An optimal phase demodulator

This paper presents the results of investigation on the optimal performance of the phase demodulator using Bucy's non-linear filtering theory. A cyclically optimal non-linear phase estimation technique has been developed for modular phase tracking systems.

This paper considers a first-order Markov or Brownian motion phase process, because of faster computation in digital simulations and for the extensive research results available in Weiper optimum phase-lock loop for comparison purposes. However, the technique developed in this paper is equally applicable to higher-order phase process models.

The actual performance of the non-linear filter was investigated using Monte Carlo techniqes. The classical phase-lock loop was also simulated as a reference against which the optimal non-linear filter was compared. The cyclic phase non-linear filter appears to be about 0.7 dB better than the phase lock with respect to noise alone where the maximum conceivable improvement is 2.2 dB, or the excess noise relative to the ideal is about one-third less in dB than that of the phase-lock loop.