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Coordinated multi-point (CoMP) transmission is a promising technique for improving spectral efficiency of full frequency reuse cellular systems. However, its performance will be severely degraded if the feedback strategies are not carefully designed for providing channel information through limited uplink resources to the coherently cooperated base stations. In this paper, we study per-cell codebook based limited feedback scheme, which is highly desirable for CoMP systems due to its scalability and flexibility. Specifically, we investigate the issues related to phase ambiguity (PA), which comes from the per-cell codebook structure. We first analyze how many bits are required for the PA feedback to ensure an allowed performance loss. We then propose an adaptive bit allocation algorithm to divide a given amount of feedback bits between the per-cell codebooks for single-cell channel direction quantization and a codebook for PA quantization, aiming at minimizing the average global channel direction quantization error. Finally we provide a scaling law of the number of feedback bits per-user when the bit allocation algorithm is used. Simulation results show that the proposed bit allocation algorithm significantly improves the throughput of coherent CoMP systems either with equal number or different number of antennas at each base station.