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 measuring 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, accumulating the signal measurements into a first matrix, generating a second matrix representing the transmissions of the system user, cross-correlating the first and second matrices to form a third matrix, and multiplying the third matrix with a product of the second matrix to form a fourth matrix in which the elements of the fourth matrix characterize the radio channel traversed by transmissions of the system user.