Page 250 - Fundamentals of Radar Signal Processing

FIGURE 4.13 (a) Pulse burst waveform, M = 3, (b) matched filter output.

(4.59)

where the last step uses s (mT) = 0 when T > τ. In this equation E is the energy
p
p
in the single pulse x (t), while E is the energy in the entire M-pulse waveform.
p
Note that the peak response is M times that achieved with a single pulse of the
same amplitude. Recall the radar range equation signal processing gain factor
G of Eq. (2.85). The increase in the matched filter output peak for the pulse
sp
burst waveform represents a coherent signal processing gain of a factor G = M
sp
that will improve the SNR compared to a single-pulse waveform, aiding
detection probability and measurement precision.

4.5.2 Pulse-by-Pulse Processing
The structure of Eq. (4.58) suggests that it is not necessary to construct an
explicit matched filter for the entire pulse burst waveform x(t), but rather that
the matched filter can be implemented by filtering the data from each individual
pulse with the single-pulse matched filter and then combining those outputs. This
process, called pulse-by-pulse processing, uses separable two-dimensional

processing in fast time and slow time. It provides a much more convenient
implementation and is consistent with how pulse burst waveforms are processed
in real systems.
Define the matched filter impulse response for the individual pulse in the
burst, assuming T = 0
M

(4.60)

The output from this filter for the mth transmitted pulse, assuming a target at
some delay t , is
l

(4.61)

Assume that the echo from the individual pulse matched filter for the first pulse
(m = 0) is sampled at t = t ; that value will be y (tl) = sp(0). Now sample the
l
0
filter response to each succeeding pulse at the same delay after its transmission