Signal processing in satellite applications is usually performed either on-ground or on-board, i.e. at the gateway station or in the payload. Within the framework of the European Space Agency (ESA) SatNEx III study, a hybrid approach has been considered by splitting the processing between the satellite and the gateway, aiming to strike a better balance between performance and payload complexity. The design of a highcapacity multi-beam system has been carried out, to assess the potential applicability of a hybrid space-ground processing architecture (DIGISAT) for satellite broadband systems; this is achieved via hybrid space-ground beamforming, MIMO and MIMO-MUD, Precoding, as well as Digital Feeder link techniques. ; Peer Reviewed ; Postprint (published version)