omega-k algorithm simulation in matlab

Question

I want to simulate omega k algorithm to focus synthetic aperture radar raw data based on cumming's book, "Digital Processing of Synthetic Aperture Radar Data". First I simulated point target raw data in stripmap mode and do everything which is mentioned in the book. But my target doesn't focused. To make sure my raw data is made truly, I focused it with conventional RDA algorithm and my point target focused in true position which means that my raw data simulation routine is Ok.

Here is my matlab code for omega k algorithm:

%% __________________________________________________________________________
fr          = linspace(-fs/2,fs/2,nfftr);
faz         = linspace(-PRF/2,PRF/2,nffta);
fr_prime    = sqrt((f0+fr).^2-(c*faz'/(2*vp)).^2)-f0;
Rref        = rs(ceil(Ns/2));
theta_ref   = 4*pi*Rref/c*(fr_prime+f0)+pi*fr.^2/kr;
%2D FFT
S_raw       = fftshift(fft2(s_raw,nffta,nfftr));
%RFM
S_BC        = S_raw.*exp(1j*theta_ref);
for idx = 1:Na
    S_int(idx,:) = interp1(fr_prime(idx,:)+f0,S_BC(idx,:),fr+f0,'pchip');
end
S_c = S_int.*exp(-1j*4*pi*fr*Rref/c);
s_c = ifft2(S_c,Na,Nr);
%% __________________________________________________________________________

in this code:

• f0 : center frequency
• kr : Chirp Rate in Range
• fs : Sampling frequency in range
• vp : platform velocity
• rs : range array (form near range to far range)
• Rref : Reference range (Hear I take it as middle range cell)
• Ns : number of range cells
• Na : number of samples in Azimuth
• s_c : Focused Image

three targets are positioned at [10 , Ns/2 , Ns-10] in range and Na/2 in azimuth. here is my results:

Data after Bulk Compression in Time Domain

Data after stolt Interpolation in Time Domain

I examined several interpolation methods like sinc interp , linear interp , pchip and others, but non of them worked for me. I appreciate everyone who could help me and tell me whats my mistake... thank you...

Answer 1

In the accurate version of Omega-k, Cumming did not ask to multiply with a matched filter again after stolt interpolation. The focusing should be complete just with a 2D iFFT.