Performance analysis of code-aided iterative hard/soft decision-directed carrier phase recovery

Code-aided (CA) iterative carrier phase synchronizer can improve the phase estimation performance significantly. However, due to the coupling involved between phase recovery and decoding, most studies depend on extensive simulations rather than on theoretical analysis to evaluate the performance of CA phase recovery. In this paper, we propose analytical methods to fill this void. The first step is to model the cross-talks caused by phase offset as an additional Gaussian noise at low signal-to-noise ratios (SNRs). 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 performance of CA iterative hard/soft decision-directed phase synchronizers are derived in closed-form. The analytical results explicitly reveal how extrinsic information contributes to the performance improvement of carrier phase estimation. Monte Carlo simulation results corroborate that the proposed methods are able to accurately characterize the performance of CA iterative carrier phase recovery for systems with different channel codes.