This paper studies the performance of code-aided (CA) soft-information based carrier phase recovery, which iteratively exploits the extrinsic information from channel decoder to improve the accuracy of phase synchronization. To tackle the problem of strong coupling between phase recovery and decoding, a semi-analytical model is proposed to express the distribution of extrinsic information as a function of phase offset. Piecewise approximation of the hyperbolic tangent function is employed to linearize the expression of soft symbol decision. Building on this model, open-loop characteristic and closed-loop performance of CA iterative soft decision-directed (ISDD) carrier phase synchronizer are derived in closed-form. Monte Carlo simulation results corroborate that the proposed expressions are able to characterize the performance of CA ISDD carrier phase recovery for systems with different channel codes.

This paper investigates the non-data-aided (NDA) carrier frequency estimation of amplitude and phase shift keying (APSK) signals. The true Cramer-Rao bound (CRB) for NDA frequency estimation of APSK signals are derived and evaluated numerically. Characteristic and jitter variance of NDA Luise and Reggiannini (L&R) frequency estimator are analyzed. Verified by Monte Carlo simulations, the analytical results are shown to be accurate for medium-to-high signal-to-noise ratio (SNR) values. Using the proposed closed-form expression, parameters of the algorithm are optimized efficiently to minimize the jitter variance.

A low complexity log-likelihood ratio (LLR) calculation for high-order amplitude phase shift keying (APSK) signals is proposed. Using proper constellation partitioning together with a look-up table, the number of terms for the comparison of Euclidean distances can be significantly reduced. Compared with the log-sum LLR approximation, the proposed method reduces the computational complexity by more than 65% and 75% for 16-APSK and 32-APSK signals, respectively, with very small bit error rate performance degradation.