An Innovative Semiparametric Density Model for the Statistical Characterization of Ground-Vehicle Radar Cross Sections

Accurately characterizing the statistical fluctuations of vehicle radar cross sections (RCSs) across polarization states and azimuthal sectors is essential for evaluating detection performance, conducting probabilistic simulations, and analyzing target features in millimeter-wave radar systems. Existing one-dimensional RCS statistical models, including Weibull, Chi-square, Lognormal, Rice, and Gaussian distributions, are often limited by their restricted functional expressiveness, making it difficult to simultaneously capture skewness, tail thickness, and azimuthal dependence under narrow angular-domain conditions. In addition, purely nonparametric approaches tend to produce spurious modes under finite-sample conditions and lack interpretable structural priors. To address these limitations, this paper proposes a Unimodal RCS Semiparametric Density Estimator (URCS-SDE) tailored for ground-vehicle targets. The proposed approach adopts kernel density estimation (KDE) as a data-driven baseline representation and incorporates physically plausible structural constraints through unimodal shape projection. Then a beta-type tail template is further introduced in the normalized amplitude domain to regulate boundary decay behavior. Finally, weighted least-squares calibration is performed on the histogram grid of the empirical probability density function (PDF), achieving a balanced trade-off between fitting accuracy and stability in both the peak and tail regions. Using multi-azimuth RCS measurements of two representative ground vehicles, the URCS-SDE is systematically compared with five classical parametric distributions and a representative regularized mixture density network (MDN) baseline. Performance is evaluated under both full-azimuth and directional-window conditions using the sum of squared errors (SSE), root mean squared error (RMSE), coefficient of determination (R-square) and held-out negative log-likelihood (NLL). The results show that the URCS-SDE consistently provides the most accurate and stable density estimates, especially in narrow angular windows. In addition, a threshold-based detection-support example derived from the fitted PDFs demonstrates that the advantage of the URCS-SDE transfers from density reconstruction to a directly engineering-relevant downstream quantity.