A characterization of `cycle´ slipping in a digital PLL based MPSK demodulator

The authors analyze cycle slipping in the ideal pulse shape matched filter, decision-directed digital phase-locked loop (DPLL)-based demodulator for multiple phase shift keying (MPSK) modulation in additive white Gaussian noise. A characterization of the first-order, decision-directed DPLL as a discrete-time Markov chain is presented. Traditional Markov analysis techniques utilizing absorbing states are used to analyze the mean time to slip between attractor points. The mean time is numerically evaluated for the first-order loop with unmodulated, binary phase shift keying (BPSK), quadrature PSK (QPSK), and 8PSK modulated signals