In the ppt of lecture 4, there is a block diagram of SAR processing. The matlab code of SAR basically matches this.
The matlab code is divided into two files, SBAND_RMA_opendata is to read the data, and call SBAND_RMA_IFP to process the data after reading.
One thing to note is that the default do_all_plots is 0, and many codes for plotting intermediate data are not really used.
Below is SBAND_RMA_opendata.m
%-------------------------------------------%
%Process raw data here
clear all;
close all;
%read the raw data .wave file here
[Y,FS,NBITS] = wavread('towardswarehouse.wav');
%constants
c = 3E8; %(m/s) speed of light
%radar parameters
Tp = 20E-3; %(s) pulse time
Trp = 0.25; %(s) min range profile time duration
N = Tp*FS; %# of samples per pulse
fstart = 2260E6; %(Hz) LFM start frequency
fstop = 2590E6; %(Hz) LFM stop frequency
%fstart = 2402E6; %(Hz) LFM start frequency for ISM band
%fstop = 2495E6; %(Hz) LFM stop frequency for ISM band
BW = fstop-fstart; %(Hz) transmti bandwidth
f = linspace(fstart, fstop, N/2); %instantaneous transmit frequency
%the input appears to be inverted
trig = -1*Y(:,1);
s = -1*Y(:,2);
clear Y;
%parse data here by position (silence between recorded data)
rpstart = abs(trig)>mean(abs(trig));
count = 0;
Nrp = Trp*FS; %min # samples between range profiles
for ii = Nrp+1:size(rpstart,1)-Nrp
if rpstart(ii) == 1 & sum(rpstart(ii-Nrp:ii-1)) == 0
count = count + 1;
RP(count,:) = s(ii:ii+Nrp-1);
RPtrig(count,:) = trig(ii:ii+Nrp-1);
end
end
%parse data by pulse
count = 0;
thresh = 0.08;
clear ii;
for jj = 1:size(RP,1)
%clear SIF;
SIF = zeros(N,1);
start = (RPtrig(jj,:)> thresh);
count = 0;
jj
for ii = 12:(size(start,2)-2*N)
[Y I] = max(RPtrig(jj,ii:ii+2*N));
if mean(start(ii-10:ii-2)) == 0 & I == 1
count = count + 1;
SIF = RP(jj,ii:ii+N-1)' + SIF;
end
end
%hilbert transform
q = ifft(SIF/count);
sif(jj,:) = fft(q(size(q,1)/2+1:size(q,1)));
end
sif(find(isnan(sif))) = 1E-30; %set all Nan values to 0
%SAR data should be ready here
clear s;
s = sif;
save routsidewarehouse2 s; %for image data
%-------------------------------------------%
%load additional varaibles and setup constants for radar here
clear all;
c = 3E8; %(m/s) speed of light
%load IQ converted data here
load routsidewarehouse2 s; %load variable sif %for image data
for ii = 1:size(s,1)
s(ii,:) = s(ii,:) - mean(s,1);
end
%sif = s-sif_sub; %perform coherent background subtraction
%sif = sif_sub; %image just the background
sif = s; %image without background subtraction
clear s;
clear sif_sub;
%***********************************************************************
%radar parameters
fc = (2590E6 - 2260E6)/2 + 2260E6; %(Hz) center radar frequency
B = (2590E6 - 2260E6); %(hz) bandwidth
cr = B/20E-3; %(Hz/sec) chirp rate
Tp = 20E-3; %(sec) pulse width
%VERY IMPORTANT, change Rs to distance to cal target
%Rs = (12+9/12)*.3048; %(m) y coordinate to scene center (down range), make this value equal to distance to cal target
Rs = 0;
Xa = 0; %(m) beginning of new aperture length
delta_x = 2*(1/12)*0.3048; %(m) 2 inch antenna spacing
L = delta_x*(size(sif,1)); %(m) aperture length
Xa = linspace(-L/2, L/2, (L/delta_x)); %(m) cross range position of radar on aperture L
Za = 0;
Ya = Rs; %THIS IS VERY IMPORTANT, SEE GEOMETRY FIGURE 10.6
t = linspace(0, Tp, size(sif,2)); %(s) fast time, CHECK SAMPLE RATE
Kr = linspace(((4*pi/c)*(fc - B/2)), ((4*pi/c)*(fc + B/2)), (size(t,2)));
%Save background subtracted and callibrated data
save sif sif delta_x Rs Kr Xa;
%clear all;
%run IFP
SBAND_RMA_IFP;
What it does is similar to the previous distance measurement, reading the data (pulse) when each square wave is turned on.
