Page 469 - Fundamentals of Radar Signal Processing

For large values of x, ; then

(6.56)

The constant term on the right of Eq. (6.56) can be incorporated into the
threshold in Eq. (6.44), while the linear term in x quickly dominates the
logarithmic term for x 1. This leads to the linear detector approximation for

large x

(6.57)

Figure 6.9 illustrates the fit between the square law and linear approximations
and the exact ln[I (·)] functions. The square law detector is an excellent fit for x
0
< 3 dB, while the linear detector fits the ln[I (x)] very well for x >10 dB.
0

FIGURE 6.9 Approximation of the ln[I (·)] detector characteristic by the square
0
law detector when its argument is small, and the linear detector when its
argument is large.

Finally, note that it is easy enough to compute the squared magnitude of a
complex-valued test sample as simply the sum of the squares of the real and