  We propose an analytical framework based on stochastic geometry (SG)
formulations to estimate a radar's detection performance under generalized
discrete clutter conditions. We model the spatial distribution of discrete
clutter scatterers as a homogeneous Poisson point process and the radar
cross-section of each extended scatterer as a random variable of the Weibull
distribution. Using this framework, we derive a metric called the radar
detection coverage probability as a function of radar parameters such as
transmitted power, system noise temperature and radar bandwidth; and clutter
parameters such as clutter density and mean clutter cross-section. We derive
the optimum radar bandwidth for maximizing this metric under noisy and
cluttered conditions. We also derive the peak transmitted power beyond which
there will be no discernible improvement in radar detection performance due to
clutter limited conditions. When both transmitted power and bandwidth are
fixed, we show how the detection threshold can be optimized for best
performance. We experimentally validate the SG results with a hybrid of Monte
Carlo and full wave electromagnetic solver based simulations using finite
difference time domain (FDTD) techniques.
