Performance analysis of a joint estimator for timing, frequency, and phase with continuous-phase modulation

Performance analysis is presented for the joint estimation of symbol timing, frequency offset, and phase offset with continuous-phase modulation. In this study, undesirable influences on parameters to be estimated, which arise from the inaccuracy of the already estimated parameters, are computed mathematically. Based on performance analysis, a conditional Cramer-Rao bound (CRB) is put forward, and a hypothesise is made that phase offset variance with frequency error present should match with the conditional CRB for any digital phase modulation. Moreover, the hypothesis is manifested by analysing the log-likelihood function in a more general mathematical manner. To alleviate the influences, a data-aided acquisition and phase-locked loop tracking algorithm is proposed. The results of Monte Carlo simulations are presented, showing good agreement with theoretical analysis. Simulation results also show that the proposed algorithm can improve performance in terms of phase error variance at the expense of a high signal-to-noise ratio threshold.