Page 479 - Fundamentals of Radar Signal Processing

(6.84)

and the PDF of z′ is 13

(6.85)

P is found by integrating Eq. (6.85). One version of the result is (Meyer
D
and Mayer, 1973)

(6.86)

Note that the summation term in the second line of Eq. (6.86) only contributes
when N ≥ 2. Equations (6.79) and (6.86) define the performance achievable for
a nonfluctuating target with noncoherent integration using a square law detector
(Meyer and Mayer, 1973; DiFranco and Rubin, 1980).
Figure 6.11 shows the effect of the number of samples noncoherently
–8
integrated, N, on the receiver operating characteristic when P = 10 . This
FA
figure shows that noncoherent integration reduces the required single-sample
SNR required to achieve a given P and P , but not by the factor N achieved
FA
D
with coherent integration. For example, consider the single-sample SNR
required to achieve P = 0.9. For N = 1, this is 14.2 dB; for N = 10, it drops to
D
6.1 dB, a reduction of 8.1 dB, but less than the 10 dB that corresponds to the
factor of 10 increase in the number of pulses integrated. This reduction in

required single-sample SNR is called the noncoherent integration gain.