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A ground penetrating radar (GPR) system for identifying the shallow subsurface dielectric properties is proposed. It consists in a stepped frequency continuous wave (SFCW) radar operating in the 0.8-4 GHz ultrawide band combined with a dielectric filled TEM horn antenna to be used off ground in monostatic mode. This radar configuration is of practical interest since it responds to subsurface mapping requirements and allows for an efficient and realistic modeling of the radar-antenna-subsurface system. Forward modeling of the system is based on linear system response functions and on the exact solution of the three-dimensional Maxwell equations for damped wave propagation in a horizontally multilayered medium representing the shallow subsurface. The model is validated under controlled laboratory conditions. This model is destined to be inverted to reconstruct the depth dependent shallow subsurface dielectric properties from field observations.