Radar Waveforms - MATLAB Simulations for Radar Systems Design - page 163

The Matched Filter 165

Figure 3.17 shows a synthesized range profile for a moving target whose
RCS is and . The initial target range is at . All
other parameters are as before. This figure can be reproduced using the MAT-
LAB program Ðfig3_17.mÑ given in Listing 3.4 in Section 3.12.

10 m 2 σ = v = 15 ms ⁄ R = 912 m

Figure 3.17. Synthesized range profile for a moving target (4 seconds long).

3.7. The Matched Filter
The most unique characteristic of the matched filter is that it produces the
maximum achievable instantaneous SNR at its output when a signal plus addi-
tive white noise is present at the input. The noise does not need to be Gaussian.
The peak instantaneous SNR at the receiver output can be achieved by match-
ing the radar receiver transfer function to the received signal. We will show
that the peak instantaneous signal power divided by the average noise power at
the output of a matched filter is equal to twice the input signal energy divided
by the input noise power, regardless of the waveform used by the radar. This is
the reason why matched filters are often referred to as optimum filters in the
SNR sense. Note that the peak power used in the derivation of the radar equa-
tion (SNR) represents the average signal power over the duration of the pulse,
not the peak instantaneous signal power as in the case of a matched filter. In
practice, it is sometimes difficult to achieve perfect matched filtering. In such