Simplified versions of the maximum-likelihood frequency detector

Several simplifications of the maximum-likelihood frequency detector (MLFD) proposed by F.M. Gardner (ESA Final Report, 1990) to extend the acquisition range of carrier recovery loops are studied. The basic simplification concerns the implementation of the frequency-matched filter (FMF) required by this detector. Another simplification consists of replacing the original MLFD by its polarity-type version. It is shown that these simplifications do not reduce the frequency range over which the average detector output has the same sign as the frequency offset. The effect of reducing the oversampling factor in digital implementation of the detector is also investigated. The results show that the complexity of the MLFD can be substantially reduced without significantly degrading the loop acquisition performance