Since Release 8 Long-Term Evolution (LTE) by the 3rd Generation Partnership Project (3GPP), the uplink control channel called the physical uplink control channel (PUCCH) is specified. In this paper, we propose a new multi-user joint receiver processing for LTE PUCCH that counteracts the intra-cell interference (ICI). Using the fact that the received signal in PUCCH signaling follows a constrained tensor model, a multi-user receiver based on an iterative joint channel/code estimation and symbol detection is proposed. The interest in such a challenging setting relies on the overhead reduction synchronization errors defined by time offset and inaccuracies of timing align. Simulation results show remarkable performance gains of the proposed receiver compared to the conventional time-frequency decorrelator based receiver under the same conditions.