Draw a polar plot from cartesian plot of gain function

I have used MATLAB to draw the following gain function of an antenna array, the code was as follows,

    Nt=8;
    deltat=1;
    Lt=8;
    omegat=-2:0.01:2;
    for j=1:length(omegat)
    gainfunction(j)= (1/Nt) * exp(i*pi*deltat* omegat(j)* (Nt-1)) * (sin(pi*Lt*omegat(j))/sin(pi*Lt*omegat(j)*Nt^-1));
    end  
    plot(v,abs(gainfunction))
    title( 'Radiation Pattern Cartesian Plot','linewidth',30)
    grid on
    ylabel('|f(\Omega_r)|','linewidth',25)
    xlabel('\Omega_r','linewidth',15)

The image below is a radiation pattern of an antenna, i.e it shows the gain function denoted by f(\Omega) as function of $\Omega$ from -2 to 2.

My question is I would like to plot the following in *polar coordinates* to see how the main lobe is in degrees.

Any thoughts on how I can continue to the polar plot using MATLAB ?

Answer 1

[Youssef Khmou]

In the code, v is not defined, i assume is it omegat, try :

 figure; 
 polar(omegat,abs(gainfunction)); % 20*log10(abs(gainfunction)) doe dB

[DM]

You are right about the v. Can we tell the beam width of the main lobe from this figure you provided?