A Gaussian Sum Approach to Phase and Frequency Estimation

In this paper, a theory of optimaf nonlinear estimation from sampIed data signals where the a posterion probability densities are approximated by Gaussian sums is adapted for application to phase and frequency estimation in high noise. The nonlinear estimators (demodulators) require parallel processing of the received signsf. In the limit as the number of parallel processors becomes infinite the FM demodulators become optimum in a minimum mean square error sense and the PM demodulators become optimum in some well defined sense. For the clearly suboptimaf case of one processor, the demodulators can be readily simplified to the familiar phase-locked loop. On the other hand, for the intermediate case, significant extension of the phaseIocked loop threshold is ac tieved where (say) six parallel processors are involved.