In 3rd generation partnership project (3GPP) long term evolution (LTE) systems, when no resources has been assigned in the uplink to a given user equipment (UE), the control information associated with layers 1 and 2 in the protocol stack is conveyed back to the base station through the so-called physical uplink control channel (PUCCH). In PUCCH, the data streams transmitted by multiple UEs are multiplexed in the time-domain and in the frequency-domain with the aid of spreading codes. Although the spreading codes associated with UEs within the same cell can be assumed to be orthogonal, the presence of inter-cell interference (ICI) in multi-cell scenarios severely limits receiver performance. In particular, the Format 1 of PUCCH, which is associated with the transmission of hybrid automatic repeat request acknowledgements (ACK/NACK) and scheduling requests, has a major impact on system performance, since an incorrectly decoded ACK/NACK message may introduce significant delay in data transmission. In this contribution, we propose a new multi-user receiver for ICI reduction in PUCCH LTE that operates both in cooperative and non-cooperative multi-cell architectures. The proposed receiver relies on a constrained tensor modeling of the received signal in PUCCH signaling, and affords an iterative joint channel estimation and symbol detection by simultaneously exploiting the energy of the data symbols and the pilot tones present in PUCCH. The formulation of the proposed algebraic receiver model incorporates symbol-basis hopping and slot-basis hopping signaling schemes, which are interference randomization techniques existing in the 3GPP specifications of LTE system. Computer simulation results show the remarkable performance gains of the proposed receiver compared to the conventional time-frequency decorrelator based receiver.