In Long-Term Evolution (LTE) by the 3rd Generation Partnership Project (3GPP), the Radio Access Network (RAN) is totally optimized for packet-oriented applications with low latency and high-peak rates. In order to guarantee that the packets are correctly delivered to the upper layers, LTE employs a combination of ARQ (Automatic Repeat Request) and FEC (Forward Error Correction), also known as Hybrid-ARQ, which must be fed back to a base station (e.g. eNodeB). In the uplink, the uplink control channel, called the physical uplink control channel (PUCCH), is associated with the transmission of CQI, Hybrid-ARQ acknowledgements and scheduling requests (SR). Within the PUCCH, multiple UEs can share the same time-frequency resources, the UEs being multiplexed via code division multiplexing (CDM) in the frequency domain and in the time domain, simultaneously. For CQI information, CDM is achieved by cyclically shifting a code exhibiting a constant amplitude zero autocorrelation (CAZAC) property. This is based on the fact that the cross-correlation is null among cyclically shifted CAZAC codes.
However, it has been demonstrated that orthogonality between CAZAC codes can be lost in OFDM systems such as LTE, which are sensitive to timing offset or timing error. The timing offset causes a linearly growing phase error within OFDM symbols.