In this contribution we deal with the problem of accurately identifying complex permittivities of dielectric objects placed on a conducting surface. Solutions to this problem are becoming increasingly crucial in sensing security scenarios in order to detect forbidden materials concealed on the human body. The proposed approach uses the matrix pencil method (MPM) as an efficient post-processing tool for spectral analysis of multiple frequencies at the millimeter-wave range. Unlike previously reported methods for permittivity discrimination based on multiple-frequency mm-wave SAR (synthetic aperture radar), our approach does not require multiple receivers. Moreover, those previous SAR-based techniques can only be applied to ideally lossless dielectric objects. Additionally, contrasting with previous methods based on the MPM, the work herein presented requires neither bulky transmission lines nor difficult time measurements on pulse delays. Representative examples based on full wave simulations are provided to show good accuracy for complex permittivity estimation.