Performance analysis of code-aided iterative carrier phase recovery in turbo receivers

Code-aided (CA) iterative carrier phase synchroniser can greatly improve the accuracy of phase estimation in turbo receivers. However, because of the iteration involved between phase recovery and decoding, most existing studies depend on extensive simulations rather than on theoretical analysis to evaluate the performance improvement of phase recovery by exploiting the coding constraints. In this study, the authors propose analytical methods to fill this void. The first step is to approximate the cross-talks caused by phase offset as Gaussian noise at low signal-to-noise ratios. Then, a semi-analytical method is proposed to express the distribution of extrinsic information from channel decoder as a function of phase offset. Building on this model, both the open-loop and closed-loop performances of CA iterative phase synchronisers are derived in closed-form. The analytical results explicitly reveal how extrinsic information contributes to the performance of carrier phase estimation. Monte Carlo simulation results corroborate that the proposed methods are able to accurately characterise the performance of CA iterative carrier phase recovery for systems with different channel codes.