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In single-carrier frequency-division multiple-access (SC-FDMA) receivers in the long-term evolution uplink, phase noise is one of the major radio-frequency front-end impairments that degrade system performance. To address this issue, we propose a new log-likelihood ratio (LLR) computation algorithm. A signal model with residual phase noise is considered in the algorithm. Based on this model, we derive a closed-form expression of the likelihood function of the received symbol and calculate more accurate LLR information. Thus the accuracy of the decoder is increased and the performance of the SC-FDMA system is improved. Simulation results show that our proposed algorithm achieves superior bit error rate (BER) performance compared with the existing LLR calculation algorithms in high-order quadrature amplitude modulations (QAM).