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, and comparing the representations to the collected measurements to form a spatial characterization of the radio channel traversed by transmissions of the system user in which the elements of the spatial characterization represent forming a beam in the direction of the system user and directing nulls to interferers.