Optimization of the carrier tracking loop for 8PSK transmission

The performance of discrete-time decision directed (DD) first order phase locked loops (PLL) for a 8PSK modulated signal is evaluated under the disturbance of thermal noise and 1/f² phase noise. A continuous time model is developed that closely approximates the loop´s behavior. Fokker-Planck techniques are applied to compute the mean time to lose lock for both PLLs. We optimize the loop filter using the MTLL as the optimization criterion. Monte-Carlo simulation results are presented to validate the analytic analysis. Applicability of the results for second order PLL is discussed. We apply the analytic results to investigate the necessity of pilots for 8PSK reception in DVB-S2.