  This paper deals with the problem of beamforming design in a multibeam
satellite, which is shared by different groups of terminals -clusters-, each
served by an Earth station or gateway. Each gateway precodes the symbols
addressed to its respective users; the design follows an MMSE criterion, and a
regularization factor judiciously chosen allows to account for the presence of
mutually interfering clusters, extending more classical results applicable to
one centralized station. More importantly, channel statistics can be used
instead of instantaneous channel state information, avoiding the exchange of
information among gateways through backhaul links. The on-board satellite
beamforming weights are designed to exploit the degrees of freedom of the
satellite antennas to minimize the noise impact and the interference to some
specific users. On-ground beamforming results are provided as a reference to
compare the joint performance of MMSE precoders and on-board beamforming
network. A non-adaptive design complements the results and makes them more
amenable to practical use by designing a coarse beamforming network.
