Page 406 - Fundamentals of Radar Signal Processing

the target signals become the dominant components. Subsequent finite

wordlength processing will adapt the dynamic range to the targets rather than the
now-suppressed clutter. In the increasingly common floating point processors,
dynamic range is less of an issue.

5.5.2 Transient Effects
All of the discussion in this chapter has assumed a steady-state scenario in the
sense that the clutter spectrum is stationary and that filter transient effects have

been ignored. In range-ambiguous medium and high PRF modes the received
signal sample in each range bin contains contributions from multiple ranges
because of the multiple contributing pulses. Whenever the radar PRF changes
several pulses, known as clutter fill pulses, they must be transmitted before a
steady-state situation is achieved. Here “steady state” means that the physical
clutter intervals contributing to a given range bin are the same for each pulse so
that the clutter statistics can be expected to be stationary from one pulse to the

next. For example, suppose that in steady state each range gate contains
significant contributions from L = 4 pulses (four range ambiguities). Then the
clutter signature in each range bin will reach a steady-state condition only for
the fourth and subsequent pulses in a CPI. This issue was first discussed in
Chap. 4.
Steady-state operation of the digital filters used for MTI processing occurs

when the output value depends only on actual data input values rather than any
initial (typically zero-valued) samples used to initialize the processing. For FIR
filters of length N, the first and last N – 1 samples of the complete convolution
are transient in the sense that the filter impulse response does not fully overlap
the finite data sequence. These transient output samples are often discarded.
These two effects are independent. To see how many pulses are needed in
total to obtain an M-point non-transient, steady-state sequence y [m], consider
ss
Fig. 5.34. Assume P total pulses are transmitted. This sketch assumes L = 4
range ambiguities and a three pulse canceller (N = 3) MTI filter, but is labeled
for general L and N. The notional data sequence y[m] is shown as ramping up in
amplitude over the first L samples. While actual data would vary unpredictably
depending on the clutter scenario, this represents the increasing number of range
ambiguities present in each sample, stabilizing at four when m = 3 (the fourth

sample). Recall that the convolution of h and y is given by y [n] = Σ y[m]h[n –
ss
m]. The three-sample sequence in the figure represents the three-pulse canceller
filter coefficients h[n – m]. (The actual coefficient values would be {+1, –2,
+1}). It can be seen from the figure that in general the first value of n for which
the filter coefficients will overlap only with steady-state measured data occurs
when L – 1 = n – N + 1, i.e. n = L + N – 2 (n = 5 in this example). The last value
for which this is true occurs when n = P – 1. The number of output samples in

this interval is M = (P – 1) – (L + N – 2) + 1. Therefore, P = M + L + N – 2
pulses are needed to obtain M valid outputs for further processing.