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Multi-cell processing (MCP) is regarded as an effective way for interference mitigation in cellular networks. We propose a joint Base Station (BS) selection and linear precoding design algorithm for the downlink transmission in MCP enabled networks. The algorithm solves a regularized utility maximization problem to find a sparse solution for the precoding matrix. The BS selection is thus based on the sparsity pattern of the resulted precoding matrix. With the joint design, the proposed algorithm rigorously takes into account and optimizes the effect of BS selection on the overall system performance. The problem of total power minimization for target SINR, which can be cast as a Second Order Cone Program (SOCP) is used as an example for illustration. Simulation is performed to compare the proposed algorithm with the BS selection schemes in literature. It shows that our joint algorithm not only requires less power for target SINR, but also dramatically reduces the computational complexity.