Page 344 - Fundamentals of Radar Signal Processing

(5.11)

Finally, the filtered data become, using

(5.12)

Equation (5.11) is of fundamental importance and great versatility in signal
processing generally and radar signal processing in particular. It will be used in
this text not only for clutter filtering and pulse Doppler processing, but also for
space-time adaptive processing, detection, and estimation.

5.2.3 Matched Filters for Clutter Suppression
The results of the previous section can now be applied to N-point (order N – 1)

MTI filters that are more optimal than the N-pulse canceller. Equation (5.11)
shows that the linear filter that optimizes detection performance in the presence
of additive interference is the FIR matched filter, and that the coefficients of the
filter are given by the matrix equation

(5.13)

where h = N × 1 column vector of filter coefficients
S = N × N covariance matrix of the interference
I
N × 1 column vector representing the desired target signal to which
t =
the filter is matched

and the asterisk denotes the complex conjugate.
To determine the optimal filter coefficients h, models are needed for the
interference and target characteristics, S and t. For a simple example, consider
I
the first-order (length N = 2) matched filter. Assume the interference w[m]
consists of the sum of zero mean stationary white noise n[m] of power
(variance) and zero mean stationary colored clutter c[m] of power

(5.14)

The clutter exhibits a correlation from one pulse to the next given by
the first normalized