Theory of phase tracking systems of arbitrary order: Statistics of cycle slips and probability distribution of the state vector

The time-dependent distribution of the number of cycle slips in positive and negative directions, and the correlation of their time spacings, are derived from a new statistical model of an(N + l)-order phase tracking system. The probability density of the phase error and the other system variables are shown to agree with known results. Relations for the steady state are obtained in a relatively simple form. Some limiting conditions are mentioned under which the model reduces to a computationally much simpler renewal model described earlier.