阵列天线综合之切比雪夫低副瓣阵列设计Matlab

%% --------------------------------------------------------------------------
% 切比雪夫低副瓣阵列综合
% 设计一个间距为d,单元数为N，主副瓣电平比为RdB，扫描角度为theta0的切比雪夫阵列。
% 2019.11.10 
%--------------------------------------------------------------------------
%% 初始数据赋值
clear 
clc
N = 13;                                  %单元数N（3<N<=13,N取整数）
if rem(N,2)==0                          %求和项数M(奇偶不同)
    M = N/2;
else
    M = (N-1)/2+1;
end
RdB = 26;                               % 主副瓣比(dB值)
lamuda = 10;                            % 波长
d = 0.6*lamuda;                         % 单元间距
theta0 = 80/180*pi;                     % 扫描角度，相对于阵列排布方向的夹角
A = [1,0,0,0,0,0,0,0,0,0,0,0,0,0;       % chebyshev多项式Tn(x) = cos(nu)= f(x)系数矩阵A
    0,1,0,0,0,0,0,0,0,0,0,0,0,0;        % 系数矩阵A每一行表示n，从n = 0开始
    -1,0,2,0,0,0,0,0,0,0,0,0,0,0;       % 列表示x的幂次方，从0次方开始
    0,-3,0,4,0,0,0,0,0,0,0,0,0,0;
    1,0,-8,0,8,0,0,0,0,0,0,0,0,0;
    0,5,0,-20,0,16,0,0,0,0,0,0,0,0;
    -1,0,18,0,-48,0,32,0,0,0,0,0,0,0;
    0,-7,0,56,0,-112,0,64,0,0,0,0,0,0;
    1,0,-32,0,160,0,-256,0,128,0,0,0,0,0;
    0,9,0,-120,0,432,0,-576,0,256,0,0,0,0;
    -1,0,50,0,-400,0,1120,0,-1280,0,512,0,0,0;
    0,-11,0,220,0,-1232,0,2816,0,-2816,0,1024,0,0;
    1,0,-72,0,840,0,-3584,0,6912,0,-6144,0,2048,0;
    0,13,0,-364,0,2912,0,-9984,0,16640,0,-13312,0,4096];
% 初始矩阵赋值
I = zeros(1,M);                         % 电流幅度矩阵
S = zeros(M,M);                         % 阵因子系数矩阵
S_compare = zeros(1,M);                 % 系数比对矩阵
R = 10^(RdB/20);                        % 非dB 值的主副瓣比
x0 = 1/2*( (R+sqrt(R^2-1))^(1/(N-1))+...% 变量代换值x0
            (R-sqrt(R^2-1))^(1/(N-1))  );
%% 求S、S_compare和I
% 从系数矩阵中择选出M个求和项对应的系数S(奇偶分开讨论)
for i = 1:M
    if rem(N,2)==0                      % 偶数情况
        for j = 1:M                     % 第i行表示x的i次方，
            S(i,j) = A(2*j,2*i);        % 第j列表示第j个求和项系数（未除x0)
        end
        S_compare(i) = A(N,2*i);        % 比对矩阵，即下标为N-1的chebyshev多项式的系数
    else                                % 奇数情况
        for j = 1:M                     
            S(i,j) = A(2*j-1,2*i-1);    
        end
        S_compare(i) = A(N,2*i-1);     
    end
end
% 通过S和S_compare系数比对求出电流幅度
for k = 1:M
    i = M-k+1;
    if rem(N,2)==0                      % 偶数
        I(i) = (S_compare(i)*x0^(2*i-1) -...
            I*S(i,:)‘)/S(i,i);
    else                                % 奇数
        I(i) = (S_compare(i)*x0^(2*(i-1)) -...
            I*S(i,:)‘)/S(i,i);
    end
end
I = I/max(I);                         % 对I归一化
if rem(N,2)==0
    I_final = [fliplr(I),I];          % 最终的单元排列（左右对称）
else
    I_final = [fliplr(I),I(2:end)];
end
sprintf(‘天线单元归一化电流幅度：‘)
sprintf(‘%.3f  ‘,I_final)
%% 获得最终阵列方向图S_P
theta_rad = 0:0.01:pi;
theta = theta_rad*180/pi;
u = pi*d/lamuda*( cos(theta_rad)- cos(theta0));
S_P = zeros(1,length(theta_rad));       % 最终方向图
for k = 1:M
    if rem(N,2)==0
        S_P = S_P + I(k)*cos((2*k-1)*u);% 偶数
    else
        S_P = S_P + I(k)*cos(2*(k-1)*u);% 奇数
    end
end
S_P_abs = abs(S_P);                     % 对S_P取绝对值
S_PdB = 20*log10(S_P_abs/max(S_P_abs)); % 对S_P取dB值
%% 绘图
H = -ones(1,length(S_P_abs))*26;      　% 根据预先设置的主副瓣比得到的参考曲线
% 直角坐标系
figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘S Parameter (abs)-Plot‘);
plot(theta,S_P_abs,‘b‘,‘LineWidth‘,1.5)
xlabel(‘theta(°)‘)
ylabel(‘|S| ‘)
title(‘chebyshev低副瓣阵列直角坐标图‘)
figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘S Parameter (dB)-Plot‘);
plot(theta,H,‘r--‘,‘LineWidth‘,1.5)
hold on
plot(theta,S_PdB,‘b‘,‘LineWidth‘,1.5)
xlabel(‘theta(°)‘)
ylabel(‘|S| dB‘)
title(‘chebyshev低副瓣阵列直角坐标图‘)
legend(‘预设副瓣参考曲线‘,‘方向图‘)
% 极坐标系
figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘S Parameter (dB)-Polar‘);
polarplot(theta_rad,H,‘r--‘,‘LineWidth‘,1.5)
hold on
polarplot(theta_rad,S_PdB,‘b‘,‘LineWidth‘,1.5)
thetalim([0 180]);
rmin = S_PdB(1,1);
rmax = max(S_PdB);
rlim([-50 rmax]);
title(‘chebyshev低副瓣阵列极坐标图‘)
legend(‘预设副瓣参考曲线RdB‘,‘方向图(dB)‘)