Page 236 - Fundamentals of Radar Signal Processing

FIGURE 4.5 Composite matched filter response due to two scatterers separated
by cτ/2 meters: (a) target responses in phase, (b) target responses 180° out of

phase.

Scatterers that are closer together than the Rayleigh resolution may still be
resolved if the spacing is such that the individual responses add out of phase.
Figure 4.5b illustrates the case where the two responses differ in phase by 180°.
Destructive interference in the region of overlap causes a deep null in the
composite response. However, this null is very sensitive to the fine spacing of
the scatterers and cannot be relied on to resolve two targets.

4.3 Matched Filtering of Moving Targets

Suppose a simple pulse is transmitted, x(t) = 1, 0 ≤ t ≤ τ, and it echoes from a
target moving toward the radar with a radial velocity of v meters per second.
After demodulation, the received waveform (ignoring the overall time delay)
will be x′(t) = x(t)exp(jΩ t), with Ω = 4πv/λ. Because the echo is different
D
D
from x(t), a filter matched to x(t) will not be matched to x′(t). If the target
velocity is known, the matched filter for x′(t) can be constructed:

(4.23)

The frequency response of this matched filter is