Page 437 - Fundamentals of Radar Signal Processing

20. Consider a C band (5 GHz) radar using a pulse repetition frequency of PRF

= 3500 pulses per second. The radar collects 30 pulses of data. For a
given range, the slow-time data sequence is zero-padded and input to a 64-
point DFT to compute the Doppler spectrum. What is the spacing of the
DFT samples in normalized radian frequency (i.e, on the –π to +π scale)?
What is the spacing in hertz? In meters per second? What is the Rayleigh
resolution (peak-to-first null width) in Doppler, in hertz? In meters per

second?
21. An X-band (10 GHz) pulse-Doppler radar collects a fast-time/slow-time

matrix of 30 pulses by 200 range bins per pulse. This is converted to a
range-Doppler matrix by applying a Hamming window and then a 64-point
fast Fourier transform to each slow-time row. Suppose that there is a target
with a constant radial velocity of 30 m/s approaching the radar at a range
corresponding to range bin #100. The PRF is 6000 samples per second.
There is no ground clutter, and noise can be ignored as well. For which

FFT sample index k is |Y[k ]| the largest? (Remember that the DC sample
0
0
is k = 0.) What velocity in meters per second does this sample correspond
to? What is the error between the apparent velocity based on the largest
FFT sample and the actual velocity?

22. Continuing Prob. 21: in terms of the window function w[m], give an
expression for the peak value of the DTFT (not DFT) of the windowed
data in range bin #100, assuming that each slow-time sample has an
amplitude of 1 before windowing. What is the numerical value of this

peak? (MATLAB® or a similar computational tool can be used to compute
this value). Now suppose the peak value of the magnitude of the FFT of the
data |Y[k ]| = 15.45. What is the straddle loss in dB?
0
23. Continuing with Probs. 21 and 22, suppose also that |Y[k – 1]| = 11.61 and
0
|Y[k + 1]| = 14.61. Use the amplitude-based quadratic interpolation
0
technique of Eqs. (5.96) and (5.97) to estimate the velocity of the target
and the peak amplitude of the DTFT. Compute the new values of velocity
error and straddle loss and compare to those found in Probs. 21 and 22.

24. Consider two radars. The first is a 3-GHz weather radar having a desired
unambiguous range of R = 300 km and unambiguous velocity v = v /2 of
b
ua
ua
50 m/s (about 112 mph). The second is a 10-GHz airborne radar having a
desired unambiguous range of R = 100 km and unambiguous velocity v ua
ua
= v /2 of 250 m/s (about 560 mph). For each radar, is a 1 kHz PRF
b
considered to be a low, medium, or high PRF?

25. What is the lowest PRF that would be considered “high” for each of the two
radars in the previous problem?

26. Consider range ambiguity resolution using three PRFs. Suppose the three