In a previous work (Missaoui et al. in IEEE Wirel Commun Lett 6(2):150-153, 2017), we introduced a blind identification method of active users in multi-user MIMO systems, enabling to an estimation of their involved channels, with a resolution up to a discrete phase ambiguity. In this case, using exhaustive search algorithm, the phase ambiguity has been eliminated when both small numbers of colliding packets and receive antennas have been assumed. However, the exhaustive search is computationally infeasible for scenarios involving a relatively large number of receive antennas for MIMO and massive MIMO systems as one of the pivotal technologies for future wireless networks. To tackle this issue, in the current work, we propose an efficientt scheme to eliminate this phase ambiguity, based on both second-order cross-correlations of the signal flows received at the base station and blind channel estimates as obtained previously. Furthermore, to reduce the complexity of the proposed scheme, we use an iterative process to obtain a global phase ambiguity common to all receive antennas for each user. The aim is to make our solution applicable to practical systems with a large number of receive antennas and to easily eliminate this global phase ambiguity. Thus, we suggest two channel estimation and data detection approaches. In the first approach, which is blind, no pilot symbols are used, and the global phase ambiguity could be addressed using rotational-invariant coded modulations. In the second approach, which is semi-blind, only one pilot overhead symbol is needed to remove the common phase ambiguities. We show that our channel estimation and collision resolution scheme achieves a bit error rate (BER) performance which coincides with that of the single user with perfect channel state information knowledge.