A sensor module configured to be located behind a window of a vehicle to detect an object through the window and about the vehicle. The module includes a radar unit with an antenna and a controller. The antenna emits and/or receives a radar signal through the window with a selected or preferred polarization. The polarization determines a preferred angle of propagation of the radar signal through the window based on reflection characteristics of the window that vary with impingement angle and transmitted polarization. By varying the transmitted polarization vs. beam direction when a directional antenna is used, the signal propagating through the windshield can be maximized to enhance object detection over a range of signal directions. Also, by varying the transmitted polarization when an omnidirectional type antenna is used, the object can be ‘illuminated’ with variable intensity and detected with variable sensitivity.