## Abstract

Complex radar targets are often modeled as a number of individual scattering elements randomly distributed throughout the spatial region containing the target. While it is known that as the number of scatterers grows large, the distribution of the scattered signal power or intensity is asymptotically exponential, this is not true for a small number of scatterers. We study the statistics of measured power or intensity, and hence scattering cross section, resulting from a small number of constant amplitude scatterers, each having a random phase. We first derive closed form expressions for the pdf of the scattered signal inte.nsity, and then use an orthonormal series expansion for the pdf in terms of exponentially-weighted. Laguerre polynomials when the number of scatterers is larger than 3. For the multilook case, an orthogonal series expansion in terms of Gamma-weighted generalized Laguerre polynomials is us'ed to approximate the pdf. The results of the Kolmogorov-Smirnov goodness-of-fit test show that the se:ries expansions are a good fit to the actual pdfs.

## Date of this Version

7-1-1994