Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms. Caner Ozdemir

Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms - Caner Ozdemir


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yields

      (2.70)equation

      (2.71)equation

      The term (cvr)/(c + vr) is known as the dilation factor in the radar community. Notice that when the target is stationary (vr = 0), then the pulse duration remains unchanged (τ' = τ) as expected.

      Now, consider the situation in Figure 2.22c. As trailing edge of the second pulse is hitting the target, the target has traveled a distance of

      within the time frame of dt. During this period, the leading edge of the first pulse has traveled a distance of

      (2.73)equation

      On the other hand, the leading edge of the second pulse has to travel a distance of (c/fPRD) at the instant when it reaches the target. Therefore,

      (2.74)equation

      Solving for dt yields

      (2.76)equation

      The new PRF for the reflected pulse is

      (2.77)equation

      (2.78)equation

      If the center frequency of the incident and reflected waves are f0 and images, these two frequencies are related to each other with the same factor:

      (2.79)equation

      To find the Doppler shift in the frequency, fD, we should subtract the center frequency of the incident wave from the center frequency of the reflected wave as

      (2.80)equation

      where λ0 is the wavelength corresponding to the center frequency of f0. For the target that is moving away from the radar, the Doppler frequency shift has a negative sign as

      (2.82)equation

Schematic illustration of shift is caused by the target's radial velocity, vr.

      (2.83)equation

      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


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