Abstract We consider the problem of designing transmit beamformers for a multi-carrier joint processing coordinated multi-point (CoMP) transmission with finite backhaul capacity. We assume a Cloud Radio access network (CRAN) wherein the beamformers are designed centrally, quantized and sent via the backhaul to the respective base stations (BSs). The beamformer design becomes a nonconvex combinatorial problem with the user selection, which is also modeled as a part of our problem. In order to avoid the combinatorial search, we relax the binary association variable by a linear one and the nonconvex sets by a sequence of convex subsets by the successive convex approximation (SCA) method. Thereby, we design the beamformers by iteratively solving a convex subproblem in each SCA iteration. Additionally, to enforce sparsity in the relaxed binary variable, we regularize the objective with the associated entropy measure to enforce a binary solution. Since the beamformers are notified via backhaul to the respective BSs, we include the beamformer overhead also in the backhaul usage in addition to data sharing. Numerical results are provided to illustrate the performance of the proposed designs.