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This paper reports a measurement campaign carried out at 3.5 GHz to characterize the outdoor to indoor electromagnetic (EM) wave propagation penetration within buildings. A wideband channel sounder was used to collect the data using circular antenna arrays at both ends. The measurements are processed with a high resolution algorithm extracting the dominant paths. A ray-tracing based simulation tool is used to help on interpreting the collected data. The measurements show that for Non-Line of Sight situations, the diffraction of EM waves on the window frames plays an important role in the penetration inside the building.