Antenna Array: Array factor-Scan Conditions, unable to see any grating lobes

I am performing array multiplication of two arrays of different spacing respectively. I am unable to see any grating lobes in the multiplied array factor. Also, unable to understand if the plot(psi, 20log10(abs(AF))) is right or wrong. how do i measure the sidelobe levels in this plot. Not able to see any grating lobes in final plot i.e - polar(theta,abs(AF))

Code below -

 if true
%ARRAY fACTOR FOR TRANSMIT AND RECEIVE ANTENNAS
clc;
clear all;
close all;
c0=3.*(10.^8);      %SPEED OF LIGHT
f=1.*(10.^9);       %FREQUENCY
lambda=c0./f;       %WAVELENGTH
L=15.*lambda;       %LARGEST ARRAY LENGTH
p=3;                %VARIABLE THAT DETERMINES SPACING
d=lambda./2;        %EFFECTIVE SPACING OF BOTH ARRAYS IN MULTIPLICATION
a=p.*d; %SPACING BETWEEN TWO ELEMENTS FOR - Array A
b=(p-1).*d; %SPACING BETWEEN TWO ELEMENTS FOR - Array B
no_elements1=round(L./a);     %NUMBER OF ELEMENTS IN ARRAY A
no_elements2=round(L./b);     %NUMBER OF ELEMENTS IN ARRAY B
%CALCULATION OF NUMBER OF ELEMENTS OVER 15*LAMBDA WAVELENGTH
x1=-L./2:(L./(no_elements1-1)):L./2;
x2=-L./2:(L./(no_elements2-1)):L./2;
%COSINE SQUARED CURRENT DISTRIBUTION(n=2)
i1cs=(cos((pi.*x1)./L)).^2;
i2cs=(cos((pi.*x2)./L)).^2;
% %Plotting current distributions
% plot(x1,i1);
% plot(x2,i2);
%**************************************************************************
%FOR RECEIVING ANTENNA - ARRAY FACTOR CALCULATION
beta=(2.*pi)./lambda;
theta0=45.*pi./180;       %SCAN ANGLE
AFr1=zeros(1,360);
AFr2=zeros(1,360);
for theta=1:360;
 for n1=1:no_elements1
AFr1(theta)=AFr1(theta)+(i1cs(n1).*exp(1j.*beta.*n1.*a.*(cos((theta.*pi)./180)-cos(theta0))));
 end
end
for theta=1:360;
 for n2=1:no_elements2
AFr2(theta)=AFr2(theta)+(i2cs(n2).*exp(1j.*beta.*n2.*b.*(cos((theta.*pi)./180)-cos(theta0))));
 end
 end
AF=AFr1.*AFr2;
theta_plot=1:360;
psi=beta.*d.*cos(theta_plot.*pi./180);
figure
polar(theta_plot.*pi./180,abs(AFr1))
hold on
polar(theta_plot.*pi./180,angle(AFr1),'r--')
title('For array A - i1 current distribution')
figure
polar(theta_plot.*pi./180,abs(AFr2))
hold on
polar(theta_plot.*pi./180,angle(AFr2),'c--')
title('For array B - i2 current distribution')
figure
polar(theta_plot.*pi./180,(abs(AF)))
hold on
polar(theta_plot.*pi./180,angle(AF),'m--')
title('total Array Factor for given current distribution')
%**************************************************************************
end

[Renuka Kulkarni]

Quick responses will be much appreciated. Need to submit this work soon!

[David Goodmanson]

Hi Renuka, I don't really understand the subtracting off of the two cosines, or whether one of the two factors making up AF should be conjugated, but you might want to look at e.g.

     plot(theta_plot.*pi./180,log10(abs(AFr1)))    % or
    polar(theta_plot.*pi./180,log10(abs(AFr1)/min(abs(AFr1))))

which at least shows what you have.