Page 480 - Fundamentals of Radar Signal Processing

FIGURE 6.11 Effect of noncoherent integration on detection performance for a
nonfluctuating target in complex Gaussian noise as a function of single-sample
SNR.

6.3.3 Albersheim’s Equation
The performance results for the case of a nonfluctuating target in complex

Gaussian noise are given by Eqs. (6.79) and (6.86). While relatively easy to
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implement in a modern software analysis system such as MATLAB , these
equations do not lend themselves to manual calculation. Fortunately, there does
exist a simple closed-form expression relating P , P , and SNR c that can be
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computed with simple scientific calculators. This expression is known as
Albersheim’s equation (Albersheim, 1981; Tufts and Cann, 1983).
Albersheim’s equation is an empirical approximation to the results in
(Robertson, 1967) for computing the single-sample SNR χ required to achieve
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a given P and P . It applies under the following conditions:
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• Nonfluctuating target in Gaussian (i.i.d. in I and Q) noise
• Linear (not square-law) detector
• Noncoherent integration of N samples

The estimate is given by the series of calculations