Page 349 - Fundamentals of Radar Signal Processing

to implement if the interference statistics are known, it is difficult to interpret.

However, in the noise-limited case ( ), it reduces to

(5.29)

Equation (5.29) shows that in this case the optimum filter adds the two target
samples together with a phase correction to the second so that they add in phase.
In other words, the filter performs a coherent integration of the two target
samples.

5.2.4 Blind Speeds and Staggered PRFs
The frequency response of all discrete-time filters is periodic, repeating with a

period of one in the normalized cyclical frequency, corresponding to a period of
PRF = 1/T Hz of Doppler shift. Figure 5.9 illustrated this for the two- and three-
pulse cancellers. Since MTI filters are designed to have a null at zero
frequency, they will also have nulls at Doppler frequencies that are multiples of
the pulse repetition frequency. Consequently, a target moving with a radial
velocity that results in a Doppler shift equal to a multiple of the PRF will be
suppressed by the MTI filter. Velocities that result in these unfortunate Doppler
shifts are called blind speeds because the target return will be suppressed; the

system is “blind” to such targets. From a digital signal processing point of view,
blind speeds represent target velocities that will be aliased to zero velocity.
Equivalently, they correspond to Doppler shifts that will be aliased to zero
frequency.
For a given PRF, the unambiguous range is

(5.30)

The first blind speed is

(5.31)

The corresponding Doppler shift F simple equals the PRF. As the PRF is
b
increased for a given RF, the unambiguous range decreases and the first blind
speed increases. Figure 5.11 shows the unambiguous range-Doppler coverage
regions that are possible. For example, each point on the line marked “1 GHz”
represents a combination of R and v corresponding to some PRF. The dotted
b
ua
lines mark one example, corresponding to 400 m/s for the first blind speed and a
56.25 km unambiguous range. Equation (5.31) can be used to see that these