Page 322 - Fundamentals of Radar Signal Processing

millisecond is given by

(Note: This is not a possible AF because it is not time-limited to ±τ
seconds duration in the delay coordinate, but it will do for this problem.)
Suppose there are two targets in the radar’s line of sight, one at R = 10 km
and one at R = 10.1 km. Also assume that both have the same RCS and

ignore the effect of the small range difference on the received echo power.
The radar and the first target are stationary. The second target is traveling
toward the radar at 100 m/s. The radar is operating at 1 GHz. What is the
Doppler shift of the echo from the second target, in hertz? If the matched
filter output is sampled at a time delay corresponding to the range to the
first target (= 2 × (10 km)/c = 66.67 μs), the sample will contain
contributions from both the first and second targets. Use A(t, F ) to
D
determine the relative amplitude of the contribution from the second target
compared to that of the first target. Express the answer in dB.

4. Consider a simple pulse burst waveform with M = 30 pulses, each of 10 μs
duration, and a PRI of T = 100 μs. Assuming no weighting functions are
used, what are the range resolution, Doppler resolution, unambiguous
range, and unambiguous Doppler shift of this waveform?

5. Consider a linear FM waveform that sweeps from 9.5 to 10.5 GHz over a
pulse length of 20 μs. What is the bandwidth β? What is the time-
bandwidth product? What will be the Rayleigh resolution (peak to first

null) of the matched filter output in meters? What would be the Rayleigh
resolution in meters of a square pulse of the same energy (assuming both
have the same amplitude)?

6. Continuing with the same LFM waveform as in the previous problem, what
will be the frequency in hertz of the first zero of the zero delay cut of the
ambiguity function? (This will be the Doppler resolution, or Doppler
sensitivity, of the pulse.)

7. Consider an LFM waveform of bandwidth β = 1 MHz and pulse length τ = 1
ms. Suppose an echo is received from a target at a true range of 10 km that
is Doppler shifted by 1 kHz. What will be the apparent range of the target,
i.e., what will be the range corresponding to the time at which the matched

filter output peaks?

8. Consider an LFM pulse with β = 50 MHz and τ = 1 msec. Compute the
Doppler shift required to displace the matched filter output by three
Rayleigh range resolution cells. No windowing for sidelobe control is
used. At 10 GHz, compute the radial velocity associated with that value of