Page 152 - Fundamentals of Radar Signal Processing

FIGURE 2.25 Doppler shift is determined by the radial component of relative
velocity between the target and radar.

Equations (2.86) and (2.87) can be solved for the exact behavior of other
regular patterns of radar-target motion as well. The solution for constant
acceleration is given in Gray and Addison (2003). Even where a closed form
solution for h(t) is difficult or impossible to find, it can still be developed using
an iterative approximation approach.

2.6.2 The Stop-and-Hop Approximation and Phase History
The quasi-stationary assumption of Eq. (2.88) provides a simplified but very
useful model of reflection of a radar pulse from a target moving relative to the
radar. Applying it to the pulsed waveform A(t)exp[j(2πFt + ϕ )] and using the
t
0
same envelope approximations employed to obtain Eq. (2.97) gives

(2.98)

where R is the initial range at the time of pulse transmission. Equation (2.98)
0
states that the echo is received with a time delay corresponding to the range at

the beginning of the pulse transmission but with a phase modulation related to
the time variation in range. This is the “stop” part of the stop-and-hop
assumption common in radar analysis: the envelope of the echo appears as if the
target motion effectively stopped while the pulse was in transit. The “hop”