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Conventional multibeam satellite communications systems ensure coverage of wide areas through multiple fixed beams where all users inside a beam share the same bandwidth. The authors consider a new and more flexible system where each user is assigned his own beam, and the users can be very geographically dispersed. This is achieved through the use of a large direct radiating array coupled with adaptive beamforming so as to reject interferences and to provide a maximal gain to the user of interest. New fast-converging adaptive beamforming algorithms are presented, which allow one to obtain good signal to interference and noise ratio with a number of snapshots much lower than the number of antennas in the array. These beamformers are evaluated on reference scenarios.