for ii = Nrp+1:size(rpstart,1)-Nrp
if rpstart(ii) == 1 & sum(rpstart(ii-Nrp:ii-1)) == 0
count = count + 1;
RP(count,:) = s(ii:ii+Nrp-1);
RPtrig(count,:) = trig(ii:ii+Nrp-1);
end
endAfter reading, add these pulse data together
for ii = 12:(size(start,2)-2*N)
[Y I] = max(RPtrig(jj,ii:ii+2*N));
if mean(start(ii-10:ii-2)) == 0 & I == 1
count = count + 1;
SIF = RP(jj,ii:ii+N-1)' + SIF;
end
endThen do Hilbert transform
%hilbert transform
q = ifft(SIF/count);
sif(jj,:) = fft(q(size(q,1)/2+1:size(q,1)));The subsequent algorithms are all completed in SBAND_RMA_IFP.m.
%***********************************************************************
%a note on formatting, our convention is sif(Xa,t)
clear all;
load sif;
%apply hanning window to data first
N = size(sif,2);
for ii = 1:N
H(ii) = 0.5 + 0.5*cos(2*pi*(ii-N/2)/N);
end
for ii = 1:size(sif,1)
sif_h(ii,:) = sif(ii,:).*H;
end
sif = sif_h;
figcount = 1;
close_as_you_go = 0;
do_all_plots = 0;
set(0,'defaultaxesfontsize',13); %set font size on plots so we can see it in the dissertation
% NOTE: the function 'dbv.m' is just dataout = 20*log10(abs(datain));
%***********************************************************************
if do_all_plots == 1,
figure(figcount);
S_image = angle(sif);
imagesc(Kr, Xa, S_image);
colormap(gray);
title('Phase Before Along Track FFT');
xlabel('K_r (rad/m)');
ylabel('Synthetic Aperture Position, Xa (m)');
cbar = colorbar;
set(get(cbar, 'Title'), 'String', 'radians','fontsize',13);
print(gcf, '-djpeg100', 'phase_before_along_track_fft.jpg');
if close_as_you_go == 1,
close(figcount);
end
figcount = figcount + 1;
end
%along track FFT (in the slow time domain)
%first, symetrically cross range zero pad so that the radar can squint
zpad = 2048; %cross range symetrical zero pad
szeros = zeros(zpad, size(sif,2));
for ii = 1:size(sif,2)
index = round((zpad - size(sif,1))/2);
szeros(index+1:(index + size(sif,1)),ii) = sif(:,ii); %symetrical zero pad
end
sif = szeros;
clear ii index szeros;
S = fftshift(fft(sif, [], 1), 1);
clear sif;
Kx = linspace((-pi/delta_x), (pi/delta_x), (size(S,1)));
if do_all_plots == 1,
figure(figcount);
S_image = dbv(S);
imagesc(Kr, Kx, S_image, [max(max(S_image))-40, max(max(S_image))]);
colormap(gray);
title('Magnitude After Along Track FFT');
xlabel('K_r (rad/m)');
ylabel('K_x (rad/m)');
cbar = colorbar;
set(get(cbar, 'Title'), 'String', 'dB','fontsize',13);
print(gcf, '-djpeg100', 'mag_after_along_track_fft.jpg');
if close_as_you_go == 1,
close(figcount);
end
figcount = figcount + 1;
end
if do_all_plots == 1,
figure(figcount);
S_image = angle(S);
imagesc(Kr, Kx, S_image);
colormap(gray);
title('Phase After Along Track FFT');
xlabel('K_r (rad/m)');
ylabel('K_x (rad/m)');
