Page 323 - Fundamentals of Radar Signal Processing

Doppler shift. Compute the loss in peak amplitude due to the Doppler shift

in dB.

9. Suppose a radar uses a simple rectangular pulse of duration τ seconds and
processes it through the corresponding matched filter. Assume the matched
filter output is sampled at a rate equal to its Rayleigh bandwidth. What is
the worst-case straddle loss in dB? Repeat for an LFM waveform with a
sufficiently large BT product so that its spectrum is well-approximated by
a rectangle of width β Hz. Assume no weighting for sidelobe control is
used with either waveform.

10. Consider an LFM pulse of duration τ = 1 ms. Suppose that a range window

of only 1.5 km extent is of interest, so it is decided to use stretch
processing. The range window is centered on a nominal range of 100 km
(think of this as “zooming in” on targets in the vicinity of 100 km). A range
resolution of 1.5 meters is required. What is the required bandwidth β?
What will be the βτ product of the LFM pulse? What will be the bandwidth
of the stretch mixer output?

11. Continue with the same scenario and LFM waveform as in the previous
problem. Suppose that a beat frequency of 100 kHz is observed at the

mixer output. What is the range of the target, relative to the 100 km center
of the range window? Ignore any delay in the matched filter.

12. Consider a stationary X-band (10 GHz) radar transmitting a β = 500 MHz
LFM waveform and using stretch processing in the receiver. The pulse
length is τ = 10 μs. A radar is often considered “narrowband” if the
percentage bandwidth, defined as β divided by the RF frequency, is less
than 10 percent; otherwise it is “wideband.” Is this radar narrowband or
wideband? What is the expected range resolution in meters?

13. Continuing with the same LFM waveform, suppose a Hamming window is
applied to the signal at the output of the stretch mixer, before the FFT is

performed. What will be the new value for the expected range resolution,
based on the Rayleigh definition of resolution? (Hint: The peak-to-null
width of the DTFT of a Hamming window of length τ seconds is 2/τ Hz; for
a rectangular window it is 1/τ Hz.) What bandwidth β would be required to
achieve 0.3 m resolution if the Hamming window is used to keep the range
sidelobes low?

14. Continuing with the same radar and 500 MHz LFM pulse as in the previous
two problems, suppose the stretch processor is set up for a nominal range

(center of the range window) of R = 200 km and a range window of 300 m
0
(200 km ± 150 m). However, suppose the reference LFM signal is only τ =
10 μs seconds long, i.e., it is not lengthened to allow for signals arriving
from the leading or trailing edges of the range window. The reference