Page 178 - Fundamentals of Radar Signal Processing

single range bin. Develop a formula for the phase difference between the

two echoes in terms of δ, h, and the wavelength λ. If the amplitudes of the
direct and double-bounce reflections are the same (very unlikely), at what
values of h will there be a maximum total signal amplitude? At what values
of h will there be a null in the signal amplitude?

34. δR in the figure below is the maximum path length difference between a
constantrange path of length R over an integration angle θ and a straight-
line path of equal range R at the center of the integration angle. Find the
maximum integration angle θ such that δR ≤ λ/8. The answer will depend

on R. A path length difference of this amount would lead to an echo phase
change of –4πδR/λ = –π/2 radians, often used as an upper bound on the
tolerable phase error in various calculations.

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1 This ignores earth curvature effects that are significant in very long range or spaceborne radars. See
Nathanson (1991) or Skolnik (2001) for additional details.
2
A form of rain that occurs when moist air is lifted over an obstacle such as a mountain range, cooling as it
rises and condensing into rainfall.
3
RCS also varies similarly with angle over the full 3D sphere, not just in a 2D plane.
4
An unfortunate tendency in radar terminology is to use the name of the PDF of amplitude when actually
discussing the PDF of power. The most common example is to refer to a “Rayleigh RCS” target, or some
similar term. A target with an exponential PDF for RCS is almost certainly meant when this occurs. Caution
is advised to be certain as to whether a given PDF models amplitude or power.
5 2
Because the power P of a real sinusoid is related to its amplitude A according to P = A /2 instead of just P
2
= A as with a complex sinusoid, some authors present a slightly different form for the voltage distributions.
6
The autocorrelation function for any one many-scatterer target can vary significantly from the results
predicted by this analysis and the average shapes seen in Fig. 2.13; the expected value of the
autocorrelation must be estimated by averaging over many similar targets.
7 It is probably more common to define a constant-velocity target so that positive v corresponds to
increasing range, but the preference here is to define v so that a positive v gives a positive Doppler shift.