Log-Likelihood Ratio Calculation for Pilot Symbol Assisted Coded Modulation Schemes with Residual Phase Noise

This paper presents a novel log-likelihood ratio (LLR) calculation for high order coded modulation schemes over an additive white Gaussian noise channel at the presence of residual phase noise (RPN). Residual phase noise is known to significantly degrade the error rate performance of such systems, particularly at lower error rates, resulting in an early error floor. To model RPN, we consider the commonly used pilot symbol assisted modulation schemes for carrier recovery. We derive the exact formula for the calculation of LLR for such systems. To simplify the implementation, we also derive an approximation of LLR which reduces the complexity significantly with almost no loss in performance. The simulation results are presented for coded modulation schemes based on quadrature amplitude modulations and low-density parity-check codes. The simulations demonstrate significant performance improvement in the error rate as a result of using the new LLR calculation instead of the conventional calculation of LLR which ignores the RPN