Decision directed versus non-data aided plls: A comparative review

The performance of discrete-time Decision Directed (DD) and Non-Data Aided (NDA) first-order Phase Looked Loops (PLL) for a QPSK modulated signal is evaluated under the disturbance of thermal noise and 1/f² phase noise. A well known continuous-time model is presented that closely approximates the loop¿s behavior. Using the continuous time model, Fokker-Planck techniques are applied to compute the Mean Time to Lose Lock (MTLL) for both PLLs. We optimize the loop filter using the MTLL as the optimization criterion. On the basis of the optimal MTLL, we determine the regions where one PLL outperforms the other. Monte-Carlo simulation results are presented to validate the analytic analysis. For the setting under study, the NDA PLL outperforms the DD PLL for SNR below 4.5dB regardless of the phase noise level. Applicability of the results for a second-order PLL is discussed.