Page 354 - Fundamentals of Radar Signal Processing

1970; Levanon, 1988; Schleher, 2010).

A constant-PRI system with PRI T transmits pulse #m in an N-pulse
sequence at time t = mT, m = 0,…, N – 1. In a P-stagger system, the sequence
m
of sampling times {t } is
m

(5.39)

The notation ((·)) denotes evaluation of the argument modulo P. Note that the
P
{T } are the sampling time increments, not the absolute sampling times, and that
p
t – t m–1 = T ((m–1))P . The slow-time phase history of Eq. (5.21) for a constant PRI
m
and constant-velocity target is easily generalized to the following form for a
staggered PRI system:

(5.40)

4
Now consider the two-pulse canceller network of Fig. 5.8a. Using Eqs. (5.39)
and (5.40), the output z[m] = y[m] – y[m – 1] can be written explicitly as

(5.41)

The magnitude of the frequency response for the sampling + filter system
can be defined as the square root of the ratio of the power of the filter output
sequence to that of the input sequence. The power of each input sample is |y[m]| 2

= |k| . The power of the output samples |z[m]| depends on the index m due to the
2
2
varying PRIs. The average output power is therefore computed over one cycle
of the staggered PRIs. The sum from m = 0 to P – 1 of T ((m–1))P is the same as the
sum of T so the expression for the squared magnitude of the average two-pulse
m
canceller filter frequency response becomes