Page 86 - Fundamentals of Radar Signal Processing

allotted to which services), but also due to atmospheric propagation.

Based on Fig. 1.3, list two frequencies in the MMW band that might be
preferable for radar use, and two that would not be suitable. Explain.

5. Compute the bandwidth β needed to achieve range resolutions of 1 m, 1 km,
and 100 km. What is the length of a rectangular pulse having this Rayleigh
bandwidth (peak-to-first null width of the Fourier transform) for each
value of resolution?

6. In terms of D and λ, what is the peak-to-first null beamwidth (called
y
Rayleigh beamwidth) in radians of the antenna pattern for an aperture
antenna with constant illumination? Give both the general result, and a

small-angle approximation.
7. How large must a uniformly illuminated aperture antenna be (value of D ) in
y
terms of wavelengths so that its 3-dB beamwidth is 1°? What is the
estimated gain in decibels of an antenna having azimuth and elevation
beamwidths θ = ϕ = 1°, based on the approximation in Eq. (1.10)?
3
3
8. Suppose a police “speed gun” radar has a rectangular antenna. It is desired
to have a cross-range resolution ΔCR of 10 ft at a distance of one-quarter
mile. What is the required antenna width in inches if the radar frequency is
9.4 GHz? Repeat for 34.4 GHz.

9. Continuing problem 8, what is the actual cross-range resolution in feet at
each RF if the antenna width is 6 in.?

10. Starting from Eq. (1.13) and setting a = 1, derive Eq. (1.14).
n
11. What is the maximum 3-dB beamwidth θ in degrees such that the
3
approximation for the cross-range resolution, Rθ , in the last step of Eq.
3
(1.26) has an error of no more than 1 percent?
12. Determine the cross-range resolution ΔCR in meters at ranges of 10, 100,
and 1000 km for a 3-dB beamwidth θ = 3°.
3
13. Determine the approximate size of a volume resolution cell in cubic meters,

ΔV, for R = 20 km, ΔR = 100 m, and θ = ϕ = 3°.
3
3
14. Suppose Eq. (1.31) is modified to consider the magnitude-squared of the
signal-plus-noise data:

Show explicitly that z cannot be expressed as the sum of a signal-only and
a noise-only term.

The remaining problems relate to topics covered in Appendix B.