A sensing system for a vehicle includes at least one radar sensor disposed at the vehicle and having a field of sensing exterior of the vehicle. The at least one radar sensor includes an antenna array having multiple transmitting antennas and multiple receiving antennas. Sensed radar data provides a data set of radar reflection responses for an object in the field of sensing of the at least one radar sensor, and the data set of radar reflection responses is compared to stored data sets representative of particular vehicle types. Responsive to the data set of radar reflection responses being determined to correspond to a stored data set, the sensing system classifies the detected object as that particular vehicle type.