Broadband multibeam satellites may require very high feeder link bandwidths to relay all the signals to a unique gateway. This is the case if they enforce an aggressive spectrum reuse across all the user beams and the overall capacity increases accordingly. If the processing is split among different gateways, then the inter-gateway interference must be counteracted to provide acceptable quality of service. In this paper, we propose to blindly estimate the covariance matrix of the received signals at each gateway, and then perform minimum mean-squared error combining based on that estimate and on the subset of channel responses that the gateway can get to learn. Results show that, even with no collaboration among the gateways, significant throughput increases are achieved with respect to a traditional scenario with partial frequency reuse, at the cost of degraded availability levels.