Page 490 - Fundamentals of Radar Signal Processing

The analytic results in Table 6.1 are too complex for “back-of-the-envelope”

calculations or even for calculation on programmable calculators. Albersheim’s
equation provided a simple approximation for the nonfluctuating target case, but
it is not applicable to fluctuating targets in general or the Swerling models in
particular. This is a serious limitation since the nonfluctuating case provides
overly optimistic results for most parameter ranges of interest.
Fortunately, empirical approximations have also been developed for the

Swerling cases. One example is Shnidman’s equation (Shnidman, 2002).
Similar to Albersheim’s equation, this series of equations gives the single-pulse
SNR χ required to achieve a specified P and P with noncoherent integration
D
1
FA
of N samples. Unlike Albersheim’s equation, the results are for a square law
detector. However, as noted previously the differences in the required SNR for
linear and square-law detectors are typically no more than 0.2 dB.
Shnidman’s equation is given by the following series of calculations:

(6.109)

(6.110)

(6.111)