1 The basic principle

2 Source code

%%          The functionality ： Low sidelobe weighting 
clc; 
clear all;
close all;


%%               Parameter setting 
c=3e8;                  %  The speed of light 
f=22e9;                 %  signal frequency 
lamda=c/f;              %  wavelength 
d=lamda/2;              %  Element spacing 
N=12;                   %  The number of elements 
theta0=20;              %  Beam pointing angle 
bujing=1e-3;
theta=-90:bujing:90;    %  Scanning angle value range 
n = [0:1:N-1]';         %  Column vector 

RdB = 30;               %  Main and side valve ratio (dB value )

%%    Weight calculation 
tao=n*d*sind(theta0)/c;  %  Time delay 
W = exp(1j*2*pi*f*tao);  %  The weight obtained from the basic theory of phased array antenna 


%%  Calculation of array element amplitude excitation （chebyshev weighting ）
[I_final] = I_func(N,RdB);
W_low=W.*I_final;


%%   Beamforming 
 for p=1:length(theta)          %  Scanning angle value range     
     V = exp(1j*2*pi*f*n*d*sin(theta(p)*pi/180)/c); %  Direction vector 
     B(p) =abs(W'*V); %  Phased array antenna weighting  ' Represents conjugate transpose    .' Means transpose  
     B_low(p) =abs(W_low'*V);   % chebyshev weighting 
 end
Beam_F=20*log10(B/max(B));              %  normalization 
Beam_F_low=20*log10(B_low/max(B_low));  %  normalization 


%%  mapping 
figure(1)
plot(theta,Beam_F,'b','LineWidth',1.5);grid on;
xlabel(' angle / degree ');ylabel(' Range /dB');
axis([-90 90 -50 0]);
title(' Phased array antenna pattern ');

figure(2)
H = -ones(1,length(Beam_F))*RdB;    %  The reference curve obtained according to the preset main and side lobe ratio 
plot(theta,H,'r--','LineWidth',1.5);hold on;
plot(theta,Beam_F_low,'b','LineWidth',1.5);grid on;
axis([-90 90 -50 0]);
xlabel('theta(°)');ylabel(' Range /dB');
title('chebyshev Rectangular coordinate diagram of low sidelobe array ');
legend(' Preset sidelobe reference curve ',' Directions ');

function [I_final] = I_func(N,RdB)

if rem(N,2)==0  %  Sum items M( Parity is different )
    M = N/2;
else
    M = (N-1)/2+1;
end

%  Initial matrix assignment 
I = zeros(1,M);         %  Current amplitude matrix 
S = zeros(M,M);         %  Matrix factor coefficient matrix 
S_compare = zeros(1,M); %  Coefficient comparison matrix 
R = 10^(RdB/20);        %  Not dB  Value of the main and side lobe ratio 
x0 = 1/2*( (R+sqrt(R^2-1))^(1/(N-1))+(R-sqrt(R^2-1))^(1/(N-1)) );%  Variable substitution value x0


A = [1,0,0,0,0,0,0,0,0,0,0,0,0,0; % chebyshev polynomial Tn(x) = cos(nu)= f(x) coefficient matrix A
0,1,0,0,0,0,0,0,0,0,0,0,0,0;      %  coefficient matrix A Each line represents n, from n = 0 Start 
-1,0,2,0,0,0,0,0,0,0,0,0,0,0;     %  Column means x Power square , from 0 The power starts 
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];


%%  seek S、S_compare and I

%  Select... From the coefficient matrix M The coefficient corresponding to a summation term S( Parity is discussed separately )
for i = 1:M
    if rem(N,2)==0 %  Even numbers 
        for j = 1:M %  The first i Row representation x Of i Power ,
            S(i,j) = A(2*j,2*i); %  The first j List No j A summation coefficient ( Not removed x0)
        end
        S_compare(i) = A(N,2*i); %  Comparison matrix , That is, the subscript is N-1 Of chebyshev The coefficients of polynomials 
    else %  Odd numbers 
        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

%  adopt S and S_compare Calculate the current amplitude by coefficient comparison 
for k = 1:M
    i = M-k+1;
    if rem(N,2)==0 %  even numbers 
        I(i) = (S_compare(i)*x0^(2*i-1) -I*S(i,:)')/S(i,i);
    else %  Odd number 
        I(i) = (S_compare(i)*x0^(2*(i-1)) -I*S(i,:)')/S(i,i);
    end
end
I = I/max(I); %  Yes I normalization 


if rem(N,2)==0
    I_final = [fliplr(I),I]; %  The final unit arrangement ( Right and left symmetry )
else
    I_final = [fliplr(I),I(2:end)];
end
I_final=(I_final).';
sprintf(' Normalized current amplitude of antenna unit ：');
sprintf('%.3f ',I_final);


end