Generalised analysis of monomial-based Viterbi and Viterbi algorithms for NDA carrier phase estimation

For non-data-aided carrier phase recovery of M-PSK modulated signals, Viterbi and Viterbi suggested a feedforward estimator based on a modification of the Mth power nonlinearity. With respect to the jitter variance, they presented a closed-form solution for even integer values of the generic design parameter μ, 0≤μ≤M-2. It is shown that their analysis can be simplified considerably as well as extended to any real value of μ>-M-2. Furthermore, it is verified that the Cramer-Rao lower bound, as the theoretical limit, is solely approached for larger values of the signal-to-noise ratio and negligible carrier frequency offsets. Finally, to minimise the jitter performance, the closed-form solution is used for optimisation of the design parameter.