Matlab Antenna Array Factor need help

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ctyz

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my professor wanted me to design 2x2 antenna array which gives a pattern similar to cardioid but it has to be 1 everywhere except a narrow notch point. i have been trying 2 weeks around 2000 combination but i still can't find it. my matlab code is :

Code:
clear all
    f       = 1e6;
    c       = 3e8;
    lamd    = c/f;
    k       = 2*pi/lamd;
    dx      = [0.25*lamd/2 : 0.25*lamd/2 :2 * lamd/2];
    dy      = [0.25*lamd/2 : 0.25*lamd/2 :2 * lamd/2];
    
    phi     = [0:0.1:360];
    phir    = phi / 180 * pi;
    theta   = [0:0.1:180];
    thetar  = theta / 180 * pi;
    
    AX1      = 1;
    AX2      = 1; 
    AY1      = 1; 
    AY2      = 1; 
    
    BX1      = pi; %phases of each antennas
    BX2      = 0;
    BY1      = pi/2;
    BY2      = 3*pi/2;

    len     = length(dx);
    
    for ix=1:len
        
        for iy=1:len
    
    kdx     = k * dx(ix) ;
    kdy     = k * dy(iy) ;
    AFX1     = AX1 .* exp( i .* (kdx .* cos(phir) + BX1));
    AFX2     = AX2 .* exp(-i .* (kdx .* cos(phir) + BX2));
    AFY1     = AY1 .* exp( i .* (kdy .* sin(phir) + BY1));
    AFY2     = AY2 .* exp(-i .* (kdy .* sin(phir) + BY2));
    
    AF      = AFX1 + AFX2 + AFY1 + AFY2;
    aAF     = abs(AF);
    figure(1);hold off
    fprintf('Dx = %.2f lamd Dy = %.2f lamd\n',dx(ix)/lamd*2,dy(iy)/lamd*2);
    polar(phir,aAF);
    pause;

        end
    end
 
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