Page 357 - Fundamentals of Radar Signal Processing

shortest of the unambiguous ranges for each individual PRI

(5.44)

The unambiguous range for the reference unstaggered system is R = cT /2.
ua
avg
The ratio is

(5.45)

which is 6/7 for this example, about a 14 percent reduction. The increase in the
total range-Doppler coverage is the product of Eqs. (5.38) and (5.45),

(5.46)

For mutually prime staggers, lcm({1/k }) = 1 and this reduces to simply
p
min[{k }], equal to a factor of three in the example above. Thus, the use of two
p
PRIs with a 3:4 stagger ratio has reduced the unambiguous range by 14 percent,
but has expanded the Doppler coverage by 350 percent and the combined range-
Doppler coverage by 300 percent.

Figure 5.13b illustrates the frequency response obtained using Tg = 100 μs
and five mutually prime staggers in the ratio 51:62:53:61:58 with a two-pulse
5
canceller. Only the staggered response is shown; the equivalent unstaggered
response would have nulls every 175.4 Hz. The insert expands the power
spectrum around zero Doppler shift to make the clutter null more visible. The

first blind Doppler shift is at 10 kHz, a 57× increase as expected from Eq.
(5.38). The unambiguous range reduction is 10.5 percent. The combined range-
Doppler coverage is increased by 51×.
Additional examples, special cases suited to weather radar, and the use of
both infinite impulse response (IIR) filters and time-varying filters for MTI are
discussed in Shrader and Gregers-Hansen (2008). An alternative design
approach based on randomized PRIs to extend the blind speed is discussed in

Vergara-Domingues (1993).

5.2.5 MTI Figures of Merit
The goal of MTI filtering is to suppress clutter. In doing so, it also attenuates or
amplifies the target return, depending on the particular target Doppler shift. The
change in signal and clutter power then affects the probabilities of detection and