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Limited feedback techniques, that employ codebook-based quantisation, are used in coordinated multi-point (CoMP) transmission to convey the channel direction information between the mobile user and each base station in the cooperative set and also among the cooperating base stations. However, unlike single-cell multiple-user multiple input multiple output (MU-MIMO) systems, CoMP systems face additional challenges in this codebook design. Among these challenges are the huge feedback overhead and the need for dynamic codebook size. These problems are solved when CoMP uses the so-called per-cell codebook, in which the channel to each cell is quantised separately. However, this results in a further problem, that is having random phase values between the quantised per-cell channels of the same user. In this study, the phase ambiguity problem is explained and its effect on performance degradation is quantified. A new quantisation technique is proposed where the quantisation of each of the real and the imaginary parts is performed independently using the same real codebook. This novel solution prevents the phase ambiguity problem instead of trying to mitigate its effects, in addition to simplifying the codebook design. The proposed quantisation technique outperforms two recently introduced solutions in the literature. The first solution is to quantise phase ambiguity as part of channel state information (CSI), whereas the other avoids phase ambiguity by an iterative selection procedure. Mathematical validations and simulations are provided to verify these findings.