Performance analysis of all-digital PSK carrier tracking loops

The performance of PSK (phase shift keying) carrier-tracking loops having a structure suitable for an all-digital implementation is analyzed. The analysis is based on the stochastic difference equation that governs the evolution of the loop phase error sequence. General expressions for the phase error variance, obtained through a linear analysis of the loop difference equation, are derived. An approximate nonlinear analysis is applied to first-order digital loops, yielding analytical expressions for the phase error steady-state probability density and variance. These results are used to assess the tracking performances of binary PSK and quadrature PSK all-digital carrier tracking circuits