cbar = colorbar;
set(get(cbar, 'Title'), 'String', 'radians','fontsize',13);
print(gcf, '-djpeg100', 'phase_after_along_track_fft.jpg');
if close_as_you_go == 1,
close(figcount);
end
figcount = figcount + 1;
end
if do_all_plots == 1,
figure(figcount);
S_image = dbv(fftshift(fft(S, [], 2), 2));
imagesc(linspace(-0.5, 0.5, size(S, 2)), Kx, S_image, [max(max(S_image))-40, max(max(S_image))]);
colormap(gray);
title('Magnitude of 2-D FFT of Input Data');
xlabel('R_{relative} (dimensionless)');
ylabel('K_x (rad/m)');
cbar = colorbar;
set(get(cbar, 'Title'), 'String', 'dB','fontsize',13);
print(gcf, '-djpeg100', 'mag_after_2D_fft.jpg');
if close_as_you_go == 1,
close(figcount);
end
figcount = figcount + 1;
end
%**********************************************************************
%matched filter
%create the matched filter eq 10.8
for ii = 1:size(S,2) %step thru each time step row to find phi_if
for jj = 1:size(S,1) %step through each cross range in the current time step row
%phi_mf(jj,ii) = -Rs*Kr(ii) + Rs*sqrt((Kr(ii))^2 - (Kx(jj))^2);
phi_mf(jj,ii) = Rs*sqrt((Kr(ii))^2 - (Kx(jj))^2);
Krr(jj,ii) = Kr(ii); %generate 2d Kr for plotting purposes
Kxx(jj,ii) = Kx(jj); %generate 2d Kx for plotting purposes
end
end
smf = exp(j*phi_mf); %%%%%%%%%%%%
%note, we are in the Kx and Kr domain, thus our convention is S_mf(Kx,Kr)
%appsly matched filter to S
S_mf = S.*smf;
clear smf phi_mf;
if do_all_plots == 1,
figure(figcount);
S_image = angle(S);
imagesc(Kr, Kx, S_image);
colormap(gray);
title('Phase After Matched Filter');
xlabel('K_r (rad/m)');
ylabel('K_x (rad/m)');
cbar = colorbar;
set(get(cbar, 'Title'), 'String', 'radians','fontsize',13);
print(gcf, '-djpeg100', 'phase_after_matched_filter.jpg');
if close_as_you_go == 1,
close(figcount);
end
figcount = figcount + 1;
end
clear S;
if do_all_plots == 1,
figure(figcount);
S_image = dbv(fftshift(fft(S_mf, [], 2), 2));
imagesc(linspace(-0.5, 0.5, size(S_mf, 2)), Kx, S_image, [max(max(S_image))-40, max(max(S_image))]);
colormap(gray);
title('Magnitude of 2-D FFT of Matched Filtered Data');
xlabel('R_{relative} (dimensionless)');
ylabel('K_x (rad/m)');
cbar = colorbar;
set(get(cbar, 'Title'), 'String', 'dB','fontsize',13);
print(gcf, '-djpeg100', 'mag_after_downrange_fft_of_matched_filtered_data.jpg');
if close_as_you_go == 1,
close(figcount);
end
figcount = figcount + 1;
end
%**********************************************************************
%perform the Stolt interpolation
%FOR DATA ANALYSIS
kstart =73;
kstop = 108.5;
%kstart = 95;
%kstop = 102;
Ky_even = linspace(kstart, kstop, 1024); %create evenly spaced Ky for interp for real data
clear Ky S_St;
%for ii = 1:size(Kx,2)
count = 0;
for ii = 1:zpad;
%for ii = round(.2*zpad):round((1-.2)*zpad)
count = count + 1;
Ky(count,:) = sqrt(Kr.^2 - Kx(ii)^2);
%S_st(ii,:) = (interp1(Ky(ii,:), S_mf(ii,:), Ky_even)).*H;
S_st(count,:) = (interp1(Ky(count,:), S_mf(ii,:), Ky_even));
end
S_st(find(isnan(S_st))) = 1E-30; %set all Nan values to 0
clear S_mf ii Ky;
if do_all_plots == 1,
figure(figcount);
S_image = angle(S_st);
imagesc(Ky_even, Kx, S_image);
%imagesc(S_image);
colormap(gray);
title('Phase After Stolt Interpolation');
xlabel('K_y (rad/m)');
ylabel('K_x (rad/m)');
cbar = colorbar;
set(get(cbar, 'Title'), 'String', 'radians','fontsize',13);
print(gcf, '-djpeg100', 'phase_after_stolt_interpolation.jpg');
if close_as_you_go == 1,
close(figcount);
end
figcount = figcount + 1;
end
%apply hanning window to data, cleans up data ALOT
N = size(Ky_even,2);
for ii = 1:N
H(ii) = 0.5 + 0.5*cos(2*pi*(ii-N/2)/N);
end
for ii = 1:size(S_st,1)
S_sth(ii,:) = S_st(ii,:).*H;
end
%S_st = S_sth;
%*********************************************************************
%perform the inverse FFT's
%new notation: v(x,y), where x is crossrange
%first in the range dimmension
clear v Kr Krr Kxx Ky_even;
v = ifft2(S_st,(size(S_st,1)*4),(size(S_st,2)*4));
%bw = (3E8/(4*pi))*(max(xx)-min(xx));
bw = 3E8*(kstop-kstart)/(4*pi);
max_range = (3E8*size(S_st,2)/(2*bw))*1/.3048;
figure(figcount);
S_image = v; %edited to scale range to d^3/2
S_image = fliplr(rot90(S_image));
cr1 = -80; %(ft)
cr2 = 80; %(ft)
dr1 = 1 + Rs/.3048; %(ft)
dr2 = 350 + Rs/.3048; %(ft)
%data truncation
dr_index1 = round((dr1/max_range)*size(S_image,1));
dr_index2 = round((dr2/max_range)*size(S_image,1));
cr_index1 = round(( (cr1+zpad*delta_x/(2*.3048)) /(zpad*delta_x/.3048))*size(S_image,2));
cr_index2 = round(( (cr2+zpad*delta_x/(2*.3048))/(zpad*delta_x/.3048))*size(S_image,2));
trunc_image = S_image(dr_index1:dr_index2,cr_index1:cr_index2);
downrange = linspace(-1*dr1,-1*dr2, size(trunc_image,1)) + Rs/.3048;
crossrange = linspace(cr1, cr2, size(trunc_image, 2));
%scale down range columns by range^(3/2), delete to make like
%dissertation again
clear ii;
for ii = 1:size(trunc_image,2)
trunc_image(:,ii) = (trunc_image(:,ii)').*(abs(downrange*.3048)).^(3/2);
end
trunc_image = dbv(trunc_image); %added to scale to d^3/2
imagesc(crossrange, downrange, trunc_image, [max(max(trunc_image))-40, max(max(trunc_image))-0]);
colormap('default');
title('Final Image');
ylabel('Downrange (ft)');
xlabel('Crossrange (ft)');
axis equal;
cbar = colorbar;
set(get(cbar, 'Title'), 'String', 'dB','fontsize',13);
print(gcf, '-djpeg100', 'final_image.jpg');
if close_as_you_go == 1,
close(figcount);
end
figcount = figcount + 1;I did fft first, I don't know if it is the calibration matrix mentioned in the ppt.
%along track FFT (in the slow time domain)
%first, symetrically cross range zero pad so that the radar can squint
zpad = 2048; %cross range symetrical zero pad
szeros = zeros(zpad, size(sif,2));
for ii = 1:size(sif,2)
index = round((zpad - size(sif,1))/2);
szeros(index+1:(index + size(sif,1)),ii) = sif(:,ii); %symetrical zero pad
end
sif = szeros;
clear ii index szeros;
S = fftshift(fft(sif, [], 1), 1);
clear sif;
Kx = linspace((-pi/delta_x), (pi/delta_x), (size(S,1)));Then there is the matched filter
%matched filter
%create the matched filter eq 10.8
for ii = 1:size(S,2) %step thru each time step row to find phi_if
for jj = 1:size(S,1) %step through each cross range in the current time step row
%phi_mf(jj,ii) = -Rs*Kr(ii) + Rs*sqrt((Kr(ii))^2 - (Kx(jj))^2);
phi_mf(jj,ii) = Rs*sqrt((Kr(ii))^2 - (Kx(jj))^2);
Krr(jj,ii) = Kr(ii); %generate 2d Kr for plotting purposes
Kxx(jj,ii) = Kx(jj); %generate 2d Kx for plotting purposes
end
end
smf = exp(j*phi_mf); %%%%%%%%%%%%
%note, we are in the Kx and Kr domain, thus our convention is S_mf(Kx,Kr)
%appsly matched filter to S
S_mf = S.*smf;
clear smf phi_mf;Then there is stolt interpolation, which is the stolt transform in ppt
%perform the Stolt interpolation
%FOR DATA ANALYSIS
kstart =73;
kstop = 108.5;
%kstart = 95;
%kstop = 102;
Ky_even = linspace(kstart, kstop, 1024); %create evenly spaced Ky for interp for real data
clear Ky S_St;
%for ii = 1:size(Kx,2)
count = 0;
for ii = 1:zpad;
%for ii = round(.2*zpad):round((1-.2)*zpad)
count = count + 1;
Ky(count,:) = sqrt(Kr.^2 - Kx(ii)^2);
%S_st(ii,:) = (interp1(Ky(ii,:), S_mf(ii,:), Ky_even)).*H;
S_st(count,:) = (interp1(Ky(count,:), S_mf(ii,:), Ky_even));
end
S_st(find(isnan(S_st))) = 1E-30; %set all Nan values to 0
clear S_mf ii Ky;The last is IFFT, which is 2D IDFT on ppt
%perform the inverse FFT's
%new notation: v(x,y), where x is crossrange
%first in the range dimmension
clear v Kr Krr Kxx Ky_even;
v = ifft2(S_st,(size(S_st,1)*4),(size(S_st,2)*4));
Then you can draw
bw = 3E8*(kstop-kstart)/(4*pi);
max_range = (3E8*size(S_st,2)/(2*bw))*1/.3048;
figure(figcount);
S_image = v; %edited to scale range to d^3/2
S_image = fliplr(rot90(S_image));
cr1 = -80; %(ft)
cr2 = 80; %(ft)
dr1 = 1 + Rs/.3048; %(ft)
dr2 = 350 + Rs/.3048; %(ft)
%data truncation
dr_index1 = round((dr1/max_range)*size(S_image,1));
dr_index2 = round((dr2/max_range)*size(S_image,1));
cr_index1 = round(( (cr1+zpad*delta_x/(2*.3048)) /(zpad*delta_x/.3048))*size(S_image,2));
cr_index2 = round(( (cr2+zpad*delta_x/(2*.3048))/(zpad*delta_x/.3048))*size(S_image,2));
trunc_image = S_image(dr_index1:dr_index2,cr_index1:cr_index2);
downrange = linspace(-1*dr1,-1*dr2, size(trunc_image,1)) + Rs/.3048;
crossrange = linspace(cr1, cr2, size(trunc_image, 2));
%scale down range columns by range^(3/2), delete to make like
%dissertation again
clear ii;
for ii = 1:size(trunc_image,2)
trunc_image(:,ii) = (trunc_image(:,ii)').*(abs(downrange*.3048)).^(3/2);
end
trunc_image = dbv(trunc_image); %added to scale to d^3/2
imagesc(crossrange, downrange, trunc_image, [max(max(trunc_image))-40, max(max(trunc_image))-0]);
colormap('default');
title('Final Image');
ylabel('Downrange (ft)');
xlabel('Crossrange (ft)');
axis equal;
cbar = colorbar;
set(get(cbar, 'Title'), 'String', 'dB','fontsize',13);
print(gcf, '-djpeg100', 'final_image.jpg');
if close_as_you_go == 1,
close(figcount);
end
figcount = figcount + 1;
In addition to the calibration matrix, basically ppt and matlab codes can be matched.
As for why the sar image can be obtained according to the modules on the ppt, and how the specific matlab code implements the algorithms of those modules, you need to read the paper carefully to know.
There is an article corresponding to the Chinese translation of ppt
http://www.360doc.com/content/14/1125/00/12979957_427822702.shtml
