RMA.rar_SAR RMA_range migration_rma_sar range

%An example to RMA from the book: Carrara:"Spotlight Synthetic Aperture %Radar: Signal Processing Algortithms" Artech House 1995. %Signal Data from: Tab10_1 %% clear all,close all; clc Nf=2^10; %number of points for freq. range %array parameter dx=0.6;L=760.8; %interelement space in synthetic array (length L) Na=L/dx+1; %number of array elements X=linspace(-L/2,L/2,Na).'; %position of array elements Kx=linspace(-pi/dx,pi/dx,Na).';%azimuthal spacial wavenumber (page 410) Kx=repmat(Kx,1,Nf); Rs=1000; %distance from origin to the array plane X=X+1j*Rs; % XY antenna position as complex number. Here, image processing %in XY plane only, therefore, complex description for cartesian coordinates %is convinient. %frequency range co=299792458; %free space wave velocity fc=242.4*1E6; %last frequency in the Band of width B (in the book it should %be center freq., but the Range Freq. in Fig. 10.11 doesn't fit then.) B=133.5*1E6; %bandwidth freq=linspace(fc-B,fc,Nf); Kr=4*pi*freq/co;%Frequency wavenumber (page 410) Kr=repmat(Kr,Na,1); %target position: tar=[-200+1j*100, 200+1j*100, 0+1j*100,... -200, 0, 200,... -200-1j*100, 200-1j*100, 0-1j*100]; %3x3 grid %tar=[0, 200, -1j*100]; %(table 10.1) %simulated data, dechirped (compressed) and deskewed in range: data=my_sinthSISO_planresp( X,freq,tar ); %phase reference acc. to image origin %(see also: Sanchez "3-D Radar Imaging Using Range Migration Techniques", %IEEE; or: %http://www.lluisvives.com/servlet/SirveObras/01604307547816095212257/003402_12.pdf): data=data.*exp(1j*Rs*Kr); figure(1) imagesc(angle(data)); %fig10.7 and 10.8 data_compr=fftshift(ifft(data,[],2),2); figure(2) imagesc(abs(data_compr)); %fig10.7 %azimuth fft data=fftshift(data,1); %due to -Xmin..Xmax data=fft(data,[],1);%azimuth fft data=fftshift(data,1); %due to -Kx_min..Kx_max %azimuth fft %Kx accord to fig10.11 plot(Kx,Kr,'.') Xax=-5:1:5;Yax=5:1:10; axis([ min(Xax) max(Xax) min(Yax) max(Yax)]) set(gca,'XTick',Xax,'YTick',Yax) grid on %Kx accord to fig10.11 %fig10.11 imagesc(Kr(1,:),Kx(:,1),abs(data)) %fig10.11 %range compressed signal in Fig10.12 data_compr=fftshift(ifft(data,[],2),2); %fig10.12 imagesc(abs(data_compr)); %fig10.12 %Ky wavenumber, squared, accordingly to (10.9) Ky_sq=Kr.^2-Kx.^2; %only positive Ky is physical Neg=logical(Ky_sq < 0); % Ky_sq(Neg)=NaN; data(Neg)=NaN; Kr(Neg)=NaN; %only positive Ky is acceptable %matched filter, phase acc. to (10.8) Fmf=-Rs*Kr+Rs*sqrt(Ky_sq); %figure 10.13 mesh(Kr,Kx,Fmf) axis([4 10 -2.8 2.8 -2000 0]) %figure 10.13 data=data.*exp(1j*Fmf); %data matching by matched filter %fig. 10.14 middle data_compr=fftshift(ifft(data,[],2),2); imagesc(abs(data_compr)); %fig. 10.14 middle %stolt interpolation %Fig 10.15 (a) plot(Kx,Kr,'.') %Fig 10.15 (a) Ky=sqrt(Ky_sq); %cross-range wavenumber by (10.9) %Fig 10.15 (b) plot(Kx,Ky,'.') %Fig 10.15 (b) Ky_int=Ky(Na/2-0.5,:);%data interpolation to Ky_int cross-range wavenumber data=my_spline(Ky,data,Ky_int);%1D data interpolation by spline function %stolt interpolation %processing window in Ky dimension Ny=750; data=data(:,1:Ny); Ky_int=Ky_int(1:Ny); %range compression data=fftshift(ifft(data,[],2),2); %fig10.20 (a) imagesc(abs(data)); %fig10.20 (a) %azimuth compression data=fftshift(data,1);%compare to azimuth fft above data=ifft(data,[],1); data=fftshift(data,1); %% dy=2*pi/(Ky_int(end)-Ky_int(1)); %step in cross-range dimension Y=-Ny/2*dy:dy:(Ny/2-1)*dy;%cross-range axis %fig10.20 (b) imagesc(Y,X,abs(data)); ylabel('Cross-Range, m') xlabel('Range, m') axis([ -300 300 -300 300]) colormap('pink') figure;contour(abs(data),30) %fig10.20 (b)