基本问题

如何通过不同的表达式得到均匀面阵的方向图

源代码

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   均匀面阵方向图的三种不同的表达式%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%clc; close all;clear all;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%             参数设置%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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)=（45,180）theta0=45;fine0=180;theta=1:1:90;   % 俯仰角取值范围fine=1:1:360;   % 方位角取值范围x=d*(0:M-1);y=d*(0:N-1);z=0; % 阵元位置（x，y,z）r=0;f1=[];f2=[];f3=[];%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%           第一种表达式%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%for i=1:length(theta)      % 俯仰角取值范围    for j=1:length(fine)   % 方位角取值范围        % 64个阵元功率叠加        for p=1:M  % x            for q=1:N  % y                position=[x(p) y(q) 0]; %阵元的位置坐标                direction_vector0=[sind(theta0)*cosd(fine0) sind(theta0)*sind(fine0) cosd(theta0)];                direction_vector=[sind(i) * cosd(j)  sind(i) * sind(j) cosd(i)]; % 单位方向矢量                 w=exp(1i*position*direction_vector0.'/c*2*pi*f); % 权值                 v=exp(1i*position*direction_vector.'/c*2*pi*f);  % 相对于原点接收到的归一化的信号                 r=r+w'*v;  % 64个阵元功率叠加    '表示共轭转置   .'表示转置%                  r=r+exp(1i*2*pi/lamda*(x(p)*(sind(i) * cosd(j)-sind(theta0)*cosd(fine0))  + y(q)* (sind(i) * sind(j)-sind(theta0)*sind(fine0)) )  );            end        end        f1(i,j)=r; % 将64个阵元的合成场强放到对应的扫描角度上        r=0;      % 每扫描一个角度时，将上一个角度的64个阵元功率清0    endendF1=abs(f1);      % 取实部figure(1)mesh(fine,theta,F1);xlabel('方位角');ylabel('俯仰角');zlabel('方向图');%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%           第二种表达式%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%for i=1:length(theta)      % 俯仰角取值范围    for j=1:length(fine)   % 方位角取值范围        % 64个阵元功率叠加        for p=1:M  % x            for q=1:N  % y                 r=r+exp(1i*2*pi/lamda*(x(p)*(sind(i) * cosd(j)-sind(theta0)*cosd(fine0))  + y(q)* (sind(i) * sind(j)-sind(theta0)*sind(fine0)) )  );            end        end        f2(i,j)=r; % 将64个阵元的合成场强放到对应的扫描角度上        r=0;      % 每扫描一个角度时，将上一个角度的64个阵元功率清0    endendF2=abs(f2);      % 取实部figure(2)mesh(fine,theta,F2); hold on;xlabel('方位角');ylabel('俯仰角');zlabel('方向图'); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%           第三种表达式%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%for i=1:length(theta)      % 俯仰角取值范围    for j=1:length(fine)   % 方位角取值范围        t1(i,j)=2*pi/lamda*d*( sind(i) * cosd(j) - sind(theta0)*cosd(fine0) );        F1(i,j)=sin(M/2*t1(i,j))/sin(1/2*t1(i,j));        t2(i,j)=2*pi/lamda*d*( sind(i) * sind(j) - sind(theta0)*sind(fine0) );        F2(i,j)=sin(N/2*t2(i,j))/sin(1/2*t2(i,j));        f3(i,j)= F1(i,j)*F2(i,j);    endendF3=abs(f3);% 取实部figure(3)mesh(fine,theta,F3);xlabel('方位角');ylabel('俯仰角');zlabel('方向图');%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%           第4种表达式%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%                 权值%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%W =[];for m=1:M    for n=1:N        x = (m-1)*sind(theta0)*cosd(fine0)+(n-1)*sind(theta0)*sind(fine0)+0;% 波程差        W(m,n) = exp(1j*2*pi*f*d*x/c);        endendW1=reshape(W,[],1); % 将8*8的矩阵变成64*1的向量%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%            开始目标搜索过程%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%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)*sind(theta(p))*cosd(fine(q))+(n-1)*sind(theta(p))*sind(fine(q));                 V(m,n) = exp(1j*2*pi*f*d*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                E(p,q)=W1'*V1;% 相控阵天线的方向图        E(p,q)=abs(E(p,q));    endendfigure(4)mesh(fine,theta,E);xlabel('方位角');ylabel('俯仰角');zlabel('方向图');