Principles of Modern Radar - Volume 2 1891121537

334 CHAPTER 7 Stripmap SAR6. [MATLAB slant range and phase] Write MATLAB code to calculate the slant rangeto a scatterer at any desired down-range r and a cross-range x. Use (x,r) = (0, r 0 ) forthis exercise. Evaluate and plot the slant range for a set of along-track sample locationseparated by the along-track sampling interval and spanning the SAR baselines for theL-band and X-band systems. Multiply these slant-range vectors by 4π/λ c to generatethe phase history at their corresponding center frequencies. Plot these phase histories.7. [MATLAB signal model] Extend the one-dimensional phase histories produced inproblem 6 to two dimensions, where the second dimension is frequency. Samplediscretely about the L-band and X-band center frequency over an extent that covers therequired waveform bandwidth and by a uniform interval equal to 100 kHz. Plot thesefrequencies. Take the resulting two-dimensional (frequency and along-track position)phase histories and convert them to complex signal histories using exp(– j*phase).Ignore any power variations due to range-to-the-fourth, antenna gain patterns, andso on, by using a magnitude of 1.0. Generate an image of the phase angle of eachsignal. (At this point you have a simple and generic SAR data generation environmentcapable of producing stepped-frequency records as a function of along-track positionof the platform. You may vary center frequency, bandwidth, frequency sampling, SARbaseline length, along-track sampling, and range to scene center to perform parametricanalyses. Another loop may be added to coherently sum the returns from multiplescatterers in the scene.)8. [MATLAB pulse compression] Use IFFT over frequency to generate pulse-compressedmeasured data as a function of along-track location and time delay, d(u,t). Create animage of the magnitude of the L-band and X-band data. Depict the phase by creatingan image of the real part of the pulse-compressed data. (The image of the realdata is easier to interpret if a linear phase progression over time is detrended. Thisis easily accomplished by first IFFTSHIFTing over frequency prior to the IFFT fromfrequency to time. Multiplying the data by a phase offset of −90 ◦ ,or−1 j, improvesinterpretability further.)9. [DBS imaging] Generate the range-compressed data as in problem 8 omitting theIFFTSHIFT and the phase offset described toward the end of the problem. PerformDBS imaging as documented in Figure 7-5. Begin by Fourier transforming over thealong-track position with an FFT and then place zero cross-range in the middle ofthe image by applying an FFTSHIFT over cross-range. Index pixels to their raw(k u ,ω) locations initially, then use the mapping in the text to locate pixels to crossrange/down-range(x,r).10. [DBS-AD imaging] Implement DBS with AD as documented in Figure 7-10 andcompare the resulting imagery with DBS imagery for L-band and X-band.11. [RDA PSF] Generate the frequency-domain (k u ,ω) form of the PSR for the swathcenter r 0 for the L-band and X-band cases. Use the RF support (vector) correspondingto the raw data generated in problem 7 and the spatial-frequency support (vector)created in problem 9. Produce phase images of these PSRs. Pulse-compress the PSRsas in problem 8 by inverse Fourier transforming (using the IFFT) from frequency totime and create images of the Doppler-domain time-delay profiles. (Recall this formof the PSR has been offset to put the closest point of approach at down-range r 0 attime delay equals zero, so the output should be FFTSHIFTed and the time-delay axisrecalculated accordingly.) Finally, examine the PSR as a function of (u,t) by inverse