Information Theory Extended analysis of Viterbi-Viterbi synchronizers

For non-data-aided carrier phase recovery of M-ary phase-shift keying (MPSK) as modulation scheme, Viterbi and Viterbi (V&V) suggested a feedforward (FF) variant of the Mth-power non-linearity. With respect to the jitter variance, a closed-form solution has been presented for even integer values of the generic design parameter m, 0 ≤ m ≤ M. Basically, the V & V principle may be applied to feedback (FB) systems as well, where little is found in the open literature. To this end, the characteristic of the open loop (S-curve) is derived in closed form for any value of m. The jitter variance of the linearized FB synchronizer is then computed using the slope in the stable equilibrium point of the S-curve. Furthermore, in order to minimize the jitter variance, it is shown that the optimized value mopt   1 for increasing values of the signal-to-noise ratio (SNR), whereas in the opposite case mopt  M. Finally, it is verified that the developed relationships are also valid for FF estimators if they are operated with negligible carrier frequency offsets. Copyright © 2004 AEI.