I'm not sure if you mean m.^2.*f.^2./16.*r or m.^2.*f.^2./(16.*r) in your equations.
I assumed that your equations.png is correct.
u=[1 2 0.1 0.1 3 4 30 40 50 60];
a = u(1:2);
r = u(3:4);
f = u(5:6);
theta = u(7:8);
phi = u(9:10);
fmax=10;
m=(1:5).';
xo = sum(a.*exp(-1i*((pi/fmax).*(-m.*f/2).*sind(theta).*cosd(phi)+m.^2.*f.^2./16.*r).*(1-sind(theta).^2.*cosd(phi).^2)),2)
yo = sum(a.*exp(-1i*((pi/fmax).*(-m.*f/2).*sind(theta).*sind(phi)+m.^2.*f.^2./16.*r).*(1-sind(theta).^2.*sind(phi).^2)),2)
