A radar system for recording the environment of a motor vehicle includes transmission antennas for emitting transmission signals, receiver antennas for receiving transmission signals reflected by objects in the environment, and a signal processor for processing the received signals. The antennas are planar and are situated on a level surface. Received signals are acquired from different combinations of the transmitter and receiver antennas. In the signal processor, the angular position of objects in a spatial direction R is estimated from the received signals, based on recognition that the received signals from an individual object have different phase positions depending on the angular position of the object in the spatial direction R. Two of the transmitter and receiver antennas overlap in the spatial direction R without coinciding, by special arrangements or configurations of the transmitter and receiver antennas.