clc; clear all;
close all;

Ratio between wavelength and distance between individual elements Linear Array of N isotropic radiators

N    = 64;
alfa = -90:0.1:90;       % Zenith angle
d_l  = [0.1,0.5,1,2,5] ; % Ratio
for i = 1:5
    Ed = abs(sin(N*pi*d_l(i)*sind(alfa))./sin(pi*d_l(i)*sind(alfa)))/N;
    fig = figure(i);
    set(fig,'Position', [100, 100, 1049, 400]);
    subplot(2,2,[1 3]);
    plot(alfa,Ed);
    grid on;
    axis([-90 90 0 1]);
    xlabel('Zenith angle [deg]');
    ylabel('Normalized radiation pattern');
    title(['Ratio between distance and wavelength d/\lambda = ',num2str(d_l(i))]);

    subplot(2,2,[2 4]);
    polar(alfa*pi/180,Ed);
    hold on;
    polar((alfa+180)*pi/180,Ed);
    xlabel(['Polar plot for the radiation pattern d/\lambda = ',num2str(d_l(i))]);
    hold off;
end

Distance between individual elements

f_EISCAT =  233E6;   % Centre frequency 233 Hz
c = 3*10^8;          % Light Speed m/s
l = c/f_EISCAT;
d = [0.1,0.5,1,2,3];  % m
for i = 1:5
    % Normalizied gain
    Ed = abs(sin(N*pi*d(i)/l*sind(alfa))./sin(pi*d(i)/l*sind(alfa)))/N;
    % Ed - Array Factor, Radiation patern for isotropic radiators
    fig = figure(i+5);
    set(fig,'Position', [100, 100, 1049, 400]);
    subplot(2,2,[1 3]);
    plot(alfa,Ed);
    grid on;
    axis([-90 90 0 1]);
    xlabel('Zenith angle [deg]');
    ylabel('Normalized radiation pattern');
    title([' Distance between individual elements (space weighting) = ',...
        num2str(d (i)),' m,  F = 233Mhz']);
        subplot(2,2,[2 4]);
    polar(alfa*pi/180,Ed);
    hold on;
    polar((alfa+180)*pi/180,Ed);
    xlabel('Polar plot for the radiation pattern');
    hold off;
 end

Number of antenna elements The distance between individual elements equals to the half wavelength of the signal

d_l = 0.5;
N   = [4 16 64 100 169]; % Number of elements was varied from 4 to 256.
for i = 1:5
    Ed = abs(sin(pi*d_l*N(i)*sind(alfa))./sin(pi*d_l*sind(alfa)))/N(i);
    fig = figure(i+10);
    set(fig,'Position', [100, 100, 1049, 400]);
    subplot(2,2,[1 3]);
    plot(alfa,Ed);
    grid on;
    axis([-90 90 0 1]);
    xlabel('Zenith angle [deg]');
    ylabel('Normalized array factor,Radiation pattern');
    title(['Number of elements = ',num2str(N(i)),', d/\lambda = 0.5']);
    subplot(2,2,[2 4]);
    polar(alfa*pi/180,Ed);
    hold on;
    polar((alfa+180)*pi/180,Ed);
    xlabel('Polar plot for the radiation pattern');
    hold off;
end

Radiation pattern change when the beam is not pointed vertically

clc;clear all;
N = 8;
d_l = 0.5;
alfa0 = 30;
alfa = -180:0.1:180;       % Zenith angle
Ed = abs(sin(pi*d_l*N*(sind(alfa) - sind(alfa0) ))./...
                        sin(pi*d_l*(sind(alfa) - sind(alfa0))))/N;
Ed0 = abs(sin(pi*d_l*N*(sind(alfa)))./...
                        sin(pi*d_l*sind(alfa)))/N;
Edl = 20*log10(Ed);
Edl0= 20*log10(Ed0);
    fig = figure(16);
    set(fig,'Position', [100, 100, 1049, 400]);
    subplot(2,2,[1 3]);
    plot(alfa,Ed);
    hold on;
    plot(alfa,Ed0,'r');
    grid on;
    axis([-90 90 0 1]);
    xlabel('Zenith angle [deg]');
    ylabel('Normalized array factor,Radiation pattern');
    title(['Number of elements = ',num2str(N),', d/\lambda = 0.5']);
    legend('\beta = 30 deg','\beta = 0 deg','Location','NorthWest')
    subplot(2,2,[2 4]);
    polar(alfa*pi/180,Ed);
    hold on;
    polar(alfa*pi/180,Ed0,'r');
    hold on;
    xlabel('Polar plot for the radiation pattern');
    hold off;
    figure(17);
    plot(alfa,Edl);
    hold on;
    plot(alfa,Edl0,'r');
    grid on;
    legend('\beta = 30 deg','\beta = 0 deg','Location','NorthWest')
    axis([-90 90 -100 0]);
    xlabel('Zenith angle [deg]');
    ylabel('Radiation pattern dB');
    title(['Number of elements = ',num2str(N),', d/\lambda = 0.5']);

Electrical weighting techniques

N     = 64;
d_l   = 0.1;
Ed = abs(sin(pi*d_l*N*(sind(alfa) ))./...
                        sin(pi*d_l*sind(alfa)))/N;
Edl = 20*log10(Ed);
% Try to lower the first side lobe relative to main lobe
% To be able to reduce the side lobe levels, we design the array so its radiate
% more power towards the center, and less at the edges.
w  = zeros(1,N);
ws = zeros(1,N);
n = 1:N;
E = 0;Es = 0;
for n = 1:N;
    if n <= N/2
        w(n) = (n-1)/30.5;
    else
        w(n) = w(65 - n);
    end
    ws(n) = sin((n-1)*pi/(N-1));
    E  = E + (w(n)*exp(complex(0,((2*pi*(n-1)*d_l)*sind(alfa)))));
    Es  = Es + (ws(n)*exp(complex(0,((2*pi*(n-1)*d_l)*sind(alfa)))));
end
figure(19);
hold on; grid on;
plot(w,'g');
plot(ws,'r');
axis([1 64 0 1]);
ylabel('Normalized tapering weight');
xlabel('Array elements index');
legend('polynomial','sin');
hold off;
E = abs(E);
E = 20*log10(E/max(E));
Es = abs(Es);
Es = 20*log10(Es/max(Es));
    fig = figure(18);
    set(fig,'Position', [100, 100, 600, 700]);
    hold on;
    subplot(3,1,1);
    plot(alfa,Edl);
    grid on;
    axis([-90 90 -100 0]);
    legend('Isotropic');
    ylabel('Radiation pattern dB');
    title(['Number of elements = ',num2str(N),', d/\lambda = ',num2str(d_l)]);
    subplot(3,1,2);
    plot(alfa,Es,'r');
    axis([-90 90 -100 0]);
    ylabel('Radiation pattern dB');
    grid on;
    legend('Weighted Sin');
    subplot(3,1,3);
    plot(alfa,E,'g');
    axis([-90 90 -100 0]);
    grid on;
    xlabel('Zenith angle [deg]');
    ylabel('Radiation pattern dB');
    legend('Weighted Poly');
    hold off;