  In automotive radar applications, multiple radars are used in all vehicles
for improving the imaging quality. However this causes radar-to-radar
interference from neighbouring vehicles, thus reducing the imaging quality. One
metric to measure the imaging quality is ranging success probability. The
ranging success probability is the probability that a multiple radar system
successfully detects an object at a given range, under certain operating
conditions. In state-of-the-art literature, closed form expressions for ranging
success probability have been derived assuming no fading in desired signal
component. Similarly in literature, though distribution of fading in
interferers is assumed to be arbitrary, closed form expression is derived only
for no-fading assumption in interferers. As fading is always present in a
wireless channel, we have derived ranging success probability assuming desired
channel experiences the popular Rayleigh fading. And we have assumed
generalized $\kappa$-$\mu$ shadowed fading for interfering channels that
generalizes many popular fading models such as Rayleigh, Rician, Nakagami-$m$,
$\kappa$-$\mu$ etc. The interferers are assumed to be located on points drawn
from a Poisson point process distribution. We have also studied how the
relationship between shadowing component and number of clusters can affect the
impact of LOS component on ranging success probability.
