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.

The additive noise response of a charge pump phase-locked loop in the synchronous mode of operation has been studied. In order to determine the tracking and noise performances of the loop, mean square values of tracking error and local oscillator phase jitter have been analytically obtained. Analytical results agree well with the simulation results obtained here and elsewhere. The analysis performed can be used in choosing different system parameters for optimum system operation.