In order to design advanced reentry vehicle window systems, both the interior and exterior electromagnetic field problems must be accurately analyzed. For phase i of this project, we propose to develop a theoretical method of analysis. This will include the effect of systems of windows, plus their internal microwave networks, on the radar cross section of the vehicle, as well as their antenna performance. We will first investigate single windows, and then systems of such windows, such as phased arrays. The proposed theoretical methods are applicable to low and intermediate frequencies through the method of moments, and to high frequencies through the physical theory of diffraction. The method of analysis to be used is that formulated in the paper "a generalized network formulation for aperture problems." this method is basically applicable to both low frequencies and high frequencies, but it has never been systematically applied to antenna and radar scattering problems. Antenna windows reentry vehicle radar cross section phased arrays diffraction frequency analy effect