Page 65 - Fundamentals of Radar Signal Processing

(1.32)

The phase correction aligns the signal component phases so that they add
coherently. The noise phases are still random with respect to one another. Thus,
2 2
the integrated signal power is again N A , while the integrated noise power is
again , and therefore an integration gain of N is again achieved.
Compensation for the phase progression so that the compensated samples add in

phase is an example of phase history modeling: if the sample-to-sample pattern
of target echo phases can be predicted or estimated (at least to within a constant
overall phase), the data can be modified with a countervailing phase so that the
full coherent integration gain is achieved. Phase history modeling is central to
many radar signal processing functions and is essential for achieving adequate
gains in SNR.
In noncoherent integration, the phases are discarded and some function of

the magnitudes of the measured data samples are added, such as the magnitude,
magnitude-squared, or log-magnitude. If the magnitude-squared is chosen, then z
is formed as

(1.33)

The important fact is that phase information in the received signal samples is
discarded.
The first line of Eq. (1.33) defines noncoherent square-law integration. The
next two lines show that, because of the nonlinear magnitude-squared operation,
z cannot be expressed as the sum of a signal-only part and a noise-only part due

to the presence of the third term involving cross-products between signal and
noise components. A similar situation exists if the magnitude or log-magnitude
is chosen for the noncoherent integration. Consequently, a noncoherent
integration gain cannot be simply defined as it was for the coherent case.
It is possible to define a noncoherent gain implicitly. For example, in
Chap. 6 it will be seen that detection of a constant-amplitude target signal in