Page 355 - Fundamentals of Radar Signal Processing

(5.42)

2
where the notation |H (F)| indicates the power gain or attenuation of an N-
N, P
pulse canceller using P staggers when the input is a sinusoid of frequency F .
0
Generalizing the specific F to an arbitrary frequency F and renaming the
0
summation index gives the squared magnitude of the frequency response of the
two-pulse canceller with staggered PRIs

(5.43)

The actual frequency in hertz rather than normalized frequency is used in Eq.
(5.43) because the nonuniform sampling rate invalidates the usual definition of
normalized frequency. The response of more general MTI filters can be
obtained using a similar approach.

Figure 5.13a compares the frequency response of a two-pulse canceller
using two (P = 2) PRIs versus the reference baseline single-PRF system. The
staggered case uses PRIs of 4/3 ms and 1 ms (thus PRFs of 750 and 1000 pulses
per second). T = 1/3 ms, giving F = 3 kHz. The set of staggers k is {3, 4}. The
g
g
p
first blind Doppler shift F occurs at the least common multiple of 750 and
bs
1000 Hz, which is also 3000 Hz. The reference unstaggered PRF and blind
Doppler F , which is the reciprocal of the average PRI T = 7/6 ms, is 857.14
avg
b
Hz. The baseline unstaggered response collected using PRI = T shows blind
avg
Doppler frequencies at integer multiples of 857.14 Hz. Thus, staggering the PRF
has increased the blind Doppler frequency and thus the velocity and Doppler
coverage by a factor of 3.5 (= 3000/857.14) consistent with Eq. (5.38).