The multi-beam broadband satellite systems have been deployed to provide broadband services to their under-served geo-graphical area. In one hand, with assuming full frequency reuse among beams the resulting interference requires either a pre- or post-cancellation process. On other hand, by increasing the number of beams, the ground and space units must employ an extensive communication e ort on the feeder link (i.e. the link between gateway and satellite) to exchange all of the feed signals, yet maintaining a low processing responsibility to the payload. Since the feeder link spectral resources are scarce, it is desirable to use an on-board beam generation process which leads to a signi cant feeder link bandwidth reduction. In this context, a hybrid space/ground processing (i.e. both the gateway and the satellite digitally process the transmitted/received data) shall be employed. This work presents a design of the corresponding on-board beam generation process and precoding in the forward link (i.e. from gateway to users in coverage area) of satellite system. In order to e ective limit inter-beam interference, this work also predicts a zero forcing precoding technique taking into account the per feed power constraint for practi- cal issues. To this end, we formulate the precoding problem with considering individual on-board feed in order to e cient and more realistic use of payload power resources. This is done by considering the zero forcing and its relation to the theory of generalized inverse in the linear algebra.

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