Channel estimation in a MIMO communications system includes performing a decomposition of an initial channel matrix estimate associated with a first subcarrier of a plurality thereof defined in the channel to identify eigenvectors associated with that subcarrier of the received signal, and defining a first beamforming transformation to be applied to the received signal on the basis of the eigenvectors. For each of the other subcarriers, an additional decomposition is performed in order to determine a further beamforming transformation for each subcarrier. The additional decompositions are carried out incrementally such that information determined in one of said decompositions contributes to a later executed decomposition. Further described is a method of transmitting from a multiple antenna transmitter defining a plurality of subcarriers in space, and time or frequency, comprising the same iterative process. Transmission can be carried out using smoothed beamforming applied in accordance with aspects of the invention.