Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms. Caner Ozdemir

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Figure 2.23 Doppler shift is caused by the target's radial velocity, v_r.

It is clear from these equations that Doppler frequency shift is directly proportional to the velocity of the target. If the velocity increases, the shift in the frequency increases as well. If the target is stationary with respect to radar (v_r = 0), then the Doppler frequency shift is zero. The velocity v_r in the above equation corresponds to the velocity along the RLOS direction. If the target is moving along another direction, v_r refers to the velocity projected toward the direction of radar. If the target's velocity is v as illustrated in Figure 2.23, then the Doppler frequency shift in terms of the target's original velocity will be equal to

      (2.83)

2.8 Matlab Codes

Below are the Matlab source codes that were used to generate all of the Matlab‐produced figures in this chapter. The codes are also provided in the CD that accompanies this book.

      Matlab code 2.1 Matlab file “Figure2‐9.m”

      %--------------------------------------------------------- % This code can be used to generate Figure 2.9 %--------------------------------------------------------- %---Figure 2.9a--------------------------------------------- clear close all fo=1e3; % set the frequency t=-4e-3:1e-7:4e-3; % choose time vector s=cos(2*pi*fo*t); % time domain CW signal plot(t*1e3,s,'k','LineWidth',2); grid minor set(gca,'FontName', 'Arial', 'FontSize',12,'FontWeight','Bold'); xlabel('\ittime, ms'); ylabel('\itamplitude, V'); axis([-4 4 -1.2 1.2]) %---Figure 2.9(b)------------------------------------------- N=length(t); df=1/(t(N)-t(1)); % Find frequency resolution f=-df*(N-1)/2:df:df*(N-1)/2; % set frequency vector figure; S=fft(s)/N; % frequency domain CW signal plot(f*1e-3,fftshift(abs(S)),'k','LineWidth',2); grid minor set(gca,'FontName', 'Arial', 'FontSize',12,'FontWeight','Bold'); xlabel('\itfrequency, KHz'); ylabel('\itamplitude, V'); axis([-.8e1 .8e1 0 .6])

      Matlab code 2.2 Matlab file “Figure2 ‐ 11.m”

      %-------------------------------------------------------- % This code can be used to generate Figure 2.11 %-------------------------------------------------------- clear close all fo=100; % set the base frequency t=0:1e-7:4e-3; % choose time vector k=3e6; % select chirp rate m=sin(2*pi*(fo+k*t/2).*t); % time domain FMCW signal plot(t*1e3,m,'k','LineWidth',2); grid minor set(gca,'FontName', 'Arial', 'FontSize',12,'FontWeight','Bold'); xlabel('\ittime, ms'); ylabel('\itamplitude, V'); axis([0 4 -1.1 1.1])

      Matlab code 2.3 Matlab file “Figure2 ‐ 15.m”

%-------------------------------------------------------- % This code can be used to generate Figure 2.15 %-------------------------------------------------------- clear close all c=.3; % speed of light [] f=2:.002:22; % choose frequency vector Ro=50; % choose range of target [m] k=2*pi*f/c; Es=1*exp(-1i*2*k*Ro); % collected SFCW electric field df=f(2)-f(1); % frequency resolution N=length(f); % total stepped frequency points dr=c/(2*N*df); % range resolution R=0:dr:dr*(length(f)-1); %set the range vector plot(R, 20*log10(abs(ifft(Es))),'k','LineWidth',2) grid minor set(gca,'FontName', 'Arial', 'FontSize',12,'FontWeight','Bold'); xlabel('\itrange, m'); ylabel('\itamplitude, dBsm'); axis([0 max(R) -90 0])

      Matlab code 2.4 Matlab file “Figure2 ‐ 16.m”

%--------------------------------------------------------- % This code can be used to generate Figure 2.16 %--------------------------------------------------------- clear close all t=0:0.01e-9:50e-9; % choose time vector N=length(t); pulse(201:300)=ones(1,100); % form rectangular pulse pulse(N)=0; % Frequency domain equivalent dt=t(2)-t(1); % time resolution df=1/(N*dt); % frequency resolution f=0:df:df*(N-1); % set frequency vector pulseF=fft(pulse)/N; % frequency domain signal %---Figure 2.16(a)------------------------------------------ plot(t(1:501)*1e9,pulse(1:501),'k','LineWidth',2); grid minor set(gca,'FontName', 'Arial', 'FontSize',12,'FontWeight','Bold'); xlabel('\ittime, ns'); ylabel('\itamplitude, V'); axis([0 5 0 1.1]); %---Figure 2.16(b)------------------------------------------ figure plot(f(1:750)/1e9,20*log10(abs(pulseF (1:750))),'k','LineWidth',2); grid minor set(gca,'FontName', 'Arial', 'FontSize',12,'FontWeight','Bold'); axis([0 f(750)/1e9 -85 -20]); xlabel('\itfrequency, GHz'); ylabel('\itamplitude, dB');

      Matlab code 2.5 Matlab file “Figure2 ‐ 17.m”

%--------------------------------------------------------- % This code can be used to generate Figure 2.17 %--------------------------------------------------------- clear close all t=-25e-9:0.01e-9:25e-9; % choose time vector N=length(t); sine(2451:2551)=-sin(2*pi*1e9*(t(2451:2551))); % form sine pulse sine(N)=0; % Frequency domain equivalent dt=t(2)-t(1); % time resolution df=1/(N*dt); % frequency resolution f=0:df:df*(N-1); % set frequency vector sineF=fft(sine)/N; % frequency domain signal %---Figure 2.17(a)------------------------------------------------ plot(t(2251:2751)*1e9,sine (2251:2751),'k','LineWidth',2); grid minor set(gca,'FontName', 'Arial', 'FontSize',12,'FontWeight','Bold'); xlabel('\ittime, ns'); ylabel('\itamplitude, V'); axis([-2.5 2.5 -1.1 1.1]); %---Figure 2.17(b)------------------------------------------------ figure plot(f(1:750)/1e9,20*log10(abs(sineF (1:750))),'k','LineWidth',2); grid minor set(gca,'FontName', 'Arial', 'FontSize',12,'FontWeight','Bold'); axis([0 f(750)/1e9 -85 -20]); xlabel('\itfrequency, GHz'); ylabel('\itamplitude, dB');

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