RD.rar_RD_rd算法_傅里叶卷积_分数阶_分数阶卷积

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=70.; % radar/platform forward velocity Tp=1.e-6; % transmitted pulse width fc=1.e+9; % carrier frequency FsFactor = 1.0 lamda=c/fc; % wavelength B=k_r*c/2./res_r; % required transmitted bandwidth Fs=B*FsFactor; % A/D sampling rate bin_r=c/2./Fs; % range bin gama=B/Tp; % range chirp rate delta_theta=k_a*lamda/2/res_a; % required azimuth opening angle % corresponding to processed bandwith % (should be less than azimuth 3dB opening angle) La=Ra*delta_theta; % required synthetic aperture Ta=La/va; % required synthetic aperture time thetas_c=pi/2; % zero squint fdc=2*va*cos(thetas_c)/lamda; % doppler centriod fdr=-2*va*va*sin(thetas_c)^2/lamda/Ra; % doppler rate Bd=abs(fdr)*Ta; % doppler bandwidth prf=100.; % PRF %%%(II) echo return modelling(point target) na=fix(Ta*prf/2); % azimuth sampling number ta=-na:na; ta=ta/prf; % slow time along azimuth xa=va*ta; % azimuth location along flight track na=2*fix(na); %x0=[0 0 0 0 0 0 -60 -30 30 60]; %R0=[-10 0 10 20 30 40 0 0 0 0]; x0=[0 ]; R0=[0 ]; Npt_num = length(x0); % single point target's azimuth location % positive towards forward velocity % single point target's slant range location ra=zeros(Npt_num, length(xa)); % positive towards far range for i=1:Npt_num ra(i,:)=sqrt((Ra+R0(i)).^2+(xa+x0(i)).^2); % single point target's slant range history end rmax=max(max(ra)); % max. slant range rmin=min(min(ra)); % min. slant range rmc=fix((rmax-rmin)/bin_r); % range migration rg=0*ra; rg=fix((ra-rmin)/bin_r+1); % range gate beause of range migration rgmax=max(max(rg)); rgmin=min(min(rg)); nr=round(Tp*Fs); % min range samples tr=1:fix(nr)+1; tr=tr/Fs-Tp/2; % fast time along range [m,Na]=size(ta); Nr=nr+rgmax; Na Nr 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*gama*(tr).^2); end end disp('end of echo return modelling') %figure %contour(abs(sig)) %%%=============================================================================== for i=1:Na sig(i,:)=fftshift(fft(sig(i,:))); end disp('end of range fft') dfr=Fs/Nr; fr=((0:Nr-1)-Nr/2)*dfr; phase1=exp(-j00*pi*(fr).^2/gama); for i=1:Na sig(i,:)=ifft(fftshift( sig(i,:).*phase1) ); end disp('end of range compression') %figure %contour(abs(sig)) for i=1:Nr sig(:,i)=fftshift(fft(sig(:,i))); end disp('end of azimuth fft') fdr=-2*va*va/lamda/Ra; dfa=prf/Na; fa=((0:Na-1)-Na/2)*dfa; figure %contour(abs(sig(Na,:))) plot(abs(sig(Na,:))) R=4; Up00=zeros(size(1:Nr*R+2000)); kkk=1:Nr; for i=1:Na Up00=0*Up00; Up00(1:Nr*R)=interp(sig(i,:),R); dRa=Ra/sqrt(1-(lamda*fa(i)/2/va)^2)-Ra; kpos(i)=round(R*dRa/bin_r); sig(i,:)=Up00((kkk-1)*R+kpos(i)+1); end %figure %contour(abs(sig)) figure %contour(abs(sig(Na,:))) plot(abs(Up00)) disp('Range motion correction') rr=rmin+((1:Nr)-1)*bin_r; delt_beta = sqrt(1-(lamda/2/va*fa).^2)-1; phase2 = exp((j00*4*pi/lamda)*(delt_beta'*rr)); sig = sig.*phase2; for i=1:Nr sig(:,i)=ifft(sig(:,i)); end figure contour(abs(sig));