Page 189 - Fundamentals of Radar Signal Processing

spectrum via a DTFT of the slow time signal in the appropriate range bin, the

blind Doppler and velocity intervals are F = 3 kHz and v = 45 m/s,
Db
b
respectively. The unambiguous Doppler shift and velocity are then 1.5 kHz and
22.5 m/s. The DTFT will be interpreted as covering [–1.5, +1.5) kHz and [–
22.5, +22.5) m/s. The target’s Doppler shift and velocity are outside of these
intervals and will therefore be aliased into them. With n = 2 in Eq. (3.8), it is
seen that the apparent Doppler and velocity are F = 0.67 kHz and v = +10
Da
a
m/s.
The PRF also sets a limit on the range swath. In particular, the maximum
range from which the end of the echo of one pulse can be received before the
next pulse is transmitted is the unambiguous range R . It must satisfy 2R /c + τ
ua
ua
< T, so

(3.9)

The approximation in the second line applies when T τ and is often cited as
the definition of R . The far edge of the sampled range swath (R in Fig. 3.1)
ua
2
must be limited to R m or less so the full pulse echo from a scatterer at R is
2
ua
received before the next pulse is transmitted.
In general, it is desirable to be able to choose the PRF to provide the
desired unambiguous range and Doppler bandwidth simultaneously. However,
unambiguous range increases with decreasing PRF, while the blind Doppler
interval increases with increasing PRF. Equations (3.7) and (3.9) can be
combined to make this explicit:

(3.10)

Because the right-hand side of either version of Eq. (3.10) is a constant for a
given RF, increasing R requires decreasing F or v . As a result, in many
Db
b
ua
situations it is not possible to simultaneously obtain the desired unambiguous
velocity interval and unambiguous range with a single PRF.
To illustrate the effect of the PRF on range measurements more fully,
consider the idealized signals of Fig. 3.6a. In the first line, a pulse is transmitted
at time t = 0. It is assumed that there are two targets present at ranges R and R ,
1
2
and that the PRF is such that the unambiguous range falls between these two.
The target echoes occur 2R /c and 2R /c seconds after transmission, as shown.
2
1
Now suppose a second pulse is transmitted at a PRI T = 2R /c. Assume τ T
ua