fine)   % 方位角取值范围
        t1=2*pi/lamda*d*( sind(theta(p)) * cosd(fine(n)) - sind(theta0)*cosd(fine0) );
        beam1(p,n)=sin(M/2*t1)/sin(1/2*t1);
        t2=2*pi/lamda*d*( sind(theta(p)) * sind(fine(n)) - sind(theta0)*sind(fine0) );
        beam2(p,n)=sin(N/2*t2)/sin(1/2*t2);
        f3(p,n)= beam1(p,n)*beam2(p,n);
    end
end
Beam_F3=abs(f3);% 取实部
figure(3)
mesh(fine,theta,Beam_F3);
xlabel('方位角');ylabel('俯仰角');zlabel('方向图');





max(max(Beam_F1-Beam_F2))
max(max(Beam_F1-Beam_F3))
max(max(Beam_F2-Beam_F3))