High throughput satellite systems are expected to rely in the user link on multi-beam architectures with small beam footprints and strong frequency reuse among beams, and will therefore operate in an interference limited regime. In this paper, the focus is set on the forward link of a multi-beam broadband satellite system, and linear precoding is considered to mitigate this increased level of interference among users. The contribution of the present work is twofold. First, assuming a single gateway scenario, we analytically prove the benefit of considering the precoding in the feed space, that is, not considering the presence of on-board beamforming. Second, for taking into account realistic feeder link bandwidth restrictions, we consider a multiple gateways scenario where each gateway is serving a cluster of adjacent cells. We propose an architecture which includes precoding in the feed space at each gateway, and derive a zero-forcing precoder design which mitigates both the inter and intra-cluster interfere ce.