Page 485 - Fundamentals of Radar Signal Processing
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(6.94)
where p (χ) is the PDF of the SNR.
χ
For the Swerling 1 model the PDF of the SNR is exponential:
(6.95)
where is the mean value of the SNR. Using Eqs. (6.93) and (6.95) in Eq.
(6.94) gives the characteristic function averaged over the signal fluctuations:
(6.96)
The N = 1 and N > 1 cases are best handled separately. For N = 1 the CF
simplifies to just . The inverse is the PDF of z′ under
hypothesis H for Swerling case 1 and N = 1,
1
(6.97)
The inverse of the more general CF for N > 1 of Eq. (6.96) is the PDF
(6.98)
Integrating the PDF of Eqs. (6.97) and (6.98) from the threshold T to + ∞ leads
to the following expression for the probability of detection in the Swerling 1
case (Meyer and Mayer, 1973):
(6.99)
