% for two seconds at Fs=1000Hz, a vctor of 2000 samples is sufficient
Fd=1; % in Hz
% generate Fs*T (1000*2) IID Gaussian (in Time Domain)
X1=randn(1,2000);
Y1=randn(1,2000);

% asssume Doppler spectrum is generated by generating uniformly distributed
% angles [0 2pi] and then normalized to one

xf=fft(X1);
yf=fft(Y1);

Ds=Fd*cos(2*pi*rand(1,2000));

xdf=xf.*Ds;
ydf=yf.*Ds;

R=(xdf.^2+ydf.^2).^0.5;

R=ifft(R);
x=1:1:length(R);
plot(x,abs(R))