Page 151 - Fundamentals of Radar Signal Processing

(2.97)

The key result is that, to an excellent approximation, the pulse echoed from a
constant-velocity target exhibits a Doppler shift of 2vF/c = 2v/λ Hz and a phase
t
shift of –(1 + β )4π/λR radians.
v
0
The numerical values of Doppler shift are small compared to the RF
frequencies. Table 2.8 gives the magnitude of the Doppler shift corresponding to
a velocity of 1 m/s at various radar frequencies. The Mach 1 aircraft observed

with the L band radar would cause a Doppler shift of only 2.27 kHz in the 1
GHz carrier frequency.

TABLE 2.8 Doppler Shift Resulting from a Velocity of 1 m/s

For a monostatic radar and a constant-velocity target, the observed

Doppler shift is proportional to the component of velocity in the direction of the
radar, called the radial velocity. If the angle between the velocity vector
relative to the radar of a target traveling at v meters per second and the vector
from the radar position to the target position (sometimes called the cone angle)
i s ψ, the radial velocity is v · cosψ meters per second. The geometry is
illustrated in two dimensions in Fig. 2.25. The magnitude of the Doppler shift is
maximum when the target is traveling directly toward or away from the radar.

The Doppler shift is zero, regardless of the target velocity, when the target is
crossing orthogonally to the radar boresight.