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Cloud-radio access networks (C-RAN) help in overcoming the scarcity of radio resources by enabling dense deployment of base-stations (BSs) and connecting them to a central-processor (CP). This paper considers the downlink of a C-RAN, where the cloud is connected to the BSs via limited-capacity backhaul links. We propose and optimize a C-RAN transmission scheme that combines rate splitting, common message decoding, and beamforming vectors design and clustering. To this end, this paper optimizes a transmission scheme that combines rate splitting (RS), common message decoding (CMD), and clustering and coordinated beamforming. In this paper, we focus on maximizing the weighted sum-rate subject to per-BS backhaul capacity and transmit power constraints, so as to jointly determine the RS-CMD mode of transmission, the cluster of BSs serving private and common messages of each user, and the …