Steady-state analysis of the carrier synchronizer for QPSK signals†

In this paper, the steady-state analysis of the carrier synchronizer consisting of the cascade of a bandpass filter (BPF), and non-linearity (NL) and a phase-locked loop (PLL) for a quadrature phase shift keyed (QPSK) signal corrupted by white gaussian noise is presented. The analysis is based on the transform method and the harmonic representation of cyclostationary processes. Some of the conclusions are similar to those obtained from the non-return to zero (NRZ) pulse amplitude modulated (PAM) synchronizer. Among these include: (1) the odd symmetry NL cannot be adopted to restore the carrier; (2) there is an optimum bandwidth of the BPF to minimize the phase jitter of the synchronizer output signal; and (3) conventional design theory still applies for the PLL in the QPSK carrier synchronizer. In addition to these results, we also conclude that: (1) we have to choose a harmonic with order of at least 4; and (2) the PLL output phase variance is more sensitive to the synchronizer input signal-to-noise rati...