Spatial and temporal characteristics of received radio signals in a multiple user radio system can be estimated based on signals received from the users. In one embodiment, the invention includes collecting measurements of radio frequency signals received at different elements of an antenna system over time, the received signals corresponding at least in part to transmissions received from a system user, collecting representations of the transmissions of the system user, cross-correlating the collected measurements and the collected representations, and comparing the cross-correlation to the collected measurements to form a characterization of the radio channel traversed by transmissions of the system user.