clear all;
%======================================================================
%%% (I) parameters' definition
%======================================================================
c=3e+8; % speed of light
pi=3.1415926; % pi
j00=sqrt(-1); % square root of -1
res_a=1; % required azimuth resolution
res_r=1; % required range resolution
k_a=1.2; % azimuth factor
k_r=1.2; % range factor
Ra=4000.; % radar working distance
va=76.; % radar/platform forward velocity
Tp=1.e-6; % transmitted pulse width
fc=3e+9; % carrier frequency
FsFactor = 1.2;
theta=90*pi/180; % squint angle
%======================================================================
lamda=c/fc; % wavelength
Br=k_r*c/2./res_r; % required transmitted bandwidth
Fs=Br*FsFactor; % A/D sampling rate
bin_r=c/2./Fs; % range bin
Kr=Br/Tp; % range chirp rate
La=Ra*k_a*lamda/2/res_a/sin(theta); % required synthetic aperture length
Ta=La/va; % required synthetic aperture time
fdc=2*va*cos(theta)/lamda; % doppler centriod
fdr=-2*(va*sin(theta)).^2/lamda/Ra; % doppler rate
Bd=abs(fdr)*Ta; % doppler bandwidth
prf=round(Bd*2); % PRF
%======================================================================
%%%(II) echo return modelling (point target)
%======================================================================
Na=fix(Ta*prf); % azimuth sampling number
ta=((1:Na)-Na/2)/prf; % slow time along azimuth
xa=va*ta-Ra*cos(theta); % azimuth location along flight track
%x0=[ 0 0 0 0 0 ]; % define multi points if you want
%R0=[-20 -10 0 10 20 ]; % x0: azimuth location (positive towards forward velocity)
% R0: slant range location (positive towards far range)
x0=[ 0 0 0 50]; R0=[ -200 -50 0 0];
Npt_num = length(x0);
ra=zeros(Npt_num, length(xa)); % calculate every point target's slant range history
for i=1:Npt_num
ra(i,:)=sqrt((Ra*sin(theta)+R0(i)).^2+(xa+x0(i)).^2);
end
rmax=max(max(ra)); % max. slant range
rmin=min(min(ra)); % min. slant range
rmc=fix((rmax-rmin)/bin_r); % range sample number
rg=0*ra; % initialize
rg=fix((ra-rmin)/bin_r+1); % range gate index
rgmax=max(max(rg));
rgmin=min(min(rg));
nr=round(Tp*Fs); % samples of a pluse
tr=1:fix(nr)+1;
tr=tr/Fs-Tp/2; % fast time within a pluse duration
Nr=nr+rgmax;
%======================================================================
%%%(II) echo return modelling (point target)
%======================================================================
sig=zeros(Na,Nr);
for i=1:Na
for k=1:Npt_num
sig(i,rg(k,i):rg(k,i)+nr)=sig(i,rg(k,i):rg(k,i)+nr)+exp(-j00*4*pi/lamda*ra(k,i))*exp(-j00*pi*Kr*(tr).^2);
end
end
%======================================================================
% Range Doppler Algorithm
%======================================================================
pre_filter=exp(-j00*2*pi*fdc*ta');
for i=1:Nr
sig(:,i)=sig(:,i).*pre_filter;
end
disp('end of prefilter');
for i=1:Na
sig(i,:)=fftshift(fft(sig(i,:)));
end
dfr=Fs/Nr;
fr=((0:Nr-1)-Nr/2)*dfr;
phase1=exp(-j00*pi*(fr).^2/Kr);
for i=1:Na
sig(i,:)=ifft(fftshift( sig(i,:).*phase1) );
end
disp('end of range compression');
figure; colormap(gray); contour(abs(sig));
%%%===============================================================================
for i=1:Nr
sig(:,i)=fftshift(fft(sig(:,i)));
end
disp('end of azimuth fft')
dfa=prf/Na;
fa=((0:Na-1)-Na/2)*dfa+fdc;
figure; colormap(gray); contour(abs(sig));
%% RMC with interpolation
rr=rmin+((1:Nr)-1)*bin_r;
R=8; N_ex=2000;
Up00=zeros(size(1:Nr*R+2*N_ex));
alpha_dc=1./sqrt(1-(lamda*fdc/2/va)^2);
for i=1:Na
Up00=0*Up00;
Up00(N_ex+1:N_ex+Nr*R)=interp(sig(i,:),R);
alpha_fx = 1./sqrt(1-(lamda*fa(i)/2/va)^2);
dRa=rr*(alpha_fx-alpha_dc)*sin(theta);
kpos=R*((1:Nr)-1)+round(R*dRa/bin_r)+N_ex;
sig(i,:)=Up00(kpos);
end
disp('end of range motion correction')
figure; colormap(gray); contour(abs(sig));
%%%===============================================================================
fa=fa-fdc; fdc=0;
beta_dc = sqrt(1-(lamda*fdc/2/va).^2);
delt_beta = sqrt(1-(lamda*fa/2/va).^2)-beta_dc;
phase2 = exp((j00*4*pi*sin(theta)/lamda)*(delt_beta'*rr));
sig = sig.*phase2;
for i=1:Nr
sig(:,i)=ifft(fftshift(sig(:,i)));
end
disp('end of azimuth compression')
figure; colormap(gray); contour(abs(sig